In my previous article, I talked about the RSA cryptosystem which is widely used on the Internet for secure data transmission. The power and security of the RSA cryptosystem derives from the fact that the factoring problem is “hard.” That is, it is believed that the full decryption of an RSA ciphertext is infeasible because no efficient classical algorithm currently exists for factoring large numbers. However, in 1994 Peter Shor showed that a quantum computer could be used to factor a number in polynomial time, thus effectively breaking RSA.
It may be tempting to use the speed of a quantum computer to simply check all possible divisors in parallel. In this case, we would be performing a classical algorithm on a quantum computer, making use only of the increased speed of the quantum machine. Unfortunately, this is not going to work. In a way, it is possible for a quantum computer to try all possible divisors. However, due to the nature of quantum computing, when measuring the outcome of the computations, you will get a random possible divisor, which is almost certainly not the one you want.
How, then, can we use a quantum computer to solve the factoring problem? The key to a fast and accurate quantum factoring algorithm is to make use of the structure of the factoring problem itself. Instead of looking for factors directly, we must use some mathematical property of factoring. Fortunately, the factoring problem has plenty of special properties from which to choose. For example, given a positive integer, even if we do not know its prime factorization we do know that it has exactly one factorization. This fact does not help us solve the factorization problem, but it does give us hope that the problem has other nice mathematical properties that will.
The property we will use is the ability to reduce the prime factorization problem into a problem of order (or period) finding. Let’s start by looking at an example. Consider the sequence of numbers
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, …
Now, let’s look at this same sequence of powers of two, but taken “mod 15.” In other words, we will create a new sequence of numbers consisting of the remainders when each power of two is divided by 15. This gives us the new sequence
2, 4, 8, 1, 2, 4, 8, 1, 2, 4, …
We see that taking the powers of two mod 15 gives us a periodic sequence whose period (or order) is four. For another example, consider the same powers of two, but taken mod 21. In this case, we have the new sequence
2, 4, 8, 16, 11, 1, 2, 4, 8, 16, …
Here, we get a periodic sequence whose period is six.
In the 1760s, Euler discovered a beautiful pattern to this period finding problem. Let be the product of two prime numbers, and . Consider the sequence
If is not divisible by or , then the above sequence will repeat with some period that evenly divides .
In our examples above, we have . In the first example, we have which has the prime factors and . Then, , which is divisible by the period of 4. In the second example, we have which has the prime factors and . Then, , which is divisible by the period of 6.
But how does this help us solve the factorization problem? If we can find the period of the sequence
then we learn something about the prime factors of . In particular, we learn a divisor of . Of course, we’d rather learn the factors and themselves, but this, at least, represents progress. If we determine several random divisors of by trying different random values of , then we can multiply those divisors together to obtain itself. Once we know , we can then determine and .
However, there’s still a problem with applying our observations to the factorization problem. Even though the sequence
will eventually start repeating itself, the number of steps before it repeats could be almost as large as , which in the RSA cryptosystem is a very large number! This issue is why finding the period of the sequence does not appear to lead to a classical factoring algorithm. However, with the help of quantum mechanics, we can define a quantum algorithm that works in a reasonable amount of time.
Shor’s algorithm is composed of two parts. The first part turns the factoring problem into the period finding problem, and can be computed on a classical computer. The second part (step 2 below) finds the period using the quantum Fourier transform and is responsible for the quantum speedup of the algorithm. We begin by briefly describing all five steps. After that, we will focus on the quantum part of the algorithm (i.e. step 2). To factor a large integer (which, without loss of generality, we may assume is odd), we use Shor’s algorithm:
1. Choose a random positive integer . Compute gcd, which may be done in polynomial time using the Euclidean algorithm. If gcd, then we have found a non-trivial factor of , and we are done. If, on the other hand, gcd, proceed to step 2.
2. Use a quantum computer to determine the unknown period of the sequence
3. If is an odd integer, then return to step 1. The probability that is odd is , where is the number of distinct prime factors of . If is even, then proceed to step 4.
4. Since is even,
If , then go to step 1. If , then proceed to step 5. It can be shown that the probability that is less than , where denotes the number of distinct prime factors of .
5. Compute gcd using the Euclidean algorithm. Since , it can be shown that is a non-trivial factor of . Exit with the answer .
Thus, the task of factoring an odd positive integer reduces to the problem of finding the period of a function/sequence. Shor’s period-finding algorithm (step 2 above) relies heavily on the ability of a quantum computer to be in many states simultaneously (a superposition of states). To compute the period of a function , we evaluate the function at all points simultaneously.
Unfortunately, quantum mechanics does not allow us to access all of this information directly. Instead, a measurement must be taken which will yield only one of the possible values (destroying all others). Because of this issue, we must transform the superposition to another state that will return the correct period with high probability. This is achieved by using the quantum Fourier transform. The main components of Shor’s period-finding algorithm are as follows:
1. Create a superposition of states. This can be done by applying Hadamard gates to all qubits in the input register.
2. Implement the function as a quantum transform. To achieve this, Shor used repeated squaring for his modular exponentiation transform.
3. Perform a quantum Fourier transform.
After these transformations, a measurement will yield an approximation to the period .
Now let’s look at an example of how can be factored using Shor’s algorithm.
Step 1. Choose a random positive integer , say . Since gcd, proceed to step 2 to find the period of the function given by
Step 2. Run Shor’s period-finding algorithm on a quantum computer to find (with high probability) that the period .
Step 3. Since is even, we proceed to step 4.
Step 4. Since
proceed to step 5.
Step 5. With the Euclidean algorithm, compute
gcd= gcd= gcd
We have succeeded in using Shor’s algorithm to find a non-trivial factor of , namely .
Shor, P. W. (1997). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5), 1484-26. doi:http://dx.doi.org/10.1137/S0097539795293172
Lomonaco, Jr, S. J. (2000) Shor’s Quantum Factoring Algorithm. arXiv:quant-ph/0010034


One of the things I have a hard time intuiting, in quantum computing, is the interplay between classical bits and quantum bits. A good example of this is superdense coding. Superdense coding encodes two classical bits into a single transmitted qubit, by taking advantage of a previously shared qubit.
(Superdense coding is also fun to say.)
Thought of another way, superdense coding turns previously entangled qubits into a fuel you can store and then later consume to double your bandwidth. Which is what I mean when I say superdense coding lets you store bandwidth.
In case you don't want to watch this video explaining superdense coding (I'd recommend the whole series it's part of), I will explain it here.
In order to do superdense coding you need three things:
- A way to store qubits.
- A quantum communication channel to transmit qubits.
- The ability to do a few quantum operations to qubits.
The actual protocol is not too complicated, although understanding why it works can be. Here is a quantum circuit diagram showing what happens, which I will explain below:
Imagine that Alice is the one who wants to send information, and Bob is the one who will receive it. Alice roughly corresponds to the top of the diagram, and Bob to the bottom. The sequence of events, from left to right, is as follows.
First, ahead of time, Alice and Bob each get half of a Bell pair. That is to say, two qubits are placed into a superposition where either both are
false or both are
true, and then Alice and Bob each take one of those qubits.
There's a lot of flexibility in who actually makes the Bell pair. Alice can do it, Bob can do it, or an unrelated third party can do it. Regardless, what matters is that the Bell pair can be delivered ahead of time and stored for later use.
Second, Alice decides what information she wants to send to Bob. She can send two bits (i.e. one of four possibilities). We'll call the possible messages
Third, Alice encodes the message by applying operations to her qubit (the one from the Bell pair). The operations are based on the message she wants to send. If she wants to send
00, she does nothing. For
01, she rotates the qubit 180° around its Z axis. For
10 she instead rotates 180° around its X axis. Otherwise the message is
11 and she rotates both 180° around the X axis and then 180° around the Z axis.
Note that the
11 case is technically a rotation around the Y axis, but it's nice to split it into X and Z rotations because it makes the circuit simpler. It means Alice can just apply the X rotation if the second bit is true, and afterwards the Z rotation if the first bit is true.
Fourth, Alice sends her qubit to Bob. So Bob will end up with both halves of the Bell pair, but Alice has operated on one of them.
Fifth, Bob does a decoding operation. He conditionally-nots his qubit, conditioned on Alice's qubit. This will flip the value of his qubit in the parts of the superposition where hers is true. Then he rotates Alice's qubit by 180° around the diagonal X+Z axis (i.e. applies the Hadamard operation).
Note that the decoding operation Bob applies is actually the inverse of how the Bell pair is made. Normally the decoding operation would just "unmake" the pair, leaving Bob with two qubits set to false and not in superposition. That's why Alice applying no operation corresponds to sending
00. The reasons the other operations give the right results are a bit harder to explain, and I won't try here, but the qubits do always end up in the right state.
Finally, Bob measures the two qubits and retrieves the message.
The interesting thing about superdense coding is that, although Bob still has to receive one qubit per classical bit, one of the qubits can be sent far in advance. Then, when the actual message has to be sent, half of what's needed to reconstruct it has already arrived.
So, basically, the pre-shared Bell pairs let you store bandwidth. They are a fuel that you consume to transmit at double speed.
This would do interesting things to network design.
For example, during times of low utilization you could use the remaining capacity to share Bell pairs and build up bandwidth to be consumed during high utilization. This would smooth out traffic peaks.
Alternatively, you could double the bandwidth of a low-latency channel by continuously making Bell pairs on a secondary high latency channel. (Imagine a truck showing up every day to drop off a box filled with trillions of qubits in Bell pairs, so your internet can go faster.)
Of course all of this assumes that you'll want to use quantum channels to send classical information. Maybe classical channels will simply be more than twice as fast (do photons decohere when sent over fiber?). Maybe quantum channels will be too expensive to bother. Maybe we'll be too busy sending qubits over them to spare time to send classical bits.
There's tons of practical reasons it might not work out. But still, I enjoy the hypothetical image of trucks dropping off boxes of internet-go-fast.
exploits empowers a quantum communication channel to send, ahead of time, half of what will be needed to reconstruct a classical message. This lets you transmit at double speed until the pre-delivered qubits run out.


It’s unique and quite intriguing to discover that quantum mechanics can manifest itself in a form that could enhance the capabilities of traditional computer systems, which as we all know today work on binary. The application creates what is called as quantum computers and it harvests the principles of quantum mechanics to attain computing power that is beyond the scope of classical computers that we now use. The article gives a brief overview of this phenomenon of computing in layman terms, one that non-physicist computing geeks could possibly digest.
How traditional computers work –
All information is processed and understood by a computer using this binary language composed of bits (0 or 1). When you break a computer down, you will find a bunch of silicon chips with circuits of logic gates made up of transistors or switches which function using voltage. A high voltage represents on state of the switch equivalent to 1 and a low equivalent to 0. All forms of data be it text, music, audio, video or software are ultimately encoded and stored by the computer as binary in the computer’s memory.
Rethinking binary and transistors –
Abandoning the existing classical principles of computing, this new world of quantum computing follows its own rules, one that nature is based on. Nature is not classical. The natural world does not function at the macroscopic level and it is this fundamental aspect that quantum computing is built on, that is:
To reduce what we call “bits” or switches down to the smallest possible discrete unit or quantum level, computing like nature computes. This gives rise to “qubits” as opposed to classical bits.
How quantum computers work –
Logically, the quantum system uses, as mentioned earlier, what is coined as qubits as the smallest discrete units to represent information, which may be electrons with spins, photons with polarization, trapped ions, semiconducting circuits etc. The property of quantum mechanics comes into play as a single qubit can exist not only, in two discrete energy states, low and high (similar to 0 and 1) but it can also exist in a superposition state where in it exists in both states at once. When measured however, the superposition fades and one of the two distinct states is returned based on the probabilities of each state.
When using two qubits instead of a single qubit 4 discrete energy states exist, (2 discrete states for each qubit) and a qubit can even exist in a superposition of these states.
Similarly using n qubits, 2n states are achieved which exist as combinations of 0s and 1s in parallel.
So this gives a way to represent information. The next step is to process information, which requires manipulation of these qubits. This is brought about by the use of special quantum logic gates and quantum algorithms such as Shor’s algorithm and Grover’s algorithm which function using the principles of quantum mechanics of superposition, entanglement and measurement. Without going into the complicated details of the quantum phenomena, the state of the qubits is manipulated by application of precise electromagnetic waves, microwaves and amplification functions as defined by the algorithms.
Advantages of quantum computers –
Two key factors make quantum computers a billion times more powerful than the most powerful supercomputer known to us today. These are:
- Exponential increase in computing ability with the addition of each qubit
This gives quantum computers processing power that is beyond the scope of a classical computer.
Applications of quantum computing – Processing of billions of bytes can easily be performed by quantum computers, which can be applied in:
- Big data
- Molecular Simulations
- Protein Folding
- Drug Discovery
- Genome Sequencing
- Diagnose DNA sequence
- Catalyst Analysis
- Financial Analysis
- Climate Prediction
- Graphic searches of complicated databases
- Massive Software Testing
Work on quantum computers is an ongoing endeavor with tremendous potential to revolutionize the way we understand the digital world. It does not seek to replace classical computers but a sustainable quantum computer could aid classical computers in computationally intensive tasks that are restrictive, difficult and time consuming for our traditional Turing based computers.
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Scientists Use Real Data to Measure the Cosmos
Illustration of the concept of Baryonic Acoustic Oscillations.
Scientists from the Imperial College London have used data, rather than calculations related to general relativity, to measure large distances in the Universe for the first time.
A research team from Imperial College London and the University of Barcelona has used data from astronomical surveys to measure a standard distance that is central to our understanding of the expansion of the universe.
Previously the size of this ‘standard ruler’ has only been predicted from theoretical models that rely on general relativity to explain gravity at large scales. The new study is the first to measure it using observed data. A standard ruler is an object which consistently has the same physical size so that a comparison of its actual size to its size in the sky will provide a measurement of its distance to earth.
“Our research suggests that current methods for measuring distance in the Universe are more complicated than they need to be,” said Professor Alan Heavens from the Department of Physics, Imperial College London who led the study. “Traditionally in cosmology, general relativity plays a central role in most models and interpretations. We have demonstrated that current data are powerful enough to measure the geometry and expansion history of the Universe without relying on calculations relating to general relativity.
“We hope this more data-driven approach, combined with an ever increasing wealth of observational data, could provide more precise measurements that will be useful for future projects that are planning to answer major questions around the acceleration of the Universe and dark energy.”
The standard ruler measured in the research is the baryon acoustic oscillation scale. This is a pattern of a specific length which is imprinted in the clustering of matter created by small variations in density in the very early Universe (about 400,000 years after the Big Bang). The length of this pattern, which is the same today as it was then, is the baryon acoustic oscillation scale.
The team calculated the length to be 143 Megaparsecs (nearly 480 million light years) which is similar to accepted predictions for this distance from models based on general relativity.
Published in Physical Review Letters, the findings of the research suggest it is possible to measure cosmological distances independently from models that rely on general relativity.
Einstein’s theory of general relativity replaced Newton’s law to become the accepted explanation of how gravity behaves at large scales. Many important astrophysics models are based on general relativity, including those dealing with the expansion of the Universe and black holes. However some unresolved issues surround general relativity. These include its lack of reconciliation with the laws of quantum physics and the need for it to be extrapolated many orders of magnitude in scales in order to apply it in cosmological settings. No other physics law have been extrapolated that much without needing any adjustment so its assumptions are still open to question.
Co-author of the study, Professor Raul Jimenez from the University of Barcelona said: “The uncertainties around general relativity have motivated us to develop methods to derive more direct measurements of the cosmos, rather than relying so heavily on inferences from models. For our study we only made some minimal theoretical assumptions such as the symmetry of the Universe and a smooth expansion history.”
Co-author Professor Licia Verde from the University of Barcelona added: “There is a big difference between measuring distance and inferring its value indirectly. Usually in cosmology we can only do the latter and this is one of these rare and precious cases where we can directly measure distance. Most statements in cosmology assume general relativity works and does so on extremely large scales, which means we are often extrapolating figures out of our comfort zone. So it is reassuring to discover that we can make strong and important statements without depending on general relativity and which match previous statements. It gives one confidence that the observations we have of the Universe, as strange and puzzling as they might be, are realistic and sound!”
The research used current data from astronomical surveys on the brightness of exploding stars (supernovae) and on the regular pattern in the clustering of matter (baryonic acoustic oscillations) to measure the size of this ‘standard ruler’. The matter that created this standard ruler formed about 400,000 years after the Big Bang. This period was a time when the physics of the Universe was still relatively simple so the researchers did not need to consider more ‘exotic’ concepts such as dark energy in their measurements.
“In this study we have used measurements that are very clean,” Professor Heavens explained, “And the theory that we do apply comes from a time relatively soon after the Big Bang when the physics was also clean. This means we have what we believe to be a precise method of measurement based on observations of the cosmos. Astrophysics is an incredibly active but changeable field and the support for the different models is liable to change. Even when models are abandoned, measurements of the cosmos will survive. If we can rely on direct measurements based on real observations rather than theoretical models then this is good news for cosmology and astrophysics.”
The research was supported by the Royal Society and the European Research Council.
Publication: Alan Heavens, et al., “Standard Rulers, Candles, and Clocks from the Low-Redshift Universe,” Phys. Rev. Lett. 113, 241302, 2014; doi:10.1103/PhysRevLett.113.241302
Image: Chris Blake & Sam Moorfield
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Light travels extremely fast – in less than a second, it could travel seven times the circumference of the Earth. Most of our communication systems use light or other electromagnetic waves to send messages, which means we can talk to others on the far side of the world in almost no time at all. It’s difficult to imagine that, on Earth, we would ever need anything faster.
However, space is big: sending a message to Mars using light would take 12.5 minutes, resulting in a very jolted conversation. Sending a message to the nearest star beyond our Sun would take no less than four years. If superluminal communication (communication faster than light) were possible, it would open up doors for how we might communicate with deep space explorers in the future.
Looking at whether superluminal communication is possible takes us on a whirlwind tour around some of the most exciting places in physics, from space-warped wormholes to particles that can travel backwards in time. We begin, though, in the bizarre world of quantum mechanics.
Some of the strangest phenomena in science are described by the theory of quantum mechanics, a theory that was developed in the 1930s and has received great experimental support since. One of the strangest phenomena is known as ‘quantum entanglement’, which appears to allow quantum particles to communicate with each other at more than 10,000 times the speed of light.
Entanglement occurs when two particles are linked to each other in such a way that they behave as one and the same entity. Entangled particles can be created quite easily in the laboratory with the right equipment. Particles have a property called ‘spin’, and a particle’s spin can be either up or down. Quantum mechanics tells us that two particles that are entangled don’t have a definite spin until their spin is actually measured. This means that the act of measuring the particle actually changes the state it is in.
This is bizarre enough, but here is the crux: for entangled particles, the act of measuring one particle doesn’t just change the state that particle is in, but also changes the state of the other particle. If the first particle’s spin was measured, and found to be up, the second particle’s spin would then change from being indefinite to being down. What is especially striking is that, according to quantum mechanics, the particles have this influence on each other however far apart they are, even if they are on opposite sides of the universe. Since the 1980s, experiments have been performed demonstrating this phenomenon, with more recent experiments showing that the influence is taking place at least at 10,000 times the speed of light.
If quantum entanglement could be exploited to send messages, it would mean big things for superluminal communication. Unfortunately, however, it has been proved that quantum entanglement cannot be used to send messages superluminally, and that nor can it be used to send any kinds of messages at all. This law is known as the ‘no signaling theorem’. Its proof essentially shows that, despite the link between two entangled particles, there is nothing that one person can do to one entangled particle that would be detectable by another person with the other entangled particle.
Warped Spacetime and Wormholes
Our next stop takes us to the theory of general relativity, into the very fabric of the universe. Because of the three spatial dimensions and one temporal dimension that makes up our universe, we call this fabric ‘spacetime’. The idea of a wormhole, first introduced in the 1920s, is based on the thought that spacetime can be warped, providing a shortcut between two distant points in the universe. To conceptualise how this might work, imagine that two distant points in the universe are represented by two ends of a long thin rubber tube. The rubber tube itself represents the distance between these two points. However, if you curl (or ‘warp’) the tube so that the two ends meet, you have created a shortcut for getting from one point to the other.
If such wormholes do exist, it might be possible to use them to send messages from one point in spacetime to another. Though the message would not actually be travelling superluminally, it would certainly appear to be. However, though the theory of general relativity, which is currently our best theory of how spacetime works, does not deem them impossible, no evidence of wormholes has yet been found. Moreover, even if they did exist, it would be serious challenge to use them to send messages: they would be extremely unstable and sending a signal through it might cause it to collapse.
Moving faster than light
What if we could communicate superluminally simply by speeding up the signals that carry our messages so they go faster than the speed of light? Unfortunately, as the theory of special relativity tells us, this is not possible. The speed of light in any given medium is always constant. This means that we cannot speed up the light or other electromagnet waves that carry our messages.
Nor can we get a different particle, one with mass, to speed up so much that it crosses the barrier of the speed of light, and moves superluminally. Special relativity shows that the more and more energy you give a particle with mass, the heavier and heavier it gets; and subsequently, the harder it is to speed it up. In fact, it would take an infinite amount of energy to make a particle with mass travel at the speed of light. As we could never harness an infinite amount of energy, getting a particle to cross the speed of light is definitely a no-go.
But what about a particle that always moves superluminally. Though special relativity excludes the possibility of a particle crossing the speed of light, it has no qualms about a particle that permanently moves at more than the speed of light. Such particles were first hypothesized in the 1960s, and are called ‘tachyons’. Though tachyons have never been detected, their existence has not been ruled out either.
If tachyons do exist, they have many strange properties: to start with, their mass, derived from taking the square root of a negative number, is mathematically ‘imaginary’. Furthermore, they have negative energy: in fact, the less energy a tachyon has, the faster it moves and a tachyon with no energy moves infinitely fast. To top it all off, tachyons can actually move backwards in time.
Incorporating such characteristics into a coherent theory is something of a challenge (how can something have an imaginary mass?). But if tachyons could be used to send messages, perhaps the biggest challenge of all would be dealing with the paradoxes that arise. Consider this: suppose that Alice sends Bob a message at midday using tachyons, which, since tachyons can move backwards in time, Bob receives at 11am. The message to Bob reads: “Send Alice a message telling her to not contact you anymore”. So, at 11am, Bob sends Alice a message using tachyons, telling her to not contact him anymore, which Alice receives at 10am. Then from 10am, Alice stops all contact with Bob. So, because of the message she sends at midday, she will no longer send that message at midday. Thus arises the paradox.
It seems unlikely that we will be able to have superluminal communication in the future, because the potential avenues that may lead to it are riddled with theoretical impossibilities. However, these avenues take us through some of the most interesting areas of physics that explore the fundamental nature of our universe, where there is still so much more to learn. So, never say never.
Kruti Shrotri is studying for an MSc in Science Communication


Capacitance measurement of bilayer graphene at a high magnetic field. The vertical dark blue to orange lines are signatures of fractional quantum Hall states that are shared between the two layers of the bilayer graphene sheet. The vertical line going through the center is believed to host an intriguing type of particles: non-Abelian anyons. Credit: University of California - Santa Barbara
What kinds of 'particles' are allowed by nature? The answer lies in the theory of quantum mechanics, which describes the microscopic world.
In a bid to stretch the boundaries of our understanding of the quantum world, UC Santa Barbara researchers have developed a device that could prove the existence of non-Abelian anyons, a quantum particle that has been mathematically predicted to exist in two-dimensional space, but so far not conclusively shown. The existence of these particles would pave the way toward major advances in topological quantum computing.
In a study that appears in the journal Nature, physicist Andrea Young, his graduate student Sasha Zibrov and their colleagues have taken a leap toward finding conclusive evidence for non-Abelian anyons. Using graphene, an atomically thin material derived from graphite (a form of carbon), they developed an extremely low-defect, highly tunable device in which non-Abelian anyons should be much more accessible. First, a little background: In our three-dimensional universe, elementary particles can be either fermions or bosons: think electrons (fermions) or the Higgs (a boson).
"The difference between these two types of 'quantum statistics' is fundamental to how matter behaves," Young said. For example, fermions cannot occupy the same quantum state, allowing us to push electrons around in semiconductors and preventing neutron stars from collapsing. Bosons can occupy the same state, leading to spectacular phenomena such as Bose-Einstein condensation and superconductivity, he explained. Combine a few fermions, such as the protons, neutrons, and electrons that make up atoms and you can get either type, but never evade the dichotomy.
In a two-dimensional universe, however, the laws of physics allow for a third possibility. Known as "anyons," this type of quantum particle is neither a boson nor a fermion, but rather something completely different—and some kinds of anyons, known as non-Abelian anyons, retain a memory of their past states, encoding quantum information across long distances and forming the theoretical building blocks for topological quantum computers.
Although we don't live in a two dimensional universe, when confined to a very thin sheet or slab of material, electrons do. In this case, anyons can emerge as "quasiparticles" from correlated states of many electrons. Perturbing such a system, say with an electrical potential, leads to the entire system rearranging just as if an nayon had moved.
The hunt for non-Abelian anyons begins by identifying the collective states that host them. "In fractional quantum Hall states—a type of collective electron state observed only in two dimensional samples at very high magnetic fields—the quasiparticles are known to have precisely a rational fraction of the electron charge, implying that they are anyons," Young said.
"Mathematically, sure, non-Abelian statistics are allowed and even predicted for some fractional quantum Hall states." he continued. However, scientists in this field have been limited by the fragility of the host states in the semiconductor material where they are typically studied. In these structures, the collective states themselves appear only at exceptionally low temperatures, rendering it doubly difficult to explore the unique quantum properties of individual anyons.
Graphene proves to be an ideal material to build devices to search for the elusive anyons. But, while scientists had been building graphene-based devices, other materials surrounding the graphene sheet—such as glass substrates and metallic gates—introduced enough disorder to destroy any signatures of non-Abelian states, Zibrov explained. The graphene is fine, it's the environment that is the problem, he said.
The solution? More atomically thin material.
"We've finally reached a point where everything in the device is made out of two-dimensional single crystals," said Young. "So not only the graphene itself, but the dielectrics are single crystals of hexagonal boron nitride that are flat and perfect and the gates are single crystals of graphite which are flat and perfect." By aligning and stacking these flat and perfect crystals of material on top of each other, the team achieved not only a very low-disorder system, but one that is also extremely tunable.
"Besides realizing these states, we can tune microscopic parameters in a very well controlled way and understand what makes these states stable and what destabilizes them," Young said. The fine degree of experimental control—and elimination of many unknowns— allowed the team to theoretically model the system with high accuracy, building confidence in their conclusions.
The materials advance gives these fragile excitations a certain amount of robustness, with the required temperatures nearly ten times higher than needed in other material systems. Bringing non-Abelian statistics into a more convenient temperature range proves an opportunity for not only for investigations of fundamental physics, but reignites hope for developing a topological quantum bit, which could form the basis for a new kind of quantum computer. Non-Abelian anyons are special in that they are thought to be able to process and store quantum information independent of many environmental effects, a major challenge in realizing quantum computers with traditional means.
But, say the physicists, first things first. Directly measuring the quantum properties of the emergent quasiparticles is very challenging, Zibrov explained. While some properties—such as fractional charge—have been definitively demonstrated, definitive proof of non-Abelian statistics—much less harnessing nonabelian anyons for quantum computation—has remained far out of the reach of experiments. "We don't really know yet experimentally if non-Abelian anyons exist," Zibrov said.
"Our experiments so far are consistent with theory, which tells us that some of the states we observed should be non-Abelian, but we still don't have an experimental smoking gun."
"We'd like an experiment that actually demonstrates a phenomenon unique to non-Abelian statistics," said Young, who has won numerous awards for his work, including the National Science Foundation's CAREER Award. "Now that we have a material that we understand really well, there are many ways to do this—we'll see if nature cooperates!"


In this article, we will start a path to explain in detail all you need to know about digital quantum electronics.
In the first article published earlier, we focused on qubits as "bits" of information for quantum systems and some elements of quantum mechanics. But how are qubits physically realized? How can electronics manage these elements that belong to a quantum ecosystem? In this article, we will start a path to explain in detail all you need to know about digital quantum electronics.
The classic computer bits can be 0 and 1, and two bits form four possible states: 00, 01, 10, 11. In general, with n bits, you can build 2n distinct states. How many states can you get with n qubit? The space of the states generated by a system of n qubit has dimension 2n: each vector normalized in this space represents a possible computational state, which we will call quantum register of n qubit. This exponential growth in the number of qubits suggests the potential ability of a quantum computer to process information at a speed that is exponentially higher than that of a classical computer. Note that for n = 200 you get a number that is larger than the number of atoms in the universe.
Quantum Computer Design: An introduction
Formally, a quantum register of n qubit is an element of the 2n-dimensional Hilbert space, C2n, with a computational basis formed by 2n registers at n qubit. Let’s consider the case of two qubits. In analogy with the single qubit, we can construct the computational base of the states’ space as formed by the vectors |00>, |01>, |10>, |11>. A quantum register with two qubits is an overlapping of the form:
With the normalization on the amplitudes of the coefficients.
Like classical computers, a quantum computer is made up of quantum circuits consisting of elementary quantum logic gates. In the classical case, there is only one (non-trivial) one-bit logical port, the NOT port, which implements the logical negation operation defined through
a truth table in which 1 → 0 and 0 → 1.
To define a similar operation on a qubit, we cannot limit ourselves to establishing its action on the primary states |0> and |1>, but we must also specify how a qubit that is in an overlapping of the states |0> and |1> must be transformed. Intuitively, the NOT should exchange the roles of the two primary states and transform α |0> + β |1> into β |0> + α |1>.
Clearly |0> would turn into |1> and |1> into |0>. The operation that implements this type of transformation is linear and is a general property of quantum mechanics that is experimentally justified.
The matrix corresponding to quantum NOT is called for historical reasons X and is defined by:
With the condition of normalization|α|2 + |β|2 = 1 any quantum stateα |0> + β |1>.
Besides NOT, two important operations are represented by the Z matrix:
which acts only on the component |1> exchanging its sign, and the Hadamard port:
This last operation is very often used in the definition of quantum circuits. Its effect is to transform a base state into an overlap that results, after a measurement in the computational base, to be 0 or 1 with equal probability. The effect of H can be defined as a NOT executed in half so that the resulting state is neither 0 nor 1, but a coherent superposition of the two primaries (base) states.
The most important logical ports that implement operations on two classic bits are the AND, OR, XOR, NAND, and NOR ports. The NOT and AND ports form a universal set, i.e., any Boolean function can be achieved with a combination of these two operations. For the same reason, NAND forms a universal set.
The quantum equivalent of XOR is the CNOT (controlled-NOT) port, which operates on two qubits: the first is called the control qubit, and the second is the target qubit. If the control is zero, then the target is left unchanged; if the control is one, then the target is negated, that is:
Where A is the control qubit, B is the target and ⊕ is the classic XOR operation (Figure 1).
Another important operation is represented by the symbol in Figure 2 and consists of measuring a qubit |ψ> = α |0>+β |1>. The result is a classic bit M (indicated with a double line), which will be 0 or 1.
The CNOT port can be used to create states that are entangled. The circuit in Figure 3 generates for each state of the computational base |00>, |01>, |10> , |11> a particular entangled state. These states, which we indicate with β00, β10, β01, β11, are called Bell or EPR states by Bell, Einstein, Podolsky, and Rosen who first discovered their extraordinary properties.
The way to encode information in modern digital computers is done through voltages or currents on tiny transistors within integrated circuits that act as digital or analog elements. Each transistor is addressed by a bus that is able to define a state of 0 (low voltage) or 1 (high voltage).
Quantum computers have different similarities, and the basic idea is illustrated in figure 4. In this figure, we observe a superconducting qubit (also called SQUID – Superconducting QUantum Interference Device), which is the basic element of a quantum computer (a quantum 'transistor'). The term 'Interference' refers to electrons – which behave like waves within a quantum wave, interference patterns that give rise to quantum effects.
In this case, the basic element is niobium, not silicon, as in a classic transistor. The property of the material allows electrons to behave like qubits. When the metal is cooled, it becomes known as a superconductor and begins to show quantum mechanical effects.
The superconducting qubit structure encodes 2 states as tiny magnetic fields pointing in opposite directions. By means of quantum mechanics, we can control these states defined +1 and -1 or |ψ> = α |0>+β |1>.
By means of elements known as superconducting loop couplers, a multi-qubit processor is created. A programmable quantum device can be designed by putting together many of these elements, such as qubits and couplers (Figure 5).
To control the operation of qubits, it is important to have a switch structure consisting of Josephson junctions that direct each qubit (routes pulses of magnetic information to the correct points on the chip) and stores the information in a local magnetic memory element to each device.
The Josephson effect consists in the development of current between two superconductors separated by an insulating junction, called Josephson junction. The effect is due to the tunnel effect of the electron pairs in each of the superconductors. If the insulator is too wide, the probability of tunnel effect is low, and the effect does not occur.
Most Josephson junctions represent a quantum processing unit (QPU). The QPU has no large areas of memory (cache), as they are designed more like a biological brain than the common 'Von Neumann' architecture of a conventional silicon processor. One can think of qubits as neurons and couplers as synapses that control the flow of information between these neurons.
The requirements for a successful quantum implementation are encapsulated in the number of quantum bits that must be large enough for high efficiency. This also implies that you must be probably able to perform a lot of quantum bit operations in a short time. The algorithms require the application of many gates logic on many quantum bits. To keep the probability of error low enough, the various gates must be very precise.
The quantum structure of the computer needs very cold temperatures to work properly. In particular, a temperature reduction approximately below 80mK is required. The performance of a quantum processor increases as the temperature drops – the lower the temperature, the better. The latest generation D-Wave 2000Q system has an operating temperature of about 15 millikelvins. The QPU and parts of the input/output (I/O) system, which includes about 10 kg of material, is cooled to this temperature.
To reach temperatures close to absolute zero, the systems use liquid helium as a coolant. Liquid helium resides within a closed-loop system, where it is recycled and recondensed using pulse tube technology. This makes them suitable for remote use, as there is no need to replenish liquid helium on site.


BIJECTIVE PHYSICS FOR THE RENAISSANCE OF PHYSICS
Physics main task is to build exact models of physical reality. On the basis of the physics picture of reality, we build technology. Computer and mobile phone technology, for example, is based on the theory of electromagnetism which is such a precise picture of electromagnetic phenomena that makes the development of computers possible. Real is what works.
In physics, we have two kinds of elements. Some are obtained by measurement as for example, gravitational constant G, the other is obtained theoretically by the calculations as for example the age of the universe according to the Big Bang model.
Definitely, elements obtained by measurement are more secure than elements obtained by calculations. In physics, experimental data are of fundamental importance.
The most known element of physics which is not based on observed data is space-time where time is considered to be the 4th dimension of universal space. We are believing for more than 100 years that space-time is a fundamental arena of the universe and we do not have the support of experimental data. The Space-time model is pure speculation described by Minkowski manifold.
Also, the idea that universal space-time is “empty” is pure theoretical speculation. We talk today about “quantum fluctuations in space”, we should rather talk about “quantum fluctuations of space”. Universal space is made out of quantum fluctuation, it is not that quantum fluctuations exist in some “empty” universal space.
Bijective Physics requires that every element we use in physics is based on experimental data. The theoretical frame of bijective physics is a bijective function of set theory. The universe is set X and the model of the universe is set Y. Every element in the set X is related to its corresponding element in the set Y with the bijective function:
f: X → Y.
In this way, we get 100% extract picture of physical reality. The universe is set X, the model of the universe is set Y.
NASA has measured back in 2014 that universal space has a Euclidean shape. They measured that the sum of angles in a triangle composed out of three stellar objects is always 180 degrees. This means universal space is infinite in its volume. The research of Barbour, Fiscaletti, Sorli has proved that time has no physical existence. Time is the numerical sequential order of material changes running in universal space. Every experiment done in physics confirms that with clocks we measure numerical sequential order of material changes, i.e. motion in space. Changes have no duration on their own. Duration enters existence when being measured by the observer. This means that material changes run only in universal space which is time-invariant.
Seeing the universe developing in some physical time is a stubbornly persistent illusion. Universe develops only in space which is the primordial non-created energy of the universe. We call it today “superfluid quantum vacuum” or also “physical vacuum”. Vacuum energy is time-invariant, which is in accord with the first law of thermodynamics.
The idea of some beginning of the universe is an extension of Biblical thought in physics. In the Bible, the creation has taken 6 days, in Big Bang cosmology a fraction of the second. The elapsed time is the only difference between the Biblical model of the universe and the Big Bang model.
We are in 21 century and to progress physics wed have to disconnect with some theoretical assumptions of 20th-century physics. This is the aim of Bijective physics in the name of the Physics progress.
The Bijective physics group has the following principal researchers:
Paolo Di Sia
Amrit S. Šorli
Main published articles on the Bijective physics are the following:
1. THERE IS NO PHYSICAL TIME IN THE UNIVERSE. TIME IS NUMERICAL SEQUENTIAL ORDER OF EVENTS IN SPACE. UNIVERSAL SPACE IS TIME-INVARIANT.
Fiscaletti, D., Sorli, A. Perspectives of the Numerical Order of Material Changes in Timeless Approaches in Physics. Found Phys 45, 105–133 (2015). https://doi.org/10.1007/s10701-014-9840-y
2. UNIVERSAL SPACE IS MEDIUM OF QUANTUM ENTANGLEMENT
Fiscaletti, D., Sorli, A. Searching for an adequate relation between time and entanglement. Quantum Stud.: Math. Found. 4, 357–374 (2017). https://doi.org/10.1007/s40509-017-0110-5
3. MASS-ENERGY EQUIVALENCE EXTENTION ON UNIVERSAL SPACE IS THE BASIS OF PHYSICS AND COSMOLOGY PROGRESS
Šorli, A.S. Mass-Energy Equivalence Extension onto a Superfluid Quantum Vacuum. Sci Rep 9, 11737 (2019). https://doi.org/10.1038/s41598-019-48018-2
4. ADVANCES OF RELATIVITY https://www.preprints.org/manuscript/201912.0326/v1
5. BLACK HOLES ARE REJUVENATING SYSTEMS OF THE UNIVERSE
Sorli, A. S. (2020). Black Holes are Rejuvenating Systems of the Universe. JOURNAL OF ADVANCES IN PHYSICS, 17, 23-31. https://doi.org/10.24297/jap.v17i.8620
5. EVOLUTION OF LIFE IS CONSISTENT PART OF UNIVERSAL DYNAMICS
Sorli, A. S., & Čelan, Štefan. (2020). Integration of Life and Consciousness into Cosmology. JOURNAL OF ADVANCES IN PHYSICS, 17, 41-49. https://doi.org/10.24297/jap.v17i.8623
6. EINSTEIN VISION ON TIME IS THE BIG BANG COSMOLOGY FUNERAL
Sorli, A.S. (2020), Einstein’s Vision of Time and Infinite Universe without Singularities – The End of Big Bang Cosmology, JOURNAL OF ADVANCES IN PHYSICS
7. ENTIRE CYCLOTRON PHYSICS IS FALSE
Sorli, A.S. (2020) System Theory, Proton Stability,
Double-Slit Experiment, and Cyclotron Physics, JOURNAL OF ADVANCES IN PHYSICS (accepted in publication)


When Albert Einstein first predicted that light travels the same speed everywhere in our universe, he essentially stamped a speed limit on it: 670,616,629 miles per hour — fast enough to circle the entire Earth eight times every second.
But that’s not the entire story. In fact, it’s just the beginning.
Before Einstein, mass — the atoms that make up you, me, and everything we see — and energy were treated as separate entities. But in 1905, Einstein forever changed the way physicists view the universe. Einstein’s Special Theory of Relativity permanently tied mass and energy together in the simple yet fundamental equation E=mc 2. This little equation predicts that nothing with mass can move as fast as light, or faster.
The closest humankind has ever come to reaching the speed of light is inside of powerful particle accelerators like the Large Hadron Collider and the Tevatron.
These colossal machines accelerate subatomic particles to more than 99.99% the speed of light, but as Physics Nobel laureate David Gross explains, these particles will never reach the cosmic speed limit.
To do so would require an infinite amount of energy and, in the process, the object’s mass would become infinite, which is impossible. (The reason particles of light, called photons, travel at light speeds is because they have no mass.
Since Einstein, physicists have found that certain entities can reach superluminal (that means “faster-than-light”) speeds and still follow the cosmic rules laid down by special relativity. While these do not disprove Einstein’s theory, they give us insight into the peculiar behaviour of light and the quantum realm.
The light equivalent of a sonic boom
So, in theory, if something travels faster than the speed of light, it should produce something like a “luminal boom.”
In fact, this light boom happens on a daily basis in facilities around the world — you can see it with your own eyes. It’s called Cherenkov radiation, and it shows up as a blue glow inside of nuclear reactors, like in the Advanced Test Reactor at the Idaho National Laboratory in the image to the right.
Cherenkov radiation is named after Soviet scientist Pavel Alekseyevich Cherenkov, who first measured it in 1934 and was awarded the Nobel Physics Prize in 1958 for his discovery.
Cherenkov radiation glows because the core of the Advanced Test Reactor is submerged in water to keep it cool. In water, light travels at 75 % the speed it would in the vacuum of outer space, but the electrons created by the reaction inside of the core travel through the water faster than the light does.
Particles, like these electrons, that surpass the speed of light in water, or some other medium such as glass, create a shock wave similar to the shock wave from a sonic boom.
When a rocket, for example, travels through air, it generates pressure waves in front that move away from it at the speed of sound, and the closer the rocket reaches that sound barrier, the less time the waves have to move out of the object’s path. Once it reaches the speed of sound, the waves bunch up creating a shock front that forms a loud sonic boom.
Similarly, when electrons travel through water at speeds faster than light speed in water, they generate a shock wave of light that sometimes shines as blue light, but can also shine in ultraviolet.
While these particles are travelling faster than light does in water, they’re not actually breaking the cosmic speed limit of 670,616,629 miles per hour.
When the rules don’t apply
Keep in mind that Einstein’s Special Theory of Relativity states that nothing with mass can go faster than the speed of light, and as far as physicists can tell, the universe abides by that rule. But what about something without mass?
Photons, by their very nature, cannot exceed the speed of light, but particles of light are not the only massless entity in the universe. Empty space contains no material substance and therefore, by definition, has no mass.
“Since nothing is just empty space or vacuum, it can expand faster than light speed since no material object is breaking the light barrier,” said theoretical astrophysicist Michio Kaku on Big Think. “Therefore, empty space can certainly expand faster than light.”
This is exactly what physicists think happened immediately after the Big Bang during the epoch called inflation, which was first hypothesized by physicists Alan Guth and Andrei Linde in the 1980s. Within a trillionth of a trillionth of a second, the universe repeatedly doubled in size and as a result, the outer edge of the universe expanded very quickly, much faster than the speed of light.
Quantum entanglement makes the cut
Quantum entanglement sounds complex and intimidating but at a rudimentary level entanglement is just the way subatomic particles communicate with each other.
“If I have two electrons close together, they can vibrate in unison, according to the quantum theory,” Kaku explains on Big Think. Now, separate those two electrons so that they’re hundreds or even thousands of light years apart, and they will keep this instant communication bridge open.
“If I jiggle one electron, the other electron ‘senses’ this vibration instantly, faster than the speed of light. Einstein thought that this therefore disproved the quantum theory, since nothing can go faster than light,” Kaku wrote.
In fact, in 1935, Einstein, Boris Podolsky and Nathan Rosen, attempted to disprove quantum theory with a thought experiment on what Einstein referred to as “spooky actions at a distance.“
Ironically, their paper laid the foundation for what today is called the EPR (Einstein-Podolsky-Rosen) paradox, a paradox that describes this instantaneous communication of quantum entanglement — an integral part of some of the world’s most cutting-edge technologies, like quantum cryptography.
Dreaming of wormholes
Since nothing with mass can travel faster than light, you can kiss interstellar travel goodbye — at least, in the classical sense of rocketships and flying.
Although Einstein trampled over our aspirations of deep-space road trips with his Theory of Special Relativity, he gave us a new hope for interstellar travel with his General Theory of Relativity in 1915.
While Special Relativity wed mass and energy, General Relativity wove space and time together.
“The only viable way of breaking the light barrier may be through General Relativity and the warping of space time,” Kaku writes. This warping is what we colloquially call a “wormhole,” which theoretically would let something travel vast distances instantaneously, essentially enabling us to break the cosmic speed limit by traveling great distances in a very short amount of time.
In 1988, theoretical physicist Kip Thorne — the science consultant and executive producer for the recent film “Interstellar” — used Einstein’s equations of General Relativity to predict the possibility of wormholes that would forever be open for space travel.
But in order to be traversable, these wormholes need some strange, exotic matter holding them open.
“Now it is an amazing fact that exotic matter can exist, thanks to weirdnesses in the laws of quantum physics,” Thorne writes in his book “The Science of Interstellar.”
And this exotic matter has even been made in laboratories here on Earth but in very tiny amounts. When Thorne proposed his theory of stable wormholes in 1988 he called upon the physics community to help him determine if enough exotic matter could exist in the universe to support the possibility of a wormhole.
“This triggered a lot of research by a lot of physicists; but today, nearly thirty years later, the answer is still unknown.” Thorne writes. At the moment, it’s not looking good, “But we are still far from a final answer,” he concludes.
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How will quantum computing change the future of security? What does a quantum computer look like? Mike and Daniel sit down with Lee Barford to get some answers.
Last time we looked at “what is quantum computing” and talked about quantum bits and storing data in superstates.
00:40 Lee talks about how to crack RSA and Shor’s algorithm (wikipedia)
00:50 The history of quantum computing (wiki). The first person to propose it was Richard Feynman in the mid 1960s. There was some interest, but it died out.
In the 1990s, Peter Shor published a paper pointing out that if you could build a quantum computer with certain operational properties (machine code instructions), then you could find one factor of a number no matter how long it is.
Then, he outlined another number of things he would need, like a quantum Fast Fourier Transform (FFT).
Much of the security we use every day is both the RSA public key system and the Diffie Hellman Key Exchange algorithm.
HTTPS connections use the Diffie Hellman Key Exchange algorithm. RSA stands for “
really secure algorithm” “Rivest, Shamir, and Adelman.”
RSA only works if the recipients know each other, but Diffie Hellman works for people who don’t know each other but still want to communicate securely. This is useful because it’s not practical for everyone to have their own RSA keys.
Factoring numbers that are made up of large prime numbers is the basis for RSA. The processing power required for factoring is too large to be practical. People have been working on this for 2500 years.
Shor’s algorithm is theoretically fast enough to break RSA. If you could build a quantum computer with enough quantum bits and operate with a machine language cycle time that is reasonable (us or ms), then it would be possible to factor thousand bit numbers.
Famous professors and famous universities have a huge disparity of opinion as to when a quantum computer of that size could be built. Some say 5-10 years, others say up to 50.
What does a quantum computer look like? It’s easier to describe architecturally than physically. A quantum computer isn’t that much different from a classical computer, it’s simply a co-processor that has to co-exist with current forms of digital electronics.
If you look at Shor’s algorithm, there are a lot of familiar commands, like “if statements” and “for loops.” But, quantum gates, or quantum assembly language operations, are used in the quantum processor. (more about this)
Lee thinks that because a quantum gate operates in time instead of space, the term “gate” isn’t a great name.
What quantum computers exist today? Some have been built, but with only a few quantum bits. The current claim is that people have created quantum computers with up to 21 quantum bits. But, there are potentially a lot of errors and noise. For example, can they actually maintain a proper setup and hold time?
Continuing the Schrodinger’s Cat analogy…
In reality, if you have a piece of physics that you’ve managed to put into a superimposed quantum state, any disturbance of it (photon impact, etc.) will cause it to collapse into an unwanted state or to collapse too early.
So, quantum bits have to be highly isolated from their environments. So, in vacuums or extreme cold temperatures (well below 1 degree Kelvin!).
The research companies making big claims about the quantity of bits are not using solid state quantum computers.
The isolation of a quantum computer can’t be perfect, so there’s a limited lifetime for the computation before the probability of getting an error gets too high.
Why do we need a superposition of states? Why does it matter when the superimposed states collapse to one state? If it collapses at the wrong time you’ll get a wrong answer. With Shor’s algorithm it’s easy to check for the right answer. And, you get either a remainder of 0 or your don’t. If you get 0, the answer is correct. The computation only has to be reliable enough for you to check the answer.
If the probability of getting the right answer is high enough, you can afford to get the wrong answer on occasion.
The probability of the state of a quantum bit isn’t just 50%, so how do you set the probability of the state? It depends on the physical system. You can write to a quantum bit by injecting energy into the system, for example using a very small number of photons as a pulse with a carefully controlled timing and phase.
Keysight helps quantum computer researchers generate and measure pulses with metrological levels of precision.
The pulses have to be very carefully timed and correlated with sub nanosecond accuracy. You need time synchronization between all the bits at once for it to be useful.
What is a quantum bit? Two common kinds of quantum bits are
1: Ions trapped in a vacuum with laser trapping . The ions can’t move because they are held in place by standing waves of laser beams. The vacuum can be at room temperature but the ions are low temperature because they can’t move.
2. Josephson junctions in tank circuits (a coil capacitor) produce oscillations at microwave frequencies. Under the right physical conditions, those can be designed to behave like an abstract two state quantum system. You just designate zero and one to different states of the system.
Probabilities are actually a wrong description, it should be complex quantum amplitudes.
After working with quantum computing, it’s common to walk away feeling a lot less knowledgeable.
Stupid question section:
“If you had Schrodinger’s cat in a box, would you look or not?”
Lee says the cat’s wave function really collapsed as it started to warm up so the state has already been determined.


The Einstein-Podolsky-Rosen paradox is that measurement in quantum mechanics seems to require faster-than-light communication under certain circumstances. This, they claimed, is absurd, and proves quantum mechanics to be incomplete -- certain things must be decided in advance.
This argued towards a local hidden variables theory: a theory which maintains locality better than quantum mechanics and - more pertinently to the three theorists - lacks quantum weirdness. How was it less weird? The distributions of the properties of particles were all now statistical distributions over unknown quantities, and not intrinsic distributions over quantum operator eigenvalues.
At first, there was no known way to actually test whether the seemingly absurd result of faster-than-light communication was true or not: no one could think of a prediction quantum mechanics made that no local hidden variables theory could make. In 1951, some progress was made as David Bohm created a more tractable variant of the paradox involving spin, but still no specific different predictions could be found.
In 1964, this changed: John Bell used Bohm's special case to devise his famous inequality, which pointed out a difference between the two schema. That is, though there were a variety of ways a local hidden variables theory could make things work, there was a limit to how coordinated they could make things. Quantum mechanics could cross this limit.
To explain this notion - suppose you can make one of 3 binary measurements - A, B, or C. Measurements A and B are closely related and read, say, 75% the same, with only 25% reading the opposite way. B and C are closely related and also 75% the same, with 25% flipped. So, if you compare the results of measurements A and C, you should classically expect not more than 50% of your results to flip.
This is what quantum mechanics disagrees on. You can set up situations in which you expect 75% of the results to flip when you compare A with C. And as it turns out, you can pull this off with separated particles like EPR were talking about. It seems in this case like information must be transmitted to help A and C be more opposite than random.
Alain Aspect used a special case of the inequality to form the basis of his famous experiment, which was finished in 1982.
The final form of the Aspect experiment went so:
- Set up a device which creates Einstein-Podolsky-Rosen pairs (EPR pairs) of photons proceeding in opposite directions. What makes each pair an EPR pair is that the two photons' polarizations are oriented the opposite way*, not by picking them to be some specific opposite pair of values, but by assigning that constraint without constraining their individual polarizations. This quantum dependence is known as entanglement.
To get technical, the spinor ket of the photon pair is X | + - > + X' | - + > for some X and X', in a linear polarization basis. (There's more that could be said, but the algebra would suddenly get very intense and it wouldn't materially help.)
- Place three detectors to detect each photon, each detecting the polarization along an axis at 60° from the other two. Use only one detector at a time at each end. Let's call these A, B, and C at one end, and A', B', and C' at the other. This setup gives the sameness ratio predictions used above.
- Rapidly randomly determine which axis is used on each detector, and reset the choice after each photon is detected. Make sure the switching is good enough to keep the switching events spacelike separated.
There are two cases here: the photons' polarization is detected along the same axis, or the photons' polarization is detected along different axes. In the event that the photons were detected along the same axis (A & A', B & B', or C & C'), things are simple -- they will be read oppositely. This serves as a check on the efficiency of the setup.
In the other case, in which the photons are measured along different directions (A & B', say - 6 combinations), the Bell Inequality comes into play: quantum mechanics and local-hidden-variables theories make different predictions on how often the two spins will look 'more opposite' than 'more aligned'.
As it turned out, quantum mechanics' prediction was strongly validated.
Even after this experiment, there were a few loopholes through which it was conceivable that one could fit a local hidden variables theory: the theory could involve 'looking ahead' at the detectors and finding what orientations they would be, going so far as to examine the state of the randomization mechanism. With improving randomization, this became an increasingly wild supposition. As time progressed, the various loopholes were closed tighter and tighter: supposing local hidden variables now requires incredibly complicated and un-physics-like 'conspiracy'-style theories.
Taking this to mean that local hidden variables theories are false, what does that leave?
- Quantum mechanics
Up side: we already know what it is, it has succeeded all tests.
Down side: under the Copenhagen interpretation, locality is violated.
- A global hidden variables theory
Up side: at least Quantum mechanics and all of its weirdness isn't true.
Down side: we don't know what such a theory would be (though one has been devised, by David Bohm), and since there isn't a single difference in testable predictions between any of them and quantum mechanics, pursuing it has entered the realm of metaphysics. To snag a quote from a Nobel-Winner** "If it makes different predictions from Quantum Mechanics, I'm not interested. If it makes the same predictions as Quantum Mechanics, I'm not interested."
At first, it seems like we're stuck with nonlocality in our physical theory, whether by global variables or by a global wavefunction which collapses superluminally. This would be downright ugly. But the locality problem is not with Quantum Mechanics itself, but with the Copenhagen Interpretation: it is the collapse of the wavefunction which is a problem. If we consider the measurement process to be another case of entanglement, then the consistency of the results follows straightforwardly and involves only local information exchange -- the exchange occurring when you bring together the various results (note that this one supposition is the entire basis of the Many-Worlds Interpretation).
Entirely separate from the philosophical implications, this paradox yielded a tool of practical utility: EPR pairs form the basis of Quantum Teleportation, and play a major role in Quantum Computing.
* An entangled system can have any sort of relation, not only opposite spin. The relationship does not even have to deal with spin. There can be more than two particles, and they do not even need to be the same type. The case used in the experiment kept things as simple as possible.
** I believe it was John Schrieffer, but I could be wrong; it's hard to track these things.
Einstein, A.; Podolsky, B.; and Rosen, N. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Phys. Rev. 47, 777-780, 1935.
Bohm, D. "The Paradox of Einstein, Rosen, and Podolsky." Quantum Th., 611-623, 1951
Bell, J. S. "On the Einstein-Podolsky-Rosen Paradox." Physics 1, 195-200, 1964.
Aspect, A.; Grangier, P.; and Roger, G. "Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities." Phys. Rev. Let. 49, 91-94, 1982.


On Monday, a group of researchers from MIT published the results from recent experiments that used the light from stars emitted 7.8 billion and 12.2 billion years ago to help confirm the reality of quantum entanglement.
These results help settle a long standing debate in physics about whether entanglement is just an illusion that can actually be explained using principles of classical physics. These new results suggest that entanglement actually occurs because if it didn’t exist the universe would somehow have to have “known” 7.8 billion years ago that these MIT scientists would perform these experiments in 2018.
Quantum entanglement is the theory that particles can be connected in such a way that measuring one particle can instantaneously convey information about that measurement to the other particle, regardless of the distance between them. It almost sounds like magic, which is probably why it received a healthy dose of criticism from the physics community when the theory was first proposed nearly 100 years ago.
Albert Einstein was a particularly vocal critic of entanglement, which he famously described as “spooky action at a distance.” Part of Einstein’s beef with the quantum mechanics crowd was that he believed that particles have definite qualities that exist before they are measured and that two particles distant in space and time can’t affect one another instantaneously since they are limited by the speed of light—a viewpoint known as local realism.
Under quantum mechanics, however, the properties of a particle don’t exist independently of measurement used to determine those properties. Moreover, when it comes to entangled particles, the measurement of one particle will instantaneously influence the properties of the other entangled particle. This means that the values of these properties will be highly correlated—so highly correlated, in fact, that the degree of coincidence in their values can’t really be explained without recourse to quantum mechanics.
Nevertheless, local realism has continued to haunt the development of quantum physics. In the 1960s, the physicist John Bell calculated the upper limit on the degree of correlation between two particles if their relationship was governed by local realism rather than quantum mechanics—a value known as Bell’s inequality.
“As strange as quantum mechanics may seem, it continues to match every experimental test we can devise.”
In the past half-century, however, numerous experiments have demonstrated values in excess of Bell’s inequality, which created a serious theoretical dilemma. Either these experiments demonstrated the reality of quantum entanglement or there were some “loopholes” unintentionally introduced into the experiments that could explain the results through classical physics without invoking quantum mechanics.
One of the most pernicious loopholes is known as the “freedom of choice loophole.” This is the idea that the way a researcher sets up an experiment—from the choice of particles used to the way properties of these particles are measured—can influence the results of the measurement in unforeseen ways. In order to truly demonstrate quantum entanglement, critics argue, it is necessary to negate this freedom of choice loophole in quantum experiments.
A COSMIC SOLUTION TO FREEDOM OF CHOICE
In May, a group of researchers led by physicists from the Institute for Photonic Sciences in Spain published the results from the largest experiment to tackle the freedom of choice loophole. This experiment involved over 100,000 people from around the world playing a video game and the results of their gameplay were used in the experiment. The idea was that because the actions of these 100,000 people could not be predicted in advance, this would effectively remove any bias introduced into the experimental set up by researchers and thus close the “freedom of choice” loophole in the experiment.
Around the same time these researcher were collecting their data from participants, however, a group of physicists led by researchers from MIT were also exploring how to close the freedom of choice loophole in quantum mechanics. Yet rather than search for solutions on Earth, these physicists turned to the cosmos to eliminate human bias.
In the past, physicists have tried to close the freedom of choice loophole by generating entangled particles from a single source and then sending these entangled particles to detectors at two different locations. In the instant before the particle arrives, the detectors would use a random number generator to decide what property of the particle to measure (spin, polarity, etc.) in an effort to eliminate human bias. The problem, however, was that even this random number generator could technically be influenced by hidden, non-quantum variables that affect the measurement.
To eliminate the influence of hidden variables, the researchers from MIT ditched the random number generators in favor of stars. In their experiment, the MIT researchers trained telescopes at two detector sites on various stars at least 600 light years away and used the photons from these stars to determine which measurements would be conducted on entangled particles at the detectors. The theory was that using 600 year-old starlight would help close the freedom of choice loophole because any hidden variables in the experiment would have to have been set in motion before the photons left their host star over 600 years ago.
“The real estate left over for the skeptics of quantum mechanics has shrunk considerably,” MIT physicist David Kaiser said in a statement shortly after the results of the experiment were published last year. “We haven’t gotten rid of [the freedom of choice loophole], but we’ve shrunk it down by 16 orders of magnitude.”
In research published in Physical Review Letters on Monday, the same team of MIT physicists made some wild improvements on their previous measurements and reduced the freedom of choice loophole even more. The new experiment is more or less the same, but instead of using normal stars as their source of randomness for quantum measurements, the researchers used light from two ancient quasars that were 7.8 and 12.2 billion light years away.
“The Earth is about 4.5 billion years old, so any alternative mechanism different from quantum mechanics that might have produced our results by exploiting this loophole would’ve had to be in place long before even there was a planet Earth, let alone an MIT,” Kaiser said in a statement. “So we’ve pushed any alternative explanations back to very early in cosmic history.”
Quasars are basically dense clouds of gas that surround the massive black holes that can be found at the center of most galaxies. As the gas from the quasar falls into the black hole it emits strong bursts of energy that are smeared across the electromagnetic spectrum. In the most recent experiment, the researchers used incredibly sensitive telescopes to measure the wavelength of photons—particles of light—emitted by the quasars.
At the same time, a station between the two telescopes generated thousands of entangled photons which were then sent to detectors at the telescope. For each pair of entangled photons, the detectors would measure the wavelength of incoming interstellar photons relative to some baseline metric and use this value to determine what measurement would be performed on the incoming photons.
In total, the researchers performed this measurement on just shy of 30,000 entangled photon pairs. The correlation between the measurements performed on the photons far exceeded Bell’s inequality, which suggested that the particles were experiencing quantum entanglement. In fact, Kaiser and his colleagues calculated that the odds that this degree of correlation was the result of classical rather than quantum physics was about one in one hundred billion billion. According to MIT physicist Alan Guth, the research makes it “unbelievably implausible that a local realistic theory could be underlying the physics of the universe.”
Despite the overwhelming results in favor of quantum entanglement, there’s still the (incredibly) small possibility that local realism can account for these effects. To reduce these uncertainties even more, Kaiser, Guth and their colleagues are considering experiments that look even further back in time for a source of randomness, such as the cosmic microwave background. Performing these experiments, however, would involve overcoming a host of significant technical challenges.
“It is fun to think about new types of experiments we can design in the future, but for now we are very pleased that we are able to address this particular loophole so dramatically,” Kaiser said. “ Our experiment with quasars puts extremely tight constraints on various alternatives to quantum mechanics. As strange as quantum mechanics may seem, it continues to match every experimental test we can devise.”


A Brief History of Computing, starting in 150 BC
CS 441 Lecture, Dr. Lawlor
Folks have been using physical devices to perform computations for a long time. Notable accomplishments:
- 150 BC: Greeks, likely including Archimedes, built clockwork-like chains of gears such as the Antikythera mechanism to predict astronomical events such as eclipses, and to measure time and convert between calendars.
- 1640's: Blaise Pascal built a series of adding machines, which used a series of hand-cranked cogs to add (similar to a car's mechanical odometer), or via complement arithmetic, subtract; or via repeated addition, multiply.
- 1820's: Charles Babbage designed (but never built) a fully-mechanical polynomial evaluator, the difference engine, via the method of finite differences. He also started work on a fully programmable model, the analytical engine, but building the thing with rod logic would have taken a huge amount of labor.
- 1890: IBM corporation uses the patented electromechanical (mercury switches and relays) Hollerith tabulator to count up the punched cards that represent the 1890 census results. The 1891 Electrical Engineer raved: "This apparatus works unerringly as the mills of the gods, but beats
them hollow as to speed."
- 1941: Konrad Zuse builds the world's first fully-programmable computer, the Zuse Z3. Sadly, it used scavenged telephone switching relays, and was built in wartime Germany, so it was ignored for years.
- 1944: John von Neumann
proposes using the same memory to store both program and data, now
known as a "von Neumann machine". Previous designs used separate
memories for program and data, known as the Harvard architecture.
- 1946: ENIAC, the
first vacuum-tube electronic automatic computer, built by the US
military. ENIAC is fully programmable. Vacuum tubes can
switch in nanoseconds, like transistors, rather than milliseconds, like
- 1948: CURTA, a popular fully-mechanical pocket calculator.
- 1949: MONIAC, a hydraulic computer, models the country's financial system using water.
- 1950's: the automatic transmission, a hydraulic computer, becomes cheap enough for ordinary people to buy.
- 1956: IBM releases Fortran,
the first successful programming language. Prior to Fortran,
machines were typically programmed using wires, machine code, or assembly.
- 1960's: IBM's System/360, which adds microcode and binary backward compatability.
- 1964: Seymore Cray's CDC 6600 achieves amazing performance using superscalar
processing, caching, newfangled transistors, liquid cooling, and offloading I/O
to dedicated "peripheral processors", which were hyperthreading-style barrel processors.
- 1971: Upstart Intel creates a single-chip CPU, the 4004, which computes 4-bit values at up to 0.74MHz.
- 1972: HP-35, the first electronic pocket calculator good enough to replace the slide rule, for only $395.
- 1972: Intel's 8008, 8-bit values at up to 0.5MHz.
- 1978: Intel's 8086, 16-bit values at up to 10MHz.
- late 1970's: "micro" digital computers, like the Apple I, become cheap enough for dedicated hobbyists to buy and solder together.
- 1981: digital computers, like the IBM PC,
become cheap enough for ordinary people to buy pre-assembled. The
notion of selling software is popularized by the upstart "Micro-soft"
- 1984: Apple releases a 32-bit personal computer, the Mac 128K.
- 1985: Intel's 80386, 32-bit values at up to 40MHz.
- 1985: The notion of specialized hardware for graphics is popularized by Silicon Graphics corporation. RISC instruction sets are pushed by MIPS corporation.
- 1990: IBM introduces a superscalar RISC machine for personal computers, PowerPC.
- 1994: Intel's releases a 100MHz Pentium CPU.
- 1990's: graphics hardware for personal computers takes off with GLQuake and other 3D games.
- 2000: Intel releases a 1 GHz Pentium III CPU.
- 2002: Intel releases a 3 GHz Pentium 4 CPU, with hyperthreading.
- 2002: Graphics cards become programmable in assembly language (ARB_fragment_program), and support dozens of threads.
- 2003: NVIDIA releases "Cg", a C++-like language for programming
graphics cards. Limitations include a single write per program.
- 2003: AMD corporation introduces chips with a 64-bit extension to the x86 instruction set, which Intel later adopts.
- 2004: Intel abandons plans for a 4GHz Pentium 4 chip.
- 2006: Intel releases dual-core and quad-core CPUs at around 2GHz. The great multithreaded programming model panic begins.
- 2007: Intel announces "V8" eight-core systems.
- 2007: NVIDIA releases CUDA, a very C-like language for
programming graphics cards for non-graphics tasks. Supports
arbitrary reads and writes.
- 2008: Graphics hardware now supports between thousands and millions of threads.
- CPUs are still clocked at 2-4 GHz, just like
in 2002. So in the future, your machine won't have very many more
GHz, instead it
will have many more cores. Nobody knows how to program those
- For highly parallel problems, graphics cards already dramatically
surpass CPU parallelism and hence performance. Thousand-core
graphics software is commonplace; thousand-core CPU software is
- Technology changes, like gears to relays, relays to vacuum tubes,
or tubes to transistors, have the capability to totally re-make the
computer industry in less than 10 years. Biological/nano or
quantum computing has a similar potential!


Storing quantum bits of information, or qubits, is a lot harder than storing ordinary binary digits. It’s not simply ones or zeroes, but the whole range of subtle quantum superpositions between them. Electrons can easily slide out of those states if they’re not stored in the right materials, which is why electrical engineers at Princeton are working with a UK manufacturer to create a better storage material — synthetic diamonds — from scratch. They published an account of their success on Thursday in Science.
For decades, physicists, materials engineers, and others have been trying to achieve the conceptual promise of quantum-encrypted communications because the data transferred in that process is theoretically immune to covert surveillance. Any attempt to observe that data between parties — à la the Heisenberg Uncertainty Principle — would fundamentally alter that information, quickly revealing that it was compromised. The problem has been storing and preserving qubits and then converting them to fiber optic-ready photons, and using diamonds appears to be the route toward achieving both. But not just any diamond will do, which is why Princeton’s team has been hard at work creating a synthetic one, as they describe in their paper.
“The properties that we’re targeting are what’s relevant for quantum networks,” electrical engineer Nathalie de Leon tells Inverse. At Princeton, where de Leon is an assistant professor, her team’s focus is essentially inventing quantum hardware. “It’s applications where you want something that has a long storage time, and then also has a good interface with photons so that you can send light over very long distances.”
Photonic interactions matter a lot for high-speed international communications because all of the information traveling along fiber optic cables moves through our global infrastructure as discrete photons — cruising at 69 percent of the speed of light. (Nice.)
“That puts a lot of constraints on the optical characteristics,” de Leon says. “As one example, it’s really important that the color be stable. If the color of the photon is jumping around over time, then that’s really bad for these protocols.”
Right now, de Leon’s group is trying to craft a version of these synthetic diamonds that can convert to the standard 1,550-nanometer wavelength on which photons now traverse fiber optic cables. Currently, her team’s synthetic diamonds support 946-nanometer photon wavelengths. (Photon “color” is a bit of a euphemism here since both of these wavelengths are shades of infrared outside the visible spectrum.)
The hurdle that her team just succeeded in crossing is storing those qubits in crystalline quantum repeaters, similar to the repeaters that are currently used to prevent signal loss and degradation in today’s fiber-optic communications. The critical step in this process was producing synthetic diamonds with as little unwanted impurities as possible (nitrogen, mainly) and more of the impurities they actually did want (silicon and boron).
“Nitrogen turns out to be the predominant defect that you get in these diamonds,” de Leon says. Her group’s partners at the British diamond maker Element Six had to create above-average vacuum conditions since even ordinary vacuums can leave enough nitrogen in the chamber to contaminate the artificially-made crystals. Because nitrogen has one more free electron than carbon, nitrogen impurities disturb the unique electrical makeup that the researchers are hoping for.
Other small defects can undermine the qubit-storing potential of these diamonds, too. The goal is to have pairs of atom-sized vacancies in the crystal framework alongside a substituted silicon atom where a single carbon used to be, but sometimes those pairs can bunch up together in “vacancy clusters” that start to redistribute their electrons in annoying, counterproductive ways. Sometimes polishing and etching damage on the surface of the diamond can also cause a domino effect, messing with this pattern of electrons, too. This is where adding boron — which has one less free electron than carbon — can help.
“What we had to do,” de Leon says, “is both start with this ultra-high purity diamond and then grow in some boron to basically soak up any of the extra electrons that we couldn’t control. Then there was a lot of materials processing — boring stuff like thermal annealing and repairing the surface at the end to make sure that we still get rid of a lot of these other types of defects that give you extra charges.”
Mastering both of these challenges, many in the field suspect, are the keys to fully functional and nearly impossible to crack quantum encryption.
Before the dawn of synthetic diamonds only a few years ago, researchers in the field of quantum optics had to rely on natural diamonds to do their work — one specific diamond, in particular.
According to de Leon, everyone in the field of quantum optics had to rely on a single, naturally-made diamond from Russia that just happened to have the right percentage of boron, nitrogen, and other impurities to make their research possible. Fragments of the diamond were cleaved off and distributed to research groups across the world.
“Many of the groups had their own little piece of the ‘magic’ Russian diamond,” as de Leon told Princeton’s in-house news service in 2016. “At Harvard, we called ours ‘Magic Alice’ and ‘Magic Bob.’”
So, TL;DR, Western scientists are getting better at manufacturing their own magical quantum computing diamonds instead of depending on slivers of Russia’s magical quantum computing diamond. This is a factual sentence that sounds ridiculous. Classic 2018.


Mar 5, 2012
An international team of physicists is the first to implement in the lab an important "error correction" technique that could play a vital role in the development of practical quantum computers. Known as topological error correction (TEC), the technique is based on "clusters" that each contain eight highly entangled photons. These clusters are useful for this purpose because a measurement on one photon does not destroy the entire entangled state.
The multiparticle cluster state at the centre of the current work was first proposed in 2001 by Robert Raussendorf and Hans Briegel, who were then at the University of Munich. Now at the University of British Columbia in Canada, Raussendorf is also involved in this latest research. Such a cluster could be used to perform "one-way" quantum computing, in which the states of individual particles are measured in a specific sequence so that the quantum state of the remaining particles gives the result of the computation.
Like a doughnut
Although quantum computers promise a lot, anyone wishing to build a practical device has to deal with the tricky fact that the quantum nature of qubits fizzles away rapidly as they interact with the heat and noise of the surrounding environment. Quantum error correction offers a way of staving off this "decoherence" – at least long enough for a quantum computation process to occur – by distributing the quantum information held in one "logical" qubit among a number of entangled "physical" qubits. Subjecting these physical qubits to an error-correction algorithm can then reveal if one or more qubits has undergone decoherence and, if so, to restore quantum information.
Developed by Jian-Wei Pan and colleagues at the University of Science and Technology of China in Shanghai, along with Raussendorf and other physicists in Canada and Australia, the new experimental demonstration of TEC involves defining qubits in terms of fundamental shapes that cannot be changed by continuous deformations. A doughnut, for example, remains a doughnut if it is poked, stretched or prodded – unless the perturbation is so violent that it cuts the loop. Topological qubits are similar in the sense that they are not easily perturbed by noise and heat, and must take a big hit before they are destroyed.
The team's cluster state comprises eight entangled photons, each acting as a physical qubit that can have a value of "0" and "1" depending upon its polarization state. The state is made by creating four pairs of entangled photons from firing a laser pulse at a non-linear crystal. The pairs are separated and combined in new pairs that are entangled by having them interfere on polarization-dependent beamsplitters.
The photons can be thought of as forming a 3D cube, in which each photon is entangled with its nearest neighbours. This arrangement has a certain topology that protects a specific quantum correlation between two physical qubits – something that could be used as a building block to create logical qubits in a topological quantum computer.
The TEC is implemented on the cluster state by making a series of measurements on the photons – essentially performing a one-way quantum-computing algorithm. To test the correction scheme, the team purposely introduced errors into the system. First, the researchers caused decoherence in one specific qubit and found that the TEC algorithm could identify which photon was affected and correct the error. Next, the team introduced a fixed amount of decoherence to all photons simultaneously, and again the scheme was able to identify the problem and correct it.
"Our experiment provides a proof of principle that topological error correction would be one of the most practical approaches for designing quantum computers," Pan told physicsworld.com.
Pan points out that TEC offers several benefits when compared with conventional schemes – in particular, it can handle the highest error rates of any scheme, making it easier to use with real physical devices, which will always suffer from errors. "Moreover, the architecture used in topological error correction is rather simple: it is sufficient to create interactions between two quantum bits that neighbour each other," he adds. This means that TEC should be compatible with a range of different qubit schemes, including quantum dots and Josephson junctions. This is important because such solid-state qubits should be easier to integrate and scale up to create a practical quantum computer.
Raymond Laflamme, director of the Institute for Quantum Computing at the University of Waterloo in Canada, says that the work is an important result that shows that TEC can be implemented in principle. But given that not all types of qubits are compatible with TEC, Laflamme cautions that its future usefulness will depend on which qubit technologies are ultimately used to create practical quantum computers.
The next step in the team's research is to create cluster states involving larger numbers of qubits – to do TEC on a logical qubit rather than just a correlation. Ultimately, physicists would like to develop systems that implement TEC on topological qubits and topological quantum-logic gates.
The work is described in Nature.