These days, losing the manual for some piece of electronics you’ve purchased is notable mostly because you had a printed document to lose in the first place. In the dead-tree dominated days of yore, of course, this was less true. Documentation loss is a major problem in the effort to understand old computer systems, and it’s part of what drives ongoing data preservation efforts across the industry. Until recently, the Zuse Z4 could have been a poster child for this sort of problem.
The Z4 was the brainchild of Konrad Zuse, a German who deserves to be better known than he is for his early, groundbreaking work. Zuse had the misfortune to be making some of his biggest breakthroughs immediately prior to and during World War II. It was Zuse who designed the first high-level programming language from 1942 to 1945. This is remarkable because, as Wikipedia notes, Zuse had no training whatsoever in mechanical computing devices. He independently discovered both propositional calculus and lattice theory, calling them “combinatorics of conditionals” and “study of intervals,” respectively.
The Zuse Z4 is the oldest preserved digital computer in the world and arguably* the first digital computer. The Z4 was developed through the end of the war and was moved multiple times while under construction to keep it away from the advancing Soviet army. After the war, it was expanded and became the second digital computer in the world to be sold. The preserved model is on display at the Deutsches Museum in Munich and is pictured above.
Its documentation, however, was a different story. A recent blog post by the Association of Computing Machinery details how the rare documents were found. Archivist Evelyn Boesch, with ETH Zurich University, contacted Herbert Bruder of the ACM and informed him that her father, René Boesch, had kept a tranche of rare historical documents. These turned out to include a user manual for the Z4 Zuse, as well as notes on flutter calculations. Other documents, dated October 27, 1953, detail what the Z4 was working on. At the time, it was being used to perform flutter calculations on the Swiss FFA P-16 fighter aircraft, which was then in development. Details from the recovered documents show that it took the Z4 50 hours to simulate 2.4 seconds of flight time, which is slightly worse than the current version of Microsoft Flight Simulator.
The ACM blog post notes that “around 100 jobs were carried out with the Z4 between 1950 and 1955,” implying an average per-job computation time of about three weeks.
What We Learn From Manuals Like This
The recovered Z4 manual illustrates why this type of document preservation is so important. From their earliest days, computers were upgradeable — machines like ENIAC were outfitted with the equivalent of RAM upgrades and CPU improvements. In the Z4’s case, support for conditional jump instructions was added post-manufacture. The only problem was, nobody could remember exactly how the feature worked. ACM notes: “However, in a survey a few years ago, the few surviving eyewitnesses could not remember how it was executed.”
Page 8 of the manual provides this information. My German is rusty, my technical German is nonexistent, and frankly, the images are a bit tough to read, so I’m not going to try to translate exactly how the function worked. Without information like this, it would be impossible to precisely replicate or understand how the Z4 embodied or improved upon the computational capabilities of the time.
*The answer to “Who invented the first computer?” is essentially arbitrary and depends entirely on how you choose to define the term “computer.” The UK’s Colossus is declared the world’s first “programmable, electronic, digital computer,” by Wikipedia, but it was programmed by switches and plugs, not a stored program. The Z4 is considered to be the first commercial digital computer but it’s not electronic. The first electronic stored-program computer is the Manchester Baby, but Konrad Zuse’s earlier Z3 could store programs on tape — it just wasn’t electronic. Other obscure machines, like the Atanasoff-Berry Computer, were not Turing-complete and couldn’t store programs, but still contributed critical ideas to the development of computing.
Also, if you were taught that ENIAC was the first computer (or digital computer, or electronic digital computer, etc, ad nauseam), that’s more propaganda than fact. ENIAC was more directly based on machines like Colossus than was known at the time, because the wartime efforts of the British remained classified, while ENIAC was widely celebrated in the media.
Finally, reading up on the history of early computing is a good reminder of how many people, institutions, and companies contributed various technologies and principles to the field. One reason you can subdivide the question of “Who built the first computer” to such a fine degree is that there were so many “firsts” for someone to achieve. There was a time in the 1930s and 1940s when mechanical, electromechanical, and digital systems were sharing space and serious development dollars simultaneously. We don’t have anything remotely equivalent today, and even our wildest architectural departures from the x86 “norm” are still based on digital computing. That could change in the future, if Intel’s MESO architecture comes to fruition and proves capable of replacing CMOS in the long term.
But for now, the 1930s and 1940s represent a tremendously dynamic period in computing history that we don’t really have an equivalent for — though some of the quantum computing work is getting really interesting.
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In this article, we talked about quantum entanglement. While doing so we touched on “action at a distance”. In this article we are going to use it as an introduction to the Principle of Physical Interactivity.
Let us summarize action at a distance with a quote from the article:
Suppose you have two particles, particle A and particle B. Suppose these two particles can interact in some way such that if particle A does something, it will cause particle B to change state. Perhaps if particle A emits a smaller particle that strikes B, particle B will spin in a different direction. We will call that change in direction “event C”.
If particle A and particle B are to interact to cause event C, then some kind of physical action must occur. The particles must act upon each in some way which then causes event C.
Particle A will have to emit some particle, vibrate some physical connection between particle A and particle B. Or somehow affect some kind of physical interaction. An interaction being some kind of action taken by A which effects B.
Otherwise, how else could particle A cause particle B to change the direction of its spin? By non-physical means? Using an abstraction? I think not…
Let us try to put this more simply. Let us say that we have a computer and a wireless keyboard connected to the computer. It is connected by a wireless connection.
We will use these two macroscopic objects as our example. However, it is trivial to extend these examples to subatomic particles and apply some simple logic to them.
Even though modern physics insists the subatomic world is not rational. Or that it is not subject to the laws of logic.
Now, suppose we press the button “A” on the keyboard. As a result, the letter “A” now appears on the screen. In other words, our keyboard has interacted with the computer.
Now, what has happened here? Is this witchcraft? Should we expect the Spanish Inquisition?
I am going to explain this by laying down a simple principle, which I am going to call the Principle of Physical Interactivity.
The Principle of Physical Interactivity says that in physics, all objects that interact with one another do so by physically interacting with one another. All interactions in physics are the interactions of physical objects with each other.
What does this mean? What do I mean by physical? I mean that which has shape or “physical extension”. It is not an abstraction, not an attribute, not a relationship, not an action. It is a non-abstract entity.
So, when I say that all objects interact via physical means, I mean that this interaction takes place when two physical objects act upon one another. The interaction is not by means of abstractions. It is via the actions of physical entities.
Take the computer and the keyboard. Are they physically interacting? Yes. There are physical objects of some kind traveling from the keyboard to the computer. Or some other kind of physical activity in the keyboard which causes another physical action to take place in the computer.
That interaction might be described by saying that there are waves traveling from the keyboard to the computer. The waves are abstract descriptions of some kind of motion/relationship.
In that case, the keyboard interacts with the computer by some physical process involving the keyboard interacting with some kind of physical medium.
The point of the Principle of Physical Interactivity is that some kind of physical interaction is required.
Must Objects Touch?
What does it mean for objects to touch? I take it that they must have direct physical contact. Is this necessary?
No. The Principle of Physical Interactivity merely says that there must be physical interaction. It does not require that two objects are in direct physical contact.
Let us return to the example of our computer and wireless keyboard. For the wireless keyboard to send a signal to the computer, must the keyboard and the computer be touching? Must they be in direct contact via some part of each other?
The Principle of Physical Interactivity does not require this. It merely requires some kind of physical interaction. It does not require that the computer and the keyboard directly touch one another.
Other Forms of Contact?
Must there be some kind of invisible thread directly connecting the keyboard and the computer? The Principle of Physical Interactivity does not require this either. Physical interaction need not take place via objects such as a thread that directly connects the two objects.
How then can they interact? Well, the keyboard might send waves through a medium such as air, which the computer picks up.
Hold on now, I thought waves were abstractions? Additionally, I thought you said that the computer and the keyboard must interact by physical means?
The wave is an abstract description of objects taking some kind of action, of causing something to move through the air in a wave pattern and to hit the computer. Therefore, the keyboard and the computer do interact by physical means.
(Note that here on this site, we define waves as a kind of abstraction that describes motion or some other kind of relationship. Thus when we say “there is a water wave”, what we are talking about is an abstract description of a bunch of water molecules arranged in that shape.
The referents of the concept of wave is the water molecules, the concept of “wave” describes the fact that they related in that pattern).
This is still a kind of physical interaction between the computer and the keyboard that causes the letter “A” to appear on the screen.
To sum up, this physical interaction does require some form of physical interaction via touch or some other form of medium.


In a major step forward for an area of research that earned the 2016 Nobel Prize in Physics, an international team has found that substances with exotic electronic behaviors called topological materials are in fact quite common, and include everyday elements such as arsenic and gold. The team created an online catalog to make it easy to design new topological materials using elements from the periodic table.
These materials have unexpected and strange properties that have shifted scientists' understanding of how electrons behave. Researchers hope these substances could form the basis of technologies of the future, such as low-power devices and quantum computing.
"Once the analysis was done and all the errors corrected, the result was astonishing: more than a quarter of all materials exhibit some sort of topology," said B. Andrei Bernevig, a senior author on the paper and professor of physics at Princeton. "Topology is ubiquitous in materials, not esoteric."
Topological materials are intriguing because their surfaces can conduct electricity without resistance, so they are potentially faster and more energy-efficient than today's technologies. Their name comes from an underlying theory that draws on topology, a branch of mathematics that describes objects by their ability to be stretched or bent.
The beginnings of the theoretical understanding of these states of matter formed the basis of the 2016 Nobel Prize in Physics, shared among Princeton University professor F. Duncan Haldane, the Sherman Fairchild University Professor of Physics, J. Michael Kosterlitz of Brown University, and David J. Thouless, University of Washington-Seattle.
Until now, only a few hundred of the more than 200,000 known inorganic crystalline materials have been characterize as topological, and they were thought to be anomalies.
"When fully completed, this catalog will usher in a new era of topological material design," Bernevig said. "This is the beginning of a new type of periodic table where compounds and elements are indexed by their topological properties rather than by more traditional means."
The international team included researchers from Princeton; the Donostia International Physics Center in San Sebastian, Spain; the IKERBASQUE Basque Foundation for Science; the University of the Basque Country; École Normale Supérieure Paris and the French National Center for Scientific Research; and the Max Planck Institute for Chemical Physics of Solids.
The team investigated about 25,000 inorganic materials whose atomic structures are experimentally known with precision, and classified in the Inorganic Crystal Structure Database. The results show that rather than being rare, more than 27 percent of materials in nature are topological.
The researchers made the newly created online database available at www.topologicalquantumchemistry.com. It allows visitors to select elements from the periodic table to create compounds that the user can then explore for its topological properties. More materials are currently being analyzed and placed in a database for future publication.
Two factors allowed the complex task of topologically classifying the 25,000 compounds.
First, two years ago, some of the present authors developed a theory, known as topological quantum chemistry and published in Nature in 2017, which allowed for the classification of the topological properties of any material from the simple knowledge of the positions and nature of its atoms.
Second, in the current study, the team applied this theory to the compounds in the Inorganic Crystal Structure Database. In doing so, the authors needed to devise, write and modify a large number of computerized instructions to calculate the energies of electrons in the materials.
“We had to go into these old programs and add new modules that would compute the required electronic properties,” said Zhijun Wang, who was a postdoctoral research associate at Princeton and is now a professor at the Beijing National Laboratory for Condensed Matter Physics and the Institute of Physics, Chinese Academy of Sciences.
“We then needed to analyze these results and compute their topological properties based on our newly developed topological quantum chemistry methodology," said Luis Elcoro, a professor at the University of the Basque Country in Bilbao, Spain.
The authors wrote several sets of codes that obtain and analyze the topology of electrons in real materials. The authors have made these codes available to the public through the Bilbao Crystallographic Server. With the help of the Max Planck Supercomputer Center in Garching, Germany, the researchers then ran their codes on the 25,000 compounds.
"Computationally, it was pretty incredibly intensive stuff," said Nicolas Regnault, a professor at École Normale Supérieure, Paris, and a researcher at the French National Center for Scientific Research. "Fortunately, the theory showed us that we need to compute only a fraction of the data that we needed previously. We need to look at what the electron 'does' only in part of the parameter space to obtain the topology of the system."
"Our understanding of materials got much richer because of this classification," said Maia Garcia Vergniory, a researcher at Donostia International Physics Center in San Sebastian, Spain. "It is really the last line of understanding of properties of materials."
Claudia Felser, a professor at the Max Planck Institute for Chemical Physics of Solids in Dresden, Germany, had earlier predicted earlier that even gold is topological. "A lot of the material properties that we know — such as the color of gold — can be understood through topological reasoning," Felser said.
The team is now working to classify the topological nature of additional compounds in the database. The next steps involve identifying the compounds with the best versatility, conductivity and other properties, and experimentally verifying their topological nature. "One can then dream about a full topological periodic table," Bernevig said.
An article accompanying the database was published in the journal Nature on Feb. 28.
The study, "A complete catalogue of high-quality topological materials." By M. G. Vergniory, L. Elcoro, Claudia Felser, Nicolas Regnault, B. Andrei Bernevig and Zhijun Wang, was published online in the journal Nature on Feb. 28. DOI 10.1038/s41586-019-0954-4
Luis Elcoro was supported by the Government of the Basque Country (project IT779-13), the Spanish Ministry of Economy and Competitiveness (MINECO), and the European Fund for Economic and Regional Development (FEDER; project MAT2015-66441-P). Maia G. Vergniory was supported by MINECO (project IS2016-75862-P).
B. Andrei Bernevig and Zhijun Wang acknowledge support for the analytical work from the U.S. Department of Energy (DE-SC0016239), a Simons Investigator Award, the David and Lucile Packard Foundation, and the Eric and Wendy Schmidt Transformative Technology Fund. The computational part of the Princeton work was performed under the National Science Foundation (NSF) Early-concept Grants for Exploratory Research (EAGER): DMR 1643312 NOA-AWD1004957, ONR-N00014-14-1-0330, ARO MURI W911NF-12-1-0461 and NSF-MRSECDMR-1420541.


A new machine learning tool can calculate the energy required to make—or break—a molecule with higher accuracy than conventional methods. While the tool can currently only handle simple molecules, it paves the way for future insights in quantum chemistry.
“Using machine learning to solve the fundamental equations governing quantum chemistry has been an open problem for several years, and there’s a lot of excitement around it right now,” says co-creator Giuseppe Carleo, a research scientist at the Flatiron Institute’s Center for Computational Quantum Physics in New York City. A better understanding of the formation and destruction of molecules, he says, could reveal the inner workings of the chemical reactions vital to life.
Carleo and collaborators Kenny Choo of the University of Zurich and Antonio Mezzacapo of the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, present their work May 12 in Nature Communications.
The team’s tool estimates the amount of energy needed to assemble or pull apart a molecule, such as water or ammonia. That calculation requires determining the molecule’s electronic structure, which consists of the collective behavior of the electrons that bind the molecule together.
A molecule’s electronic structure is a tricky thing to calculate, requiring the determination of all the potential states the molecule’s electrons could be in, plus each state’s probability.
Since electrons interact and become quantum mechanically entangled with one another, scientists can’t treat them individually. With more electrons, more entanglements crop up, and the problem gets exponentially harder. Exact solutions don’t exist for molecules more complex than the two electrons found in a pair of hydrogen atoms. Even approximations struggle with accuracy when they involve more than a few electrons.
One of the challenges is that a molecule’s electronic structure includes states for an infinite number of orbitals going farther and farther from the atoms. Additionally, one electron is indistinguishable from another, and two electrons can’t occupy the same state. The latter rule is a consequence of exchange symmetry, which governs what happens when identical particles switch states.
Mezzacapo and colleagues at IBM Quantum developed a method for constraining the number of orbitals considered and imposing exchange symmetry. This approach, based on methods developed for quantum computing applications, makes the problem more akin to scenarios where electrons are confined to preset locations, such as in a rigid lattice.
The similarity to rigid lattices was the key to making the problem more manageable. Carleo previously trained neural networks to reconstruct the behavior of electrons confined to the sites of a lattice. By extending those methods, the researchers could estimate solutions to Mezzacapo’s compacted problems. The team’s neural network calculates the probability of each state. Using this probability, the researchers can estimate the energy of a given state. The lowest energy level, dubbed the equilibrium energy, is where the molecule is the most stable.
The team’s innovations made calculating a basic molecule’s electronic structure simpler and faster. The researchers demonstrated the accuracy of their methods by estimating how much energy it would take to pull a real-world molecule apart, breaking its bonds. They ran calculations for dihydrogen (H2), lithium hydride (LiH), ammonia (NH3), water (H2O), diatomic carbon (C2) and dinitrogen (N2). For all the molecules, the team’s estimates proved highly accurate even in ranges where existing methods struggle.
In the future, the researchers aim to tackle larger and more complex molecules by using more sophisticated neural networks. One goal is to handle chemicals like those found in the nitrogen cycle, in which biological processes build and break nitrogen-based molecules to make them usable for life. “We want this to be a tool that could be used by chemists to process these problems,” Carleo says.
Carleo, Choo and Mezzacapo aren’t alone in tapping machine learning to tackle problems in quantum chemistry. The researchers first presented their work on arXiv.org in September 2019. In that same month, a group in Germany and another at Google’s DeepMind in London each released research using machine learning to reconstruct the electronic structure of molecules.
The other two groups use a similar approach to one another that doesn’t limit the number of orbitals considered. This inclusiveness, however, is more computationally taxing, a drawback that will only worsen with more complex molecules. With the same computational resources, the approach by Carleo, Choo and Mezzacapo yields higher accuracy, but the simplifications made to obtain this accuracy could introduce biases.
“Overall, it’s a trade-off between bias and accuracy, and it’s unclear which of the two approaches has more potential for the future,” Carleo says. “Only time will tell us which of these approaches can be scaled up to the challenging open problems in chemistry.”
More information: Kenny Choo et al. Fermionic neural-network states for ab-initio electronic structure. Nature Communications (2020). DOI: 10.1038/s41467-020-15724-9
Image: The tetrahedral electronic distribution of a water molecule. The oxygen atom nucleus is at the center of the tetrahedron, and the hydrogen nuclei are in the center of the pink spheres. Simons Foundation.
Credit: Simons Foundation


During the past months we’ve been reporting several breakthroughs in the field of quantum computing, and now IBM seems ready to truly pave the way for quantum computers. Researchers announced they are now able to develop a superconducting qubit made from microfabricated silicon that maintains coherence long enough for practical computation. Whoa! That probably sounds like a lot to swallow, so let’s break it down.
Bits and Qubits
Information is measured in ‘bits’, and a bit may have two positions (described typically as 0 or 1). Quantum computers however don’t use these bits, and instead they use quantum bits, or ‘qubits’. But while a bit must be a 0 or a 1, a qubit can be both 0, 1, or a superposition of both. This difference might seem small and subtle, but in fact, it is absolutely humongous: a mere hundred qubits can store more classical ‘bit’ information than there are atoms in the Universe.
Needless to say a computer running on qubits would be game changing, in pretty much the same way microprocessors were in their days. But what makes quantum computing extremely difficult is a problem called ‘decoherence‘. In the quantum world, things don’t happen as they do in the ‘real world’; when a qubit will move from the 0 state to the 1 state or to a superposition, it will decohere to state 0 due to interference from other parts of the computer. Generally speaking, decoherence is the loss order of the phase angles between the components. So in order for quantum computers to be practical and scalable, the system would have to remain coherent for a long enough time to allow error-correction techniques to function properly.
“In 1999, coherence times were about 1 nanosecond,” said IBM scientist Matthias Steffen. “Last year, coherence times were achieved for as long as 1 to 4 microseconds. With these new techniques, we’ve achieved coherence times of 10 to 100 microseconds. We need to improve that by a factor of 10 to 100 before we’re at the threshold we want to be. But considering that in the past ten years we’ve increased coherence times by a factor of 10,000, I’m not scared.”
Two different approaches, one breakthrough
IBM announced they took two different approaches, both of which played a significant part in the breakthrough they revealed. The first one was to build a 3-D qubit made from superconducting, microfabricated silicon. The main advantage here is that the equipment and know-how necessary to create this technology already exists, nothing new has to be invented, thanks to developments made by Yale researchers (for which Steffen expressed a deep admiration). Using this approach, they managed to maintain coherence for 95 microseconds – “But you could round that to 100 for the piece if you want,” Steffen joked.
The second idea involved a traditional 2-D qubit, which IBM’s scientists used to build a “Controlled NOT gate” or CNOT gate, which is a building block of quantum computing. A CNOT gate connects two qubits in such a way that the second qubit will change state if the first qubit changes its state to 1. The CNOT gate was able to produce a coherence of 10 microseconds, which is long enough to show a 95% accuracy rate – a notable improvement from the 81% accuracy rate, the highest achieved until now. Of course, the technology is still years away from being actually on the shelves, but the developments are very impressive.
From quantum to reality
Given the rapid progress that is being made in the field of quantum computing, one can only feel that a quantum computer is looking more and more like a real possibility. As error correction protocols become more accurate and coherence times grow longer, we are moving more and more towards accurate quantum computing – but you shouldn’t expect a quantum smartphone just yet.
“There’s a growing sense that a quantum computer can’t be a laptop or desktop,” said Steffen. “Quantum computers may well just being housed in a large building somewhere. It’s not going to be something that’s very portable. In terms of application, I don’t think that’s a huge detriment because they’ll be able to solve problems so much faster than traditional computers.”
The next steps are simple, in principle, but extremely hard to do in practice. The accuracy rate has to be at at least 99.99%, up to the point where it achieves what is called a ‘logical qubit’ – one that, for practical purposes, doesn’t suffer decoherence. From that point, the only thing left to do is develop the quantum computer architecture, and this will prove troublesome too – but the reward is definitely worth it.
“We are very excited about how the quantum computing field has progressed over the past ten years,” he told me. “Our team has grown significantly over past 3 years, and I look forward to seeing that team continue to grow and take quantum computing to the next level.”


Quantum Machine Learning: An Overview
Quantum Machine Learning (Quantum ML) is the interdisciplinary area combining Quantum Physics and Machine Learning(ML). It is a symbiotic association- leveraging the power of Quantum Computing to produce quantum versions of ML algorithms, and applying classical ML algorithms to analyze quantum systems. Read this article for an introduction to Quantum ML.
At a recent conference in 2017, Microsoft CEO Satya Nadella used the analogy of a corn maze to explain the difference in approach between a classical computer and a quantum computer. In trying to find a path through the maze, a classical computer would start down a path, hit an obstruction, backtrack; start again, hit another obstruction, backtrack again until it ran out of options. Although an answer can be found, this approach could be very time-consuming.
In contrast, quantum computers “unlock amazing parallelism. They take every path in the corn maze simultaneously.” Thus, leading to an exponential reduction in the number of steps required to solve a problem.
The parallelism comes from the concept of ‘qubit’, 'superposition' and 'entanglement' derived from Quantum Physics.
I. Quantum Computing:
Quantum is the smallest possible unit of any physical entity, such as energy or mass. In 1900, Max Planck proposed that, at the atomic and subatomic level, energy of a body is contained in discrete packets called quanta’.
Wave-particle duality is the characteristic of quantic particles to behave as a wave sometimes and as a particle the other times, depending on the environment. Quantum theory is characterized by finding the probability of, and not the exact location of, a particle at a given point x in space.
Fig 1: The dual nature of light, which acts like both particles and waves. (Source)
A classical computer performs operations using classical ‘bits’, which are either 0 OR 1. However, a quantum computer uses quantum bits, also called ‘qubits’ to perform operations.
Qubits can be represented by:
- An electron orbiting a nucleus: where |1> and |0> are the excited state and ground state respectively
- A photon: where |1> and |0> are polarizations of the photon.
Qubits exist as both 0 AND 1 at the same time. This phenomenon is called ‘superposition’.
Although a particle can exist in multiple quantum states, once we measure that particle for its energy or position, its superposition is lost and it then exists in only one state.
Fig2 : The qubit is defined as a pair of complex vectors pointing to a spot on a unit sphere. Traditionally, a qubit pointing directly up (positive on the axis) is denoted as the column vector |0⟩ and the vector pointing down is known as |1⟩. (For example, in this case, the qubit is |0⟩).
‘Quantum entanglement’ is the phenomenon in which quantum particles interact with each other and are described with reference to each other, not independently, even if the particles are separated by a large distance.
At the time of measurement, if one entangled particle in a pair is decided to be in the spin state of ‘down’ (that is, the lowest energy state; when the electron is in alignment with its magnetic field), then this decision is communicated to the other correlated particle that now assumes the opposite spin state of ‘up’. Quantum entanglement allows qubits, including those faraway, to interact instantaneously with each other.
How does Quantum computing unlock immense parallelism?
Two interacting classical bits can take one of 4 forms: 00 or 01 or 10 or 11. Each of these 2 components of information- the first bit and the second bit, combine to represent only one binary configuration at a given time. Adding more bits to a regular computer would still represent a single binary configuration.
Fig3: One qubit in superposition before measurement, with its probabilities of ‘spin-up’ AND ‘spin-down'. (Source)
One qubit can exist in both states (0 AND 1) at once. Thus, two interacting qubits can store all 4 binary configurations simultaneously. In general, ‘n’ qubits can simultaneously represent ‘2^n’ classical binary configurations. Thus, a 300–qubit quantum computer can explore 2^300 possible solutions at the same time, unlike 1 solution at a time in a classical computer, causing immense parallelism. Adding more qubits to a quantum computer would exponentially increase the power of the computer.
A fully quantum computer has not yet been realized because adding more qubits and dealing with subatomic particles that require a low temperature of -452 F in order to be stable, is daunting and building a computer around that (a ‘quantum computer’), even more so. Thus, efforts are on to ‘simulate’ 40 qubit operations using Microsoft’s quantum simulator- LIQUi|> , extended by Microsoft Azure’s cloud computing resources.
Quantum Computing can solve specialized scientific problems such as molecular modelling, creation of high-temperature superconductors, drug modelling and testing, selection of molecules for the creation of organic batteries. It is not optimal for general-purpose tasks such as for watching videos or writing a Word document.
Now, how does Quantum Computing fit in with Machine Learning?
II. Quantum ML:
2a) Quantum versions of ML algorithms
- Finding eigenvalues and eigenvectors of large matrices:
One of the methods to perform the classical PCA algorithm is to take the eigenvalue decomposition of a data covariance matrix. However, this is not so efficient in case of high dimensional data.
Quantum PCA of an unknown low-rank density matrix, can reveal the quantum eigenvectors associated with the large eigenvalues, exponentially faster than a linearly-scaled classical algorithm.
- Finding nearest neighbours on a quantum computer:
The quantum algorithms presented here for computing nearest neighbours that are used in supervised and unsupervised learning, place an upper bound on the number of queries to the input data required to compute distance metrics such as the Euclidean distance and inner product. The best cases show exponential and super-exponential reductions in query complexity and the worst case still shows polynomial reduction in query complexity over the classical analogue.
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Quantum computers have long been touted as incredibly powerful machines that will be able to solve hugely complex computational problems much faster than any computer we have available today. But no-one can agree on the best way to make them. Who will win the race?
Superfast quantum computers could speed up the discovery of new medicines, crack the most complex cryptographic security systems, design new materials, model climate change, and supercharge artificial intelligence, computer scientists say.
But there’s currently no consensus on the best way to make them or how to make them available to the mass market.
Physicists, engineers and computer scientists around the world are trying to develop four very different types of quantum computers, based around light particles, trapped ions, superconducting qubits, or nitrogen-vacancy centres in diamonds.
Companies like IBM, Google, Rigetti, Intel and Microsoft are currently leading the quantum charge.
Each method has its pros and cons, but the overarching challenge is the fragile nature of quantum itself.
What is quantum computing?
Instead of using ones and noughts called bits, representing on or off, in long sequences as in classical computing a quantum bit – or qubit – uses the near magical properties of sub-atomic particles.
Electrons or photons, for example, can be in two states at the same time – a phenomenon called superposition. As a result, a qubit-based computer can do far more calculations much faster than a conventional computer.
“If you had a two-qubit computer and you add two qubits, it becomes a four-qubit computer. But you’re not doubling the computer power, you’re increasing it exponentially,” explains Martin Giles, San Francisco bureau chief of the MIT Technology Review.
Computer scientists sometimes describe this quantum computing effect as like being able to go down each path of a very complex maze at the same time.
Qubits can also influence each other even when they’re not physically connected, a process called “entanglement”. In computing terms, this gives them the ability to make logical leaps conventional computers never could.
The search for stability
But qubits are highly unstable and prone to interference or “noise” from other sources of energy, leading to errors in calculations. So the race is one to find a way to stabilise them for mass-production.
Computing giant IBM firmly believes that “transmon superconducting qubits” hold the most promise for quantum computing, and they have three prototype quantum processors that the public can access in the cloud.
“So far, over 94,000 people have accessed IBM quantum computers in the cloud. They’ve run over five million experiments and written 110 papers,” says Dr Robert Sutor, vice president for quantum computing strategy and ecosystem at IBM Research.
“People are learning and experimenting… we hope in three to five years to be able to point at one specific example, and say that quantum significantly improves on anything classical computers can do.”
But IBM’s method required the quantum computer to be stored within a large fridge, where the qubits are stored at temperatures close to absolute zero to ensure that they remain in their useful states.
This takes a lot of energy and means it would be extremely hard to miniaturise.
“It seems likely that superconducting qubits will be among the first technologies to enable useful quantum computation,” says Joseph Fitzsimons, a principal investigator at the National University of Singapore’s Centre of Quantum Technologies.
“However, my impression is that they are analogous to vacuum tubes in early computers, rather than transistors which came along later.
“We may yet see another technology emerge which becomes the ultimate winner.”
Microsoft and academics at the Niels Bohr Institute in Copenhagen are working on what they believe will be much more stable qubits based on so-called Majorana particles.
While other teams are working on trapping qubits in silicon – the material traditional computer chips have been made from.
And computer scientists at Oxford University are looking at ways to link smaller qubit computers rather than creating bigger computers with lots of qubits.
There are many ways to skin Schrodinger’s Cat it seems.
While we wait for quantum computers, what’s the future for conventional, or classical, computing?
In July, Ewin Tang, an 18-year-old graduate in computer science and mathematics from the University of Texas at Austin, made waves in the international computing world by developing a classical computer algorithm that can solve a problem almost as fast as a quantum computer.
The problem involved developing a recommendation engine that suggests products to users based on data about their preferences.
And the EU recently announced it is working on the next generation of computers – exascale – which would enable a billion billion calculations per second.
“Exascale means 10 to the power of 18 operations per second,” explains says Prof Scott Aaronson, a theoretical computer scientist at UT Austin who mentored Mr Tang.
“10 to the power of 18 is big, but quantum systems, which will be capable of 10 to the power of 1,000 operations per second, is much, much bigger.”
And the problem for classical computing is that we are reaching the limits of how many transistors we can fit onto a chip – Apple’s A11 squeezes in an astonishing 4.3 billion, for example.
Moore’s Law – that every two years, microprocessors will get twice as fast, use half as much energy, and take up half as much space – is finally breaking down.
Even if a stable, mass-produced quantum computer always remains elusive, the research is already yielding interesting results.
“If we hadn’t invested in quantum computing, the quantum algorithm that inspired Mr Tang wouldn’t have existed,” says Prof Robert Young, a Royal Society research fellow and director of the University of Lancaster’s Quantum Technology Centre.
More Technology of Business
Already, he says that quantum research has yielded a new way to cool devices to low temperatures; light-based chip enhancements that have improved the fibre optic broadband experience; and the invention of lab-on-a-chip technologies to speed up the diagnosis of illnesses.
“The real benefit of going to the Moon wasn’t going to the Moon, it was the peripheral technologies that were developed on the way,” says Prof Young – GPS satellite navigation and ball point pens, to name but a few.


An Entirely New Type of Quantum Computing Has Been Invented
Australian researchers have designed a new type of qubit – the building block of quantum computers – that they say will finally make it possible to manufacture a true, large-scale quantum computer.
Broadly speaking, there are currently a number of ways to make a quantum computer. Some take up less space, but tend to be incredibly complex. Others are simpler, but if you want it to scale up you’re going to need to knock down a few walls.
Some tried and true ways to capture a qubit are to use standard atom-taming technology such as ion traps and optical tweezers that can hold onto particles long enough for their quantum states to be analysed.
Others use circuits made of superconducting materials to detect quantum superpositions within the insanely slippery electrical currents.
The advantage of these kinds of systems is their basis in existing techniques and equipment, making them relatively affordable and easy to put together.
The cost is space – the technology might do for a relatively small number of qubits, but when you’re looking at hundreds or thousands of them linked into a computer, the scale quickly becomes unfeasible.
Thanks to coding information in both the nucleus and electron of an atom, the new silicon qubit, which is being called a ‘flip-flop qubit’, can be controlled by electric signals, instead of magnetic ones. That means it can maintain quantum entanglement across a larger distance than ever before, making it cheaper and easier to build into a scalable computer.
“If they’re too close, or too far apart, the ‘entanglement’ between quantum bits – which is what makes quantum computers so special – doesn’t occur,” says the researcher who came up with the new qubit, Guilherme Tosi, from the University of New South Wales in Australia.
The flip-flop qubit will sit in the sweet spot between those two extremes, offering true quantum entanglement across a distance of hundreds of nanometres.
In other words, this might be just what we’ve been waiting for to make silicon-based quantum computers scalable.
To be clear, so far we only have a blueprint of the device – it hasn’t been built as yet. But according to team leader, Andrea Morello, the development is as important for the field as the seminal 1998 paper in Nature by Bruce Kane, which kicked off the silicon quantum computing movement.
“Like Kane’s paper, this is a theory, a proposal – the qubit has yet to be built,” says Morello. “We have some preliminary experimental data that suggests it’s entirely feasible, so we’re working to fully demonstrate this. But I think this is as visionary as Kane’s original paper.”
The flip-flop qubit works by coding information on both the electron AND nucleus of a phosphorus atom implanted inside a silicon chip, and connected with a pattern of electrodes. The whole thing is then chilled to near absolute zero and bathed in a magnetic field.
The qubit’s value is then determined by combinations of a binary property called spin – if the spin is ‘up’ for an electron while ‘down’ for the nucleus, the qubit represents an overall value of 1. Reversed, and it’s a 0.
That leaves the superposition of the spin-states to be used in quantum operations.
In flip-flop, researchers are able to control the qubit using an electric field instead of magnetic signals – which gives two advantages. It is easier to integrate with normal electronic circuits and, most importantly, it also means qubits can communicate over larger distances.
“To operate this qubit, you need to pull the electron a little bit away from the nucleus, using the electrodes at the top. By doing so, you also create an electric dipole,” says Tosi.
“This is the crucial point,” adds Morello. “These electric dipoles interact with each other over fairly large distances, a good fraction of a micron, or 1,000 nanometres.”
“This means we can now place the single-atom qubits much further apart than previously thought possible. So there is plenty of space to intersperse the key classical components such as interconnects, control electrodes and readout devices, while retaining the precise atom-like nature of the quantum bit.”
“It’s easier to fabricate than atomic-scale devices, but still allows us to place a million qubits on a square millimetre.”
What this new flip-flop qubit means is a balance that could make future quantum computers small and potentially affordable.
“It’s a brilliant design, and like many such conceptual leaps, it’s amazing no-one had thought of it before,” says Morello.
The research has been published in Nature Communications.


Machines enrich and enhance our lives, whether it’s the smartphones that allow us to stay connected or the supercomputers that solve our toughest computational problems. Imagine how much more productive and innovative our world will be when computers become infinitely more powerful. Indeed, the growing field of quantum computing may make our current technological capacities look feeble and primitive in comparison. It could even transform the workings of the human brain and revolutionize how we think in ways we can’t begin to imagine.
Today, computers operate at the most basic level by manipulating two states: a zero or a one. In contrast, quantum computers are not limited to two states, but can encode information in multiple states that exist in superposition, also known as quantum bits or qubits.
In other words, this technology takes advantage of one of the most fascinating properties of the quantum world: the ability of subatomic particles to exist in more than one state at any given time. Consequently, a quantum computer can perform many calculations at the same time, whereas a traditional Turing machine can only perform a single calculation at once. Such quantum machines will be millions of times more powerful than our most powerful current computers.
The revolutionary implications of such a computing capacity are immense and will contribute to the acceleration of human thinking and progress.
Quantum computers can allow us to push the limits of artificial intelligence, derive ground-breaking insight from big data, advance cryptography, develop new materials, and even simulate virtual quantum systems like never before. According to Greg Tallant, Lockheed Martin fellow at the USC center, “The technology could be harnessed to speed the debugging of millions of lines of code or help solve the aerospace industry’s toughest computational problems.”
Many techno-optimists believe that quantum computers will allow us to expand our understanding and capabilities by giving us access to machines that think in ways we never have in multiple states and dimensions at once. But what if it wasn’t just our machines that were unfathomably more intelligent? What if we were too?
Imagine being able to ponder multiple ideas at the same time, solve several mathematical equations at once, or have a conversation with more than one person. Imagine what kind of world we would live in if every person could exist in a multitude of mental states.
One wild application of quantum computers may be to design them as a carrier for our minds. While this sounds like science fiction, we are seeing exponential growth in brain scanning and mapping technologies, along with neural engineering, which will all contribute to our ability to model the brain and develop technologies that can digitally replace some or all of its functions.
Hundreds of millions of dollars are being invested in brain-computer interfaces and implants. Neuroscientist Kenneth Hayworth writes in Skeptic magazine, “All of today’s neuroscience models are fundamentally computational by nature, supporting the theoretical possibility of mind-uploading”. Couple that with the rapidly growing advancements in quantum computing and the futuristic hope that we will one day upload our minds into machines. After all, the laws of physics don’t limit that possibility.
There are plenty of technical, scientific, and even philosophical questions yet to be answered. Even with the capability, some wonder whether our sense of self would go along for the ride, or if we would have effectively created a copy of ourselves. And perhaps instead, we may simply link more closely with computers via brain-machine interfaces.
In either case, we will undoubtedly find our capabilities enhanced.
And perhaps an even more mind-blowing aspect of quantum computing is the idea put forward by Oxford University quantum physicist, David Deutsch, who suggests that quantum computers function by distributing parallel work across many different universes. These new machines could be humanity’s first baby steps towards harnessing the computational power of a multiverse.
Will we get there?
Some are skeptical about whether quantum computers will be taking over anytime soon. There are many challenges facing experts in the field, such as designing a simple way to control complex systems of qubits. One major obstacle is that qubits are more susceptible to errors, compared to transmitters in classical computers. Another one is creating qubits that can maintain their quantum properties for a long period of time, known as the coherence time. Scott Aaronson, professor at The University of Texas, Austin has listed the main challenges to quantum computing theory.
But we are seeing progress in the field.
Tech giants like Google and Amazon are racing to develop their quantum computing technologies. Last year, teams of Google and NASA scientists showed a D-Wave quantum computer was 100 million times faster than a conventional computer in a test and successfully simulated a hydrogen molecule with it. This was a development that, according Google quantum software engineer Ryan Babbush, could allow us to “simulate even larger chemical systems” and “revolutionize the design of solar cells, industrial catalysts, batteries, flexible electronics, medicines, materials and more.”
Many also argue quantum computing will be a successor to Moore’s Law, which states that the number of transistors on a microprocessor doubles every 18 months. Moore’s law has been going steady since the 1970s, but traditional chips are approaching natural limits. What will follow? There are a number of competing technologies in the wings, but quantum computing is certainly a leading candidate in a number of powerful applications.
Regardless of whether human consciousness naturally relies on some form of quantum phenomena (many speculate that it does but we do not know for a fact), there is no doubt such a measure will push the boundaries of the human mind beyond its natural capabilities.
Image credit: Shutterstock


To mathematicians and those interested in the science of encryption, the job of a cryptographer is an interesting one.
Basically, cryptographers work on implementing encryption. This definition from Career Explorer says it well: “A cryptographer is someone who develops algorithms, ciphers and security systems to encrypt sensitive information and provide privacy for people and corporations.” (Read Encryption Vs. Decryption: What's the Difference?)
First, let's look at some of the basic things that cryptographers might be involved in. (Read Cryptography: Understanding Its Not-So-Secret Importance to Your Business.)
One such activity is the implementation of hash functions.
As we've reported before, hash cryptography involves linking the contents of some data structure to a shorter key that shows whether or not data has been changed or tampered with. The key that is ‘hashed’ from the data set is the encryption. This technique is used quite a bit in the cryptography world, and companies hiring these professionals will often ask about their expertise with hash functions.
Elliptic Curve Cryptography
Here's another part of what cryptographers may be involved in — a concept called “elliptic curve cryptography” uses the algebraic structure of elliptic curves to create public key cryptography results that are useful for digital signatures and in other parts of the encryption world — (it seems likely that this cryptography intern job ad actually spelled the designation wrong).
So what else does the job of a cryptographer look like? Here's what we found out from some professionals in the field.
From Book Ciphers to Mathematical and Algorithmic Encryption
Part of understanding what a modern cryptographer does involves contrasting today's cryptography with the disciplines that came before it. In the old days, cryptographers used simple ciphers to encode messages, for example, a letter shift that simply made each letter of the alphabet into another, or alternately, into a particular rune or symbol.
These encryptions, by modern standards, are laughably easy to decode. A few years ago, something called PGP or Pretty Good Privacy was a gold standard — these types of cryptography are much more elaborate and resistant to cracking than the old ciphers.
“Encryption has come a long way from simply moving each letter over a few places in the alphabet,” said Shayne Sherman, CEO of TechLoris. “Creating these complicated and highly secure algorithms is one job of a cryptographer. Another is analyzing encrypted data for law enforcement and military organizations to attempt to break certain encryption algorithms.”
Both Builders and Breakers
Dr. Yehuda Lindell, CEO and co-founder of Unbound Tech, said it well in responding to our questions about cryptography.
“In some areas, the cryptanalysts are the ones with the best understanding of how to build secure schemes as well, and so that they are both builders and breakers,” Lindell said. “Primarily, this is in the area of symmetric cryptography: stream ciphers, block ciphers, hash functions, and the like. However, in the area of asymmetric (public-key) cryptography, schemes are typically based on hard problems from number-theory and algebra.
As in the symmetric world, these researchers are also the most qualified to propose new hard problems. However, their skill set is usually completely different from those doing symmetric cryptanalysis. Those working in the asymmetric setting typically have very deep math background. Having said that, I would argue that almost all cryptographers are pretty good at math.”
Lindell’s co-founder Nigel Smart expounded on this idea: “One can sub-divide cryptographers into those that work on breaking schemes, those that work on creating symmetric key schemes; those that work on public key schemes; those that work on basic protocols like key agreement; those that work on more advanced protocols like MPC; those that work on efficient implementations; those that work on secure implementations which avoid side-channels; those that work on software; and those that work on hardware.”
Working on Bitcoin and Other Coins
Here's another big application of cryptography in today's fintech industry.
“Bitcoin and other decentralized forms of payment depend on the work of cryptographers,” says Anna Tatelman, a consultant for Pelicoin. “Unlike with traditional financial institutions, all Bitcoin transactions are pseudonymous. This means that all personal information such as names, addresses, and social security numbers cannot be accessed even by Bitcoin’s creators. This is thanks to diligent cryptographers who hide all users’ personal data to greatly reduce the potential of both internal and external fraud.”
From the above input, and in looking at resources showing what today's cryptographers do, we see that although the job role is pretty clearly defined, there's a diversity of techniques and strategies that cryptographers will use to secure data.
Whether it's the Bitcoin in your digital wallet, the big databases that retailers use to keep sensitive customer data, or protected secrets in government networks, cryptographers do the tough job of staying ahead of those who would crack or break the systems to get the sensitive data inside.
It's a big job, but one that builds on a long tradition of encoding and decoding, one that’s in some ways intuitive to our human intelligence. Now, we harness the incredible logical power of computers to make encryptions ever stronger — in search of the best protection from hackers and malicious intruders.
Cryptography is a game that everyone has to play — and it’s still evolving in the age of quantum computing and AI. (Read Quantum Cryptography Vs. Quantum Hacking: A Cat and Mouse Game.)


AI is another disruptive technology of our time, and just like its predecessors, it will have a profound impact on our existence.
AI is a set of algorithms designed by humans and expressed through machines that can incorporate the five human senses (seeing, smelling, tasting, hearing and feeling) and ability to communicate (speaking). The very senses that have been historically used to magnify the differences between humans and machines are now enabling machines to effectively handle ever more qualitative operations and analysis.
Recent advancements in machine learning, deep learning and quantum computing has increasingly swelled the desire and ability for people to automate processes. AI and robotic applications enable people to create a new world of accelerated process automation that we could not have achieved without the continued focus on improving intelligent systems and machines.
The History Of Human And AI Cooperation
Humans and machines have coexisted on a large scale since the Industrial Revolution in the late 1700s. It commenced a period of profound technological achievements that brought on massive social and economic change spanning almost every conceivable industry in the world — from textiles and transportation to printing and consumer goods to healthcare, schools and governments.
It was signified by machines designed by humans to replace human effort and automate repetitive, time-consuming tasks — allowing humankind the freedom to be more creative and use our imaginations to explore new ideas. More importantly, it gave us the ability to improve the quality and productivity of our work and lives and evolve as people. It was also a time of massive disruption, uncertainty and fear. And, conceivably, it marked the time when humans and machines began to coexist and develop an interdependent relationship. And while some existing jobs were eliminated and replaced by machines, new types of jobs, job functions and business models were created.
This symbiotic relationship has been playing out with every major advancement in technology, further deepening the human-machine interdependent relationship. From the transistor that introduced smaller, less expensive computers and computer processing in the late 1940s to the internet in the 1970s to the Fourth Industrial Revolution currently underway, people continue to rely on machines to solve human problems and automate human tasks.
While machine learning or neural networks have been in development since the 1950s by great minds such as Alan Turing and Marvin Minsky, what has changed is advancements in computing performance and data storage that allow us to capture and retain significant amounts of data that can be used to build AI applications. Now deep learning applications and neural networks can mirror and mimic the human brain and, in some cases, outperform our ability to solve problems and take action.
So, how can we rely on a machine that we built if it can surpass our ability to solve problems and take action? And if a machine can act like us, then what differentiates person from machine? For the human race to continue its evolutionary path, the cooperative relationship between person and machine must also remain strong.
AI Is Not Replacing Us, It’s Improving Us
The World Economic Forum (WEF) predicts that 75 million jobs will be lost to this era of smart automation. It also estimates that 133 million new jobs will be created. These new jobs require new job skills that are intended to leverage and improve AI and its applications. This change will magnify the persistent need for human and AI cooperation and cement our interdependent relationship.
AI- and robot-assisted machines are being deployed worldwide at an unprecedented pace and they’re radically improving outcomes across industries. One illuminating example of AI-assisted applications becoming better with human and AI cooperation is the virtual assistant Alexa and the smart home “connected devices” that followed — aiding humans to more efficiently control and operate lighting, security, room temperature and appliances.
There are countless other examples of AI- and robot-assisted functions and applications that are improving outcomes across industries. From health care using AI assistance in the operating room to improve surgical and patient outcomes to computer-assisted instruction in education to self-driving cars in transportation to the Department of Defense (DoD) with DARPA’s AI Next campaign, it’s clear that AI is capable of dramatically enhancing our lives and our value as humans.
In order for companies to realize benefits from human and AI collaboration, all stakeholders throughout the development supply chain must be involved — from the academics who are advancing AI theory, to data scientists who are applying these theories in industry to design models that solve business problems, to system integrators who are deploying those models into production environments.
Through building systems based on open architecture and making a customer’s data accessible to actionable, we in the industry can go a long way in building proof that increasing human and machine cooperation benefits companies in many areas, from improving business processes to fostering new skills in employees. The key is to focus on both human and human and machine collaboration throughout the solution design practice to ensure that organizations are able to maximize the value of AI.
Process automation is essentially helping us improve our lives and further define what it means to be human. It frees us from mundane, repetitive tasks and empowers us to challenge our human capabilities and focus on what we do best: imagine, improve, innovate and evolve.
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Scientists pinpoint the singularity for quantum computers
Researchers from the University of Bristol have discovered that super-powerful quantum computers, which scientists and engineers across the world are racing to build, need to be even more powerful than previously thought before they can beat today's ordinary PCs.
Quantum computers are a new type of machine that operate on quantum mechanical hardware and are predicted to give enormous speed advantages in solving certain problems.
Research groups at leading universities and companies, including Google, Microsoft and IBM, are part of a worldwide race to realise the first quantum computer that crosses into the 'quantum computational singularity'.
This represents a problem so complex that today's top supercomputer would take centuries to find a solution, while a quantum computer could crack it in minutes.
Now a team of scientists from Bristol have discovered that the boundary to this singularity is further away than previously thought.
The research is reported this week in Nature Physics.
The results apply to a highly influential quantum algorithm known as 'boson sampling', which was devised as a very direct route to demonstrate quantum computing's supremacy over classical machines.
The boson sampling problem is designed to be solved by photons (particles of light) controlled in optical chips – technology pioneered by Bristol's Quantum Engineering and Technology Labs (QETLabs).
Predicting the pattern of many photons emerging from a large optical chip is related to an extremely hard random matrix calculation.
With the rapid progress in quantum technologies, it appeared as though a boson sampling experiment that crossed into the quantum computational singularity was within reach. However, the Bristol team were able to redesign an old classical algorithm to simulate boson sampling, with dramatic consequences.
Dr Anthony Laing, who heads a group in QETLabs and led this research, said: "It's like tuning up an old propeller aeroplane to go faster than an early jet aircraft.
"We're at a moment in history where it is still possible for classical algorithms to outperform the quantum algorithms that we expect to ultimately be supersonic.
"But demonstrating such a feat meant assembling a crack team of scientists, mathematicians, and programmers."
Classical algorithms expert Dr Raphaël Clifford, from Bristol's Department of Computer Science, redesigned several classical algorithms to attack the boson sampling problem, with the 1950's Metropolised Independence Sampling algorithm giving the best performance.
The simulation code was optimised by QETLabs researcher 'EJ', a former LucasArts programmer. Expertise on computational complexity came from Dr Ashley Montanaro, of Bristol's School of Mathematics, while QETLabs students Chris Sparrow and Patrick Birchall worked out the projected performance of the competing quantum photonics technology.
At the heart of the project and bringing all these strands together was QETLabs PhD student and first author on the paper, Alex Neville, who tested, implemented, compared, and analysed, all of the algorithms.
He said: "The largest boson sampling experiment reported so far is for five photons.
"It was believed that 30 or even 20 photons would be enough to demonstrate quantum computational supremacy."
Yet he was able to simulate boson sampling for 20 photons on his own laptop, and increased the simulation size to 30 photons by using departmental servers.
Alex added: "With access to today's most powerful supercomputer, we could simulate boson sampling with 50 photons."
The research builds on Bristol's reputation as a centre of activity for quantum science and the development of quantum technologies.
Through QETLabs, the university has embarked on an ambitious programme to bring quantum technologies out of the laboratory and engineer them in to useful devices that have real-world applications for tackling some of society's toughest problems.
In addition to collaborations with tech companies such as Microsoft, Google, and Nokia, start-ups and new business activities focused on quantum technologies have emerged in Bristol.
An important theme across the overall quantum research activity is developing our understanding of exactly how quantum technologies can provably outperform conventional computers.
Recently Dr Montanaro, together with Professor Noah Linden of the School of Mathematics, organised a Heilbronn Focused Research Group on the topic of quantum computational supremacy.
This meeting brought some of the world leaders in the field, from both industry and academia, to Bristol for a week of intense discussions and collaboration. Among the attendees was one of the theorists who devised boson sampling, Professor Scott Aaronson, from UT Austin.
Although outperforming classical computers might take a little longer than originally hoped, Dr Laing is still optimistic about the prospects for building a device to do just that.
He said: "We now have a solid idea of the technological challenge we must meet to demonstrate that quantum machines can out-compute their classical counterparts. For boson sampling, the singularity lies just beyond 50 photons. It's a tougher nut to crack than we first thought, but we still fancy our chances."
With Dr Laing's group focused on practical applications of quantum technologies, the current work puts bounds on the size and sophistication of photonic devices that will be required to tackle industrially relevant problems that are beyond the capabilities of today's classical algorithms.


A recent breakthrough in the research revealed the process of making the wonder material graphene from the trash.
Graphene is cool stuff. The single-atom-thick layer of carbon has a number of properties that make it almost endlessly useful. Because of all the neat tricks, it can do, it’s popularly dubbed a “wonder material”
But over a decade and a half, after it was first isolated, the only thing I’m wondering is: where it is? Turns out the stuff is really hard to make in useful quantities, but a recent breakthrough from researchers at Rice University promises to make large amounts of graphene in a flash from your trash.
Graphene looks like this. Anyway, it’s not much to look at—it kind of resembles chicken wire. But this honeycomb lattice of carbon can do some amazing things. It is one of the thinnest, strongest, and most conductive materials we have ever discovered. This strength can be used to reinforce other materials.
Its amazing conductivity could help us make energy-dense batteries or efficient heat sinks. Its flexibility could make wearable electronics and bendable displays.
Ironic, given that it was first extracted by adding a piece of sticky tape as you might have in your home to a block of graphite and peeling it off, then re-sticking and peeling the tape off until you have thin flakes left behind. It’s like it’s taunting us.
But there’s a reason we don’t have armies of people just peeling tape apart. The graphene produced by this technique is still a few layers thick and we are after that single-atom-thick goodness. As of right now, the prevailing methods to achieve that usually involve assembling it on sheets of copper, than using plastics and chemicals to get it off.
But the process is not environment-friendly and it’s slow and expensive. A piece of 60mm x 40 mm monolayer graphene on copper will cost you about $172.
But what if we’re overthinking this? What if we could just take any old carbon source and zap it to make graphene? As far as I can tell, that’s basically the line of thinking the researchers from Rice University followed.
The method they have developed involves charging high-voltage capacitors with electricity, then releasing them all at once into almost any substance containing carbon.
The current passes through the target material, heating it to over 3,000 Kelvin and breaking every carbon-to-carbon bond in the process. The non-carbon elements sublime out, while the carbon atoms rearrange themselves as graphene.
Also Read: What is Neuromorphic Computing?
Excess energy is dispersed as light, so researchers dubbed the product “flash graphene.” The change can take as little as ten milliseconds. Not only does this produce a gram of graphene quickly and cheaply; it also makes a particular kind of graphene called turbostratic graphene.
Unlike A-B stacked graphene, which has orderly layers that are hard to pry apart, the layers of turbostratic graphene have no ordered alignment. This means they can be easily separated using
solvents or inside composite materials.
Now, this process doesn’t make large sheets of graphene, just small flakes. So, it may not be the breakthrough that leads to flexible screens you can put on a T-shirt. But it still has some very useful—albeit less flashy—applications.
The researchers envision flash graphene being added to concrete and estimate that just a fraction of a percent of graphene added in could boost cement’s strength by 35%. That translates to less building material needed, saving costs and lessening the environmental impact.
Also Read: The need for Quantum Computing
Flash graphene could be an ecological double win because it can be made with recycled plastic or food waste, or it could be an alternative use for cheap coal that doesn’t involve burning it and releasing CO2. The Department of Energy thinks turning coal into graphene looks promising and is funding the research with the goal of producing a kilogram of flash graphene a day within two years.
We are all clamoring for graphene to take the world by storm, but the reality is that it’ll take incremental steps like this to bring this wonder material into our daily lives. It’s already showing up in places that are hard to spot, like inside headphones and the coating of motorcycle helmets. Now thanks to this new work, it may soon show up in our buildings, too. And the only way you might be able to tell is if you measured the thickness of the walls or noticed there was suddenly a lot less plastic and banana peels lying around.
One of the lead researchers from Rice, James Tour, started experimenting with making graphene out of odd sources because of a bet in 2011 when a colleague challenged him to make it out of, among other things, cockroaches and dog poop.


Chinese physicists say they have built a quantum computer one trillion times faster than the most powerful supercomputer, with potential for some real-life applications.
The researchers said that using a process called “Gaussian boson sampling”, their Jiuzhang prototype quantum computer took a little over three minutes to complete a task that the world’s fastest conventional machine would not be able to complete in 600 million years.
This achievement firmly established our country’s leading position in international quantum computing research,” a team of researchers led by Professor Pan Jianwei said in a statement introducing a paper published on the website of the Science magazine on Friday.
Quantum computers rely on some counter-intuitive physics of the subatomic world, and are extremely fragile and difficult to maintain.
However, conventional computers struggle to cope with problems that involve uncertainty, such as predicting the rise and fall of the stock market, simulating the vibration of some elusive atoms, tracing the origin of a new-found virus, or guessing a bank account password.
The Jiuzhang was built to find clues in this kind of chaos. For instance, a database may contain many smaller data sets, some of which could have an unknown relation to the other. The Jiuzhang could quickly find out which data sets were related, a daunting task to traditional computers if the database contained a large amount of random information.
This unique calculation capability has a wide range of potential applications such as data mining, bioinformatics and finance, according to the researchers.
In the test reported in Friday’s paper, the Jiuzhang used light particles called photons to perform calculations. The photons must be generated in their purest possible form, because even a small physical discrepancy could lead to errors. And they must be produced one after another, a technical challenge that pushes optical precision to the limit.
“It is easy for us to have one sip of water each time, but it is difficult to drink just a water molecule each time,” said Pan, a lead scientist in China’s national quantum research programme with the University of Science and Technology of China in Hefei, Anhui province.
Though small in size, the Jiuzhang could be one of the most complex optical instruments ever built, with 25 crystals, each tailor-made and maintained at precise temperature, to manipulate the photons and simulate real-life chaos.
To obtain accurate results, Pan’s team also developed the world’s most sensitive light detectors.
But how could the results be verified?
If the machine made a mistake, Pan’s team reasoned, it could be detected by indirect measures such as abnormal spikes of temperature in some critical components, which did not happen.
They also tested the results of smaller-scale calculations on Shenwei TaihuLight, the fastest supercomputer in China.
One of those tests consumed US$400,000 worth of computer time, according to Scott Aaronson, a peer-reviewer of Pan’s paper.
“This was by far the most expensive referee report I ever wrote,” he said.
Aaronson, a computer science professor with the University of Texas, Austin, came up with the original idea of a light-based quantum computer. He told the South China Morning Post that he did not expect the pace of development to be so fast.
When he proposed the idea, some physicists said it would never work. Even Aaronson once thought the design would remain on paper forever.
The Jiuzhang is not the first quantum computer to appear to outperform a traditional computer. Google announced last year that Sycamore, a similar machine, could do a task in 200 seconds that would take 10,000 years on a supercomputer.
But researchers from IBM quickly showed that the same task could be done on a traditional computer in two days with a new algorithm. And Sycamore made a lot of mistakes due to the instability of its operation.
The Jiuzhang, named after a 2,000-year-old Chinese maths text, is China’s answer to the sceptics on quantum computer technology. It does not need to work sealed in extremely low temperatures like some other quantum computers and can operate in a stable manner for longer.
And, in the boson test, it was 10 billion times faster than Sycamore, securing a huge advantage in performance highly unlikely to be challenged by a traditional computer, according to some physicists not involved in the study.
China and the US have engaged in a heated race in quantum technology. China launched the world’s first quantum satellite and built the longest quantum communication network, but seemed losing to the Americans on the computer front.
Critics at home also say quantum technology consumes too muchtaxpayers’ money and produces too little of practical value.
The Jiuzhang cannot be used immediately in real-life applications. It will need to work with a programmable chip to perform various calculations.
And it cannot solve the factoring problem that is crucial to decoding encrypted information, so bank accounts are still safe, according to a quantum researcher not involved in the study.
“You cannot use this as an excuse to spend all your savings,” he said.
God, please protect me from my friends. I can handle my enemies.


- Quantum Supremacy - definition
- Encryptions remain uncrackable so far
- Peter Shor's Algorithm
- Final words
Google researchers completed an experiment that demonstrates the first computation that you can perform only with a quantum processor. It is something scientists call “quantum supremacy.” The quantum computer can perform tasks that no conventional processor can within a reasonable period.
If achieved, quantum supremacy would eventually change the world of cryptography forever. Deciphering a code would only take seconds or minutes instead of long years.
As a result, the current cyber encryption methods require an update. Otherwise, they won’t be able to withstand the immense computing power of a quantum processor.
The problem is that scientists and media people think differently. And no, Google’s quantum supremacy experiment will not put an end to the data encryption as we know it, at least not any time soon.
What Is Quantum Supremacy?
Quantum computing offers much higher speeds compared to regular computers when facing complex calculations. Traditional processors require months, even years, to solve complicated equations and problems. However, quantum computers can find solutions exponentially faster by using qubits.
According to the paper that Google published, their quantum processor “takes about 200 seconds to sample one instance of the quantum circuit one million times.” An existing supercomputer that uses classical computer architecture would need 10,000 years to complete a task of such complexity, the paper adds.
However, IBM was quick to rebuff Google’s claims that it reached quantum supremacy. On October 21, the company announced that its supercomputer “Summit” managed to complete the task in two and a half days. Therefore, the race is still on.
“We argue that an ideal simulation of the same task can be performed on a classical system in 2.5 days and with far greater fidelity.”IBM’s Edwin Pednault, John Gunnels, and Jay Gambetta
What makes a quantum processor work so much faster than a classical one?
Traditional computers use zeroes and ones to store data in pieces we call bits. Meanwhile, quantum processors work at the atomic level and use quantum bits instead. We call them qubits, which use zeroes, ones, and any number in between. Thus, you get far greater efficiency when processing data.
If you think it is too complicated, think again. IBM released a commercial version of its 14th quantum computer in October. It had 53 qubits of computing power, nearly double the capacity of the earlier one they released a year ago.
Did you read any news reports that an evil government uses IBM’s quantum computer to crack codes? I bet you didn’t.
Quantum Supremacy Does Not Mean Unsafe Cryptography Codes
Quantum computers do not have any practical uses at this stage. Just because they are available for commercial practices does not mean you can use them for instant budgeting, for example. And they cannot crack cryptography codes as well.
What these computers can do is process large amounts of data in parallel, resulting in markedly shorter processing time. Traditional devices, on the other hand, process data sequentially. Classical machines have been successful in reproducing the performance of quantum computers of up to 40 qubits, until recently. Google’s Sycamore processor is using 53 qubits.
But further developments in quantum computing will require building a physical quantum computer. Both Google and IBM still haven’t been able to do that. And I doubt there is one hidden somewhere in a secret R&D laboratory.
But if such a computer is available, how could it break a code that would take current classical machines tens of thousands of years to crack?
Why Shor’s Algorithm Matters
RSA, or Rivest-Shamir-Adleman, is an asymmetric encryption algorithm and a standard cryptographic technique to encrypt data on the Internet. It uses two different keys: public for encryption and private for decryption.
RSA users can create and publish a public key based on the multiplication of two large prime numbers. And anyone can use this key, since it is open, to encrypt a message. However, the prime numbers must remain secret. Otherwise, anyone can decode the information.
That’s because the prime numbers can be used as a private key to decrypt the message.
Current computers will need many years to break a 2048-bit key. If you use a 1024-bit key, anyone with a sizeable budget backing can crack it within a year. And that is where Shor’s algorithm enters the equation.
American mathematician Peter Shor offered a quantum computer algorithm for integer factorization back in 1994. It solves the following problem that concerns cryptography: Find the prime factors of any given integer.
A capable quantum computer can, in theory, crack all our current encrypted communications in no time using Shor’s algorithm.
But we are still a long way from witnessing such a computer in action. It appears that “Sycamore” demonstrates quantum supremacy within a narrow sampling task. Putting Shor’s algorithm to work requires much more.
Quantum Supremacy – Parting Words
Quantum computing is a viable technology. However, we are not yet sure whether it can do something that a conventional processor cannot.
Furthermore, quantum computers are unstable, which hinders your ability to use them for practical purposes as of today. They also need to store data for long periods to process it faster than conventional machines. But the process consumes lots of energy, which changes the state of qubits, leading to the destruction of saved information.
Everything having the word “quantum” in its name is much more complicated than it appears if you read about it in popular magazines. What it means for your cybersecurity is that current encryption methods are quite safe; for now.
Do you think scientists are on the verge of reaching quantum supremacy? Or do you believe that we are still a long way to go? Tell us what you think in the comment section below.


News and videos about quantum computers (QC) are common. ‘Quantum’ inspires awe and mystery. Astonishing speed-ups are promised. ‘Entanglement’ is thrown in the mix - people become hooked. But this computer research that inspires such fascination is an area that offers the fewest opportunities for involvement or understanding.
Want to learn to programme? Use tools like Scratch. Want to develop machine learning skills? There’s a Python package for that. Want to learn about QC? Zip through these courses on complex vector spaces, number theory, and an undergraduate introduction to quantum mechanics. Then you can start trying to understand the basics of QC!
But what about the only ‘killer app’ for QC - Shor’s Algorithm? Well, that would strain the brain of a third-year maths undergraduate. The mysteries of quantum effects are easy to understand in the maths. In the equations all is clear. But it is a mix of maths topics unusual to find in the average computer programmer.
Another approach to understanding QC involves helping other people understand it. One way to do this is to create musical problems and use QC to solve them. Discussing the solution to these problems can provide a greater insight into QC. The example in this article is the musical problem of chords, solved on a quantum D-Wave 2X.
The first company to sell quantum computers was D-Wave, who flogged a few off to people such as Google, NASA and Lockheed Martin. The D-Wave computers are adiabatic quantum computers (ADC). They are not like normal algorithmic step-by-step QC, such as those made by IBM. An adiabatic quantum computer is reminiscent of a neural network. It is based on the equations for Ising models. Ising models describe the physics of a magnetic material through the molecules within it.
An ADC solves the equations of the Ising model to minimise the energy in the simulated magnetic material. The programming involves defining properties of the simulated ‘molecules’. Over a period of 28 years, more than 10,000 publications came out in areas as wide as zoology and artificial intelligence on the applications of the Ising.
There is an ongoing debate about how the D-Wave ADC truly functions and what speedup it can provide. Google claimed large speed increases for its quantum hardware. This is thought to be due to quantum tunnelling. When searching for low energy states, a quantum system can tunnel into nearby states.
Quantum tunnelling allows physical systems to move to states in ways that would not be possible in the classical Newtonian view of the world. The systems ‘tunnel’ through to the new, usually inaccessible states instantaneously.
This particular musical problem was set up by assigning each note of the musical scale to one ‘molecule’ of the Ising model. Each molecule is modelled by a quantum bit, or Qubit. At this point, the mathematical world of quantum mechanics is entered, where everything makes sense in the equations, but not in the explanation!
Every qubit can be simultaneously a one or zero (unlike a bit which can only be one or zero). This is very simple mathematically, but makes no sense in our everyday observed world.
For example, a cat cannot be both alive and dead, as Schrodinger once observed in his famous thought experiment. He was trying to imagine the laws of quantum mechanics applying to the world beyond subatomic particles.
This, so called, ‘superposition’ of one and zero is not a form of statistical or probabilistic computing. It is something more complex. In the combination of one and zero held by this single qubit, the one and the zero also have what is known as a ‘phase’.
This can be thought of as the result of another strange consequence of quantum theory: everything is simultaneously a wave and a particle. An electron is a waveform, and a light wave is also a particle of light called a photon.
When the qubit is actually measured, its resulting value will always be 0 or 1. For definite. What’s more, the phase of the 0 and 1 in the superposition has no effect on the chance of whether a 0 or 1 is seen.
But, until that observation, not only is the result indeterminate, but these phases have dramatic effects on how qubits interact.
Things have clearly moved beyond the realms of how programming is normally thought about. The qubit being like a bit that is both 0 and 1 is a useful analogy, but it’s incomplete.
Qubits in harmony
The D-Wave 2X dealt with many underlying complexities. Connections were set up between the ‘molecules’ (the musical notes) in such a way that when the D-Wave program was triggered, it generated the form of musical chord required.
A simple musical rule is used. The D-Wave would be sent a note, and it would find three or four notes which included this note, and which were not too close together nor far apart on the piano keyboard. Try pressing three notes at the same time on the piano keyboard. If they are too close they clash, if they are too far apart they don’t sound like a chord.
Each time the D-Wave was asked to harmonise a note using this algorithm, it would send me multiple possible solutions. This highlights a key element of QC - there is no single correct solution to an algorithm. The solutions are held in a superposition, and then when observed, a single solution presents itself. This is not necessarily the precise process the D-Wave is following, but its qubits move through a number of superpositions as a solution form.
These ideas were captured and explained in a performance at the Port Eliot Music Festival in July 2017 called ‘Superposition’. It was a composition for mezzo soprano (Juliette Pochin) and electronic sounds. The electronics were generated by a real-time music system on my laptop, connected over the internet to the D-Wave 2X at USC. The mezzo-soprano’s music was pre-composed. The sounds of her voice were picked up live by the laptop, converted into energy and frequency readings, and sent to the D-Wave as a problem to be solved by the harmony generator.
The D-Wave returned multiple solutions. The local laptop took the multiple chords, spread them across the musical range, and played them together. These giant chords gave the audience some sense of the multiple solutions that may have existed in the superposition inside the quantum computer.
Universal quantum computers
The next performance planned will involve the Universal QC (UQC) of IBM. UQC have logic gate diagrams and assembly code. They have processing elements, like NOT, XOR and a form of AND gate.
But… the analogy breaks down. There are also gates that change qubit phase. The ‘Hadamard’ gate that takes as input a qubit that is definitely a 1 or 0, and turns it into an indeterminate superposition. Combine a Hadamard gate with a quantum XOR gate and you have ‘entangled’ qubits. Entanglement, vital to QC algorithms and probably the most famous element of QC, is once again simple to see in the maths, but makes little sense if explained otherwise.
Quantum computing, both adiabatic and universal, is proving a fruitful research topic. What is lagging is true public engagement. People, and most programmers, don’t know degree-level maths. So, let’s find new approaches to explain, and perhaps one day utilise, the power of quantum computing in more comprehensible ways.
Information on Alexis Kirke’s work and further projects can be found at: www.alexiskirke.com