1: The Strangest Force
Begin your exploration of gravity with Isaac Newton and the famous story of the apple. Why was it such a breakthrough to connect a falling apple with the faraway moon? Review the essential characteristics of gravity and learn why small asteroids and large planets have such different shapes.
2: Free Fall and Inertia
Review three great discoveries by the "grandfather" of gravity research, Galileo Galilei. His most famous experiment may never have happened, but his principle of inertia, law of free fall, and principle of relativity are the basis for everything that comes later in the science of gravity-including key breakthroughs by Einstein.
3: Revolution in the Heavens
Drawing on ideas and observations of Nicolaus Copernicus and Tycho Brahe, Johannes Kepler achieved a great insight about gravity by discovering three laws of planetary motion, relating to the mathematics of orbits. The cause of planetary motion, he determined, must lie in the sun.
4: Universal Gravitation
See how Newton was able to finish Kepler's revolution by formulating the law of universal gravitation, which says that every object exerts an attractive force on every other object. Also explore Newton's related discovery of the three laws of motion, which underlie the science of mechanics.
5: The Art of Experiment
Learn how distances in the solar system were first determined. Then chart Henry Cavendish's historic experiment that found the value of Newton's gravitational constant. Cavendish's work allows almost everything in the universe to be weighed. Then see a confirmation of the equivalence principle, which says that gravitational and inertial mass are identical.
6: Escape Velocity, Energy, and Rotation
Begin the first of several lectures that dig deeper into Newton's laws than Newton himself was able to go. In this lecture, apply the key concepts of energy and angular momentum to study how gravity affects motion. As an example, use simple algebra to calculate the escape velocity from Earth.
7: Stars in Their Courses-Orbital Mechanics
Newton was the first to realize that objects could, in theory, be sent into orbit around Earth. Explore how this works in practice, using the ideas of energy and angular momentum to study how satellites, moons, planets, and stars move through space.
8: What Are Tides? Earth and Beyond
Trace the origin of tides to the simple fact that gravity varies from point to point in space. This leads not just to the rise and fall of the ocean, but to the gradual slowing of Earth's rotation, Saturn's spectacular ring system, volcanoes on Jupiter's moon Io, and many other phenomena.
9: Nudge-Perturbations of Orbits
For the next three lectures, study the effects of gravity on the motions of more than two bodies. Here, see how even very small orbital changes-small perturbations-are significant. Such effects have revealed the presence of unknown planets, both in our own solar system and around other stars.
10: Resonance-Surprises in the Intricate Dance
Resonance happens whenever a small periodic force produces a large effect on a periodic motion-for example, when you push a child on a swing. Learn how resonance due to gravitational interactions between three bodies can lead to amazing phenomena with planets, asteroids, and rings of planets.
11: The Million-Body Problem
Consider the problem of gravitational interactions between millions of bodies, such as the countless stars in a galaxy. Amazingly, mathematics can reveal useful information even in these complicated cases. Discover how the analysis of the motions of galaxies led to the prediction of dark matter.
12: The Billion-Year Battle
Explore the physics of stars, which are balls of gas in a billion-year battle between the inward pull of gravity and the outward pressure produced by nuclear fusion. Follow this story to its ultimate finish-the triumph of gravity in massive stars that end their lives as black holes.
13: From Forces to Fields
For the rest of the course, focus on the revolutionary view of gravitation launched by Albert Einstein. Review new ideas about fields that allowed physics to extend beyond Newtonian mechanics. Then see how Einstein modified Newton's laws and created the special theory of relativity.
14: The Falling Laboratory
Einstein focused on gravity in his general theory of relativity. Hear about his "happiest thought"-the realization that a man in free fall perceives gravity as zero. This simple insight resolved a mystery going all the way back to Newton and led Einstein to the startling discovery that gravity affects light and time.
15: Spacetime in Zero Gravity
In an influential interpretation of relativity, Einstein's former mathematics professor Hermann Minkowski reformulated the theory in terms of four-dimensional geometry, which he called spacetime. Learn how to plot events in this coordinate system in cases where gravity is zero.
16: Spacetime Tells Matter How to Move
See how gravity affects Minkowski's spacetime geometry, discovering that motion in a gravitational field follows the straightest path in curved spacetime. The curvature in spacetime is not caused by gravity; it is gravity. This startling idea is the essence of Einstein's general theory of relativity.
18: Light in Curved Spacetime
See how Einstein's general theory of relativity predicts the bending of light in a gravitational field, famously confirmed in 1919 by the British scientist Arthur Eddington. Learn how this phenomenon creates natural gravitational lenses-and how the bending of light reveals invisible matter in deep space.
19: Gravitomagnetism and Gravitational Waves
The general theory of relativity predicts new phenomena of gravity analogous to those of electromagnetism. Discover how ultra-sensitive experiments have detected the gravitomagnetism of the Earth, and follow the search for elusive gravitational waves that travel through space.
20: Gravity's Horizon-Anatomy of a Black Hole
Plunge into the subject of black holes, which are massive objects that have collapsed completely under their own gravity. Learn how black holes distort spacetime and explore the supermassive black holes that lie at the hearts of galaxies. Then ask: Are there such things as micro-black holes?
21: Which Universe Is Ours?
Investigate what Einstein called his "greatest mistake"-his rejection of his own theory's prediction that spacetime should be dynamic and evolving. Chart the work of a group of scientists, including Alexander Friedman, Georges Lemaître, and Edwin Hubble, who advanced the realization that our universe is expanding from an apparent big bang.
22: Cosmic Antigravity-Inflation and Dark Energy
Using everything you've learned about gravity, investigate cosmic antigravity, starting with cosmic inflation, a phenomenon that exponentially increased the size of the universe during the big bang. Then, learn why dark matter cannot be made of ordinary protons and neutrons, and explore the recent discovery that the expansion of the universe is accelerating, powered by a mysterious dark energy inh...
23: The Force of Creation
Use a black hole to test the laws of thermodynamics, taking a deeper look at the capacity of gravity to pull matter together and increase entropy at the same time. Probe Stephen Hawking's most surprising discovery, and then learn that the same force that pulls the apple down and steers the stars in their courses is also nature's ultimate source of order and complexity.
24: The Next Revolution
Survey the greatest unsolved problem in theoretical physics: the search for a quantum theory of gravity. Examine string theory, loop quantum gravity, and also entropic gravity, which suggests a revolutionary link with thermodynamics. Close the course with a deepened appreciation for the connection between everyday features of gravity and the most exciting questions in contemporary physics and cosm...
Gravity is about both phenomena near at hand at the human scale, everyday and intuitive, and phenomena far off at an astronomical scale.
About Benjamin Schumacher
Dr. Benjamin Schumacher is Professor of Physics at Kenyon College, where he has taught for 20 years. He received his Ph.D. in Theoretical Physics from The University of Texas at Austin in 1990. Professor Schumacher is the author of numerous scientific papers and two books, including Physics in Spacetime: An Introduction to Special Relativity. As one of the founders of quantum information theory, he introduced the term qubit, invented quantum data compression (also known as Schumacher compression), and established several fundamental results about the information capacity of quantum systems. For his contributions, he won the 2002 Quantum Communication Award, the premier international prize in the field, and was named a Fellow of the American Physical Society. Besides working on quantum information theory, he has done physics research on black holes, thermodynamics, and statistical mechanics. Professor Schumacher has spent sabbaticals working at Los Alamos National Laboratory and as a Moore Distinguished Scholar at the Institute for Quantum Information at California Institute of Technology. He has also done research at the Isaac Newton Institute of Cambridge University, the Santa Fe Institute, the Perimeter Institute, the University of New Mexico, the University of Montreal, the University of Innsbruck, and the University of Queensland.


Einstein wasn’t alone in the search of a Unified Field Theory. From Weyl’s version of metric tensors to Kaluza’s Fifth Dimension to Eddington’s Affine connection, there were many attempting to build a Unified Theory.
Weyl’s Metric Tensor and Unified Field Theory
The first attempt at a unified field theory wasn’t made directly by Einstein himself. Instead, it was by the German physicist and mathematician Hermann Weyl. However, Einstein and Weyl were in communication during this time, and they discussed some of the aspects of this problem together. So, at least to some extent, Einstein was involved.
From Weyl’s perspective, there was one central challenge that made it so hard to combine general relativity and electromagnetism into one unified field theory. This challenge was that general relativity is a theory of geometry, while electromagnetism is not. Maxwell’s equations described the forces that act on electrically charged particles. They don’t involve any changes to the geometry of space or time.
Weyl felt that if he wanted to merge these two theories together into a common framework, he would need to find a new geometrical way to formulate the theory of electromagnetism. In general relativity, the geometry of space and time is described by a mathematical object called the metric tensor. A tensor is essentially a special kind of matrix or array of numbers.
In general relativity, the metric tensor is a 4×4 array of numbers, so it contains a total of sixteen entries. But of these sixteen quantities, six are redundant, so there are really only 10 independent numbers described by the metric tensor. And we need all 10 of these numbers just to describe the effects of gravity.
The problem in combining general relativity with electromagnetism is that when we incorporate electromagnetism we need at least four more numbers at every point in space. This made it hard to see how one could explain both gravity and electromagnetism in terms of geometry. There just aren’t enough numbers in the metric tensor to describe both gravity and electromagnetism at the same time.
To try to get around this problem, Weyl proposed a version of non-Euclidean geometry. In doing so, he argued that it was possible to construct a geometrical system that wasn’t limited to the 10 independent numbers. In addition to those 10 numbers, Weyl’s version of the metric tensor contained other additional quantities. And Weyl hoped that these additional numbers could somehow encode the effects of electromagnetism.
The theory that Weyl ultimately came up with was very complicated. Although it was mathematically sound, physically, it just didn’t make much sense. After a series of exchanges with Einstein, even Weyl became convinced that his work hadn’t gotten them any closer to viable unified field theory.
This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.
Kaluza’s Fifth Dimension and Unified Field Theory
Only a year later or so, another idea in this direction was proposed. This time by the mathematician Theodor Kaluza. Most people find Kaluza’s idea to be pretty strange and surprising. What he proposed was a unified field theory in which the space and time of our universe aren’t limited to four, but five dimensions.
To see why a fifth dimension might be helpful in building a unified field theory, we need to remember metric tensor. A tensor is a 4×4 array of numbers, for a total of sixteen entries—10 of which are independent of each other. But tensor is a 4×4 array of numbers only because it was formulated in four-dimensional spacetime. If spacetime is five-dimensional, then the metric tensor will be a 5×5 array of numbers, for a total of twenty-five entries.
After removing all of the redundant entries, the five-dimensional metric tensor contains fifteen independent quantities. 10 of these fifteen numbers are needed to describe gravity. And this leaves us with five others, which is more than enough to potentially encode the phenomena of electromagnetism.
There is, though, one immediate and obvious objection that one might raise to Kaluza’s five-dimensional theory. As far as we can tell, our universe doesn’t have a fifth dimension.
Fortunately, there is a way that a fifth dimension might be able to remain hidden in a system like Kaluza’s. In this geometrical system, the fifth dimension isn’t like the others. The three dimensions of space that we are familiar with are large, and as far as we know, they go on forever in any given direction. If there were an extra dimension like this, it would be impossible for us not to notice it.
But the fifth dimension being imagined by Kaluza doesn’t go on forever. Instead, it’s wrapped up, or curled up, into a tiny circle. If something moved even a short distance along the direction of this fifth dimension, it would simply return to where it started. If the circumference of the fifth dimension is small enough, it would be almost impossible for us to perceive it.
It was in 1919 that Kaluza described his idea to Einstein for the first time. And despite the fact that there were significant problems with the 5-dimensional theory, Einstein liked it a great deal.
With Einstein’s help, Kaluza managed to publish his theory a couple of years later, in 1921. And only a few weeks after that, Einstein himself wrote and published an article that investigated some of the aspects of similar five-dimensional unified field theories. But, despite the enthusiasm, it was pretty clear that there were serious problems with Kaluza’s theory. Einstein, though, continued to work on this theory not because he thought it was a viable unified field theory, but because he thought it might lead to something more promising.
After all, while Einstein was developing general relativity, he went through several incorrect versions of the gravitational field equations before he found the right answer.
Learn more about Quantum Entanglement.
Arthur Eddington’s Affine Connection and Unified Field Theory
Another scientist who worked on unified field theories during this period of time was the famous astronomer and physicist Arthur Eddington. However, Eddington didn’t focus on expanding the metric tensor. In fact, he didn’t focus on the metric tensor at all. Instead, he focused on a different mathematical structure, known as the ‘affine connection’. In the end, Eddington didn’t really get any closer than Weyl or Kaluza to building a viable unified field theory. But Eddington’s work was important because his approach was quite different, and along with Kaluza, Eddington probably had the most influence on Einstein’s later efforts to develop such a theory.
Learn more about what Einstein got right: Special Relativity.
Einstein’s Early Work on Unified Field Theory
Einstein himself began to focus on unified field theories in the early 1920s. During this period of time, he remained enthusiastic about the work that had been earlier done by both Kaluza and Eddington. In fact, a lot of Einstein’s early work in this area consisted of extending and building upon these earlier ideas.
Einstein was deeply enthusiastic about this program of exploration. Although in this respect, he was relatively isolated since most physicists didn’t share his excitement. Quantum physics was developing rapidly, and that was occupying the bulk of the field’s attention during this time.
Einstein was deeply unhappy with the developments occurring in quantum theory as it moved away from the predictive determinism. Einstein’s views about quantum mechanics also served to bolster his interest in unified field theories.
In addition to unifying general relativity with electromagnetism, Einstein hoped that a unified field theory might also somehow be able to restore determinism and scientific realism to the quantum world.
Common Questions about the Early Works on Unified Field Theory
Yes, it’s possible to have a unified field theory similar to that of James Clerk Maxwell who successfully combined electric and magnetic fields into Electromagnetic theory.
Unified field theory is an attempt to unify different fundamental forces and the relationships into a single theoretical framework. There have been many attempts at unified theories, some were successful, some failed.
James Clerk Maxwell was the first one to create a unified field theory. He also combined electric and magnetic fields into Electromagnetic theory.
The founding fathers of quantum theory are Niels Bohr, Max Planck, and, to a certain extent, Albert Einstein.


In 1965, Intel co-founder Gordon Moore published a remarkably prescient paper which observed that the number of transistors on an integrated circuit was doubling every two years and predicted that this pace would lead to computers becoming embedded in homes, cars and communication systems.
That simple idea, known today as Moore’s Law, has helped power the digital revolution. As computing performance has become exponentially cheaper and more robust, we have been able to do a lot more with it. Even a basic smartphone today is more powerful than the supercomputers of past generations.
Yet the law has been fraying for years and experts predict that it will soon reach its limits. However, I spoke to Bernie Meyerson, IBM’s Chief Innovation Officer, and he feels strongly that the end of Moore’s Law doesn’t mean the end of progress. Not by a long shot. What we’ll see though is a shift in emphasis from the microchip to the system as a whole.
Going Beyond Silicon
The end of Moore’s Law is not a new issue. In fact, Meyerson argues that it first began unraveling in 2003, when insulating components within transistors began failing due to quantum mechanical effects. Since then, chip manufacturers have been finding new materials that are more resistant to decay in their basic atomic properties and progress has continued.
However, sometime around 2020, these workarounds will no longer suffice as the silicon itself yields to quantum mechanical reality. Some researchers, including at IBM, are pursuing strategies like carbon nanotubes and silicon photonics that have the potential to increase chip speeds even without having to shrink chips to quantum scale.
Other approaches, such as quantum computing and neuromorphic chips, change the nature of computing itself and can be exponentially more efficient for certain tasks, such as pattern recognition in the case of neuromorphic chips and encryption in the case of quantum computers. Still, you wouldn’t want either of these running your word processor.
As Meyerson put it, “Quite frankly, for general purpose computing all that stuff isn’t very helpful and we’ll never develop it in time to make an impact beyond specialized applications over the next 5 or 10 years. For the practical future, we need to change our focus from chip performance to how systems perform as a whole by pursuing both hardware and software strategies.”
Integrating the Integrated Circuit
One way of increasing performance is by decreasing distance at the level of the system. Currently, chips are designed in two dimensions to perform specific functions, such as logic chips, memory chips and networking chips. Although none of them can do much by themselves, acting in concert they allow us to do extremely complex tasks on basic devices.
So one approach to increasing performance, called 3D stacking, would simply integrate those integrated circuits into a single three-dimensional chip. This is harder than it sounds, because entirely new chip designs have to be devised, but it would vastly reduce the time circuits need to wait for instructions from each other and increase speed significantly while decreasing power dramatically due to far shorter communication paths.
In truth, this is not a new strategy but rather one that was deployed in the 1960’s to overcome a challenge called the tyranny of numbers. Simply put, the physical requirements of wiring thousands of transistors together was putting practical limitations on what could be designed and built. That’s what led to the invention of integrated circuits in the first place.
Meyerson says, “when we moved from transistors to integrated circuits, we shrunk an entire rack measuring about 40 cubic feet down to a single board measuring 19 x 26 inches. 3D stacking will shrink that board down to less than a square inch and we can potentially get an increase in power performance of at least 10-100 fold.
Building Intelligently Agile Systems
In the 1980’s, chip manufacturers began building specialized types of chips, called ASICs, that were highly optimized for specific tasks, such as running complex financial models. These would significantly outperform conventional chips for those specific tasks, but ultimately, the process of hardwiring proved too expensive and unwieldy to be a viable strategy.
Yet Meyerson sees vastly more potential in a newer approach called FPGA, that can be re-purposed on the fly through software. He points to Intel’s recent purchase of Altera as a strong indication that things are moving in that direction. It is well known that in specific applications FPGA’s can produce gains of ten-fold or more in computing performance, but most importantly, that system level gain is not restricted to a single application.
The FPGA approach is a major improvement because rather than going through a roughly 18-month process to design and manufacture a specialized chip, the same thing can be done in a matter of weeks. However, Meyerson thinks the potential may actually be far greater than that if we can build intelligent software that can reprogram the chips autonomically.
“So for example,” Meyerson says,” while you’re writing a document, your laptop would be configured to do exactly that, but if you then needed to run a simulation of some financial data for that same report, your system would re-optimize itself for deep computations required. Such “intelligent” architectures and the enabling software are the next grand challenge in IT.”
“Take this idea a little further,” he continues “and you can see how new technologies like neuromorphic chips and quantum computing can deliver an enormous impact even as specialized systems in the cloud. Imagine being able to access the capabilities of a neuromorphic system for photo recognition and search while shopping, and then instantly switch to a quantum computer to facilitate the transaction with unbreakable encryption.”
The Future of Technology is all too human
Back in 1965, when Gordon Moore formulated his famous law, computers were enormous hunks that few people ever saw. After 20 years of continuous doubling, we got personal computers small enough to fit under our desks, but powerful enough to generate a graphical display and interact with us through a keyboard and a mouse. 20 more years gave us the mobile revolution.
The future of technology is always more human and Meyerson expects that, ”by 2020, we’ll still be improving system performance exponentially, but we’ll have to change our conception of information technology once again, this time from machines that store, analyze and retrieve information to systems that are active partners in a very natural human/machine collaboration.”
“The cognitive era will be ultimate bridge across the digital divide,” he notes, “spanning barriers of not only technology but that of language, education and skill level as well. IT will essentially become so advanced that it disappears along with previous institutional barriers. Even a teenager will have access to resources that only the most well-equipped research facilities have today and they will be able to access it in real time.”
But perhaps the most important consequence of Meyerson’s vision of cognitive computing is not how it will change how we work with computers, but with each other. Before the industrial era, people were valued for their ability to do physical work. In the knowledge economy, those with strong cognitive skills were considered “the best and the brightest.” Now, we will likely see a new shift in value.
In the future, when machines can do cognitive tasks more effectively than any human, we will likely find that competitive advantage will go to those who can collaborate effectively, with both people and machines. So the key to the future lies not so much in chips and algorithms as it does within ourselves.
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Greg Satell is a popular speaker and consultant. His first book, Mapping Innovation: A Playbook for Navigating a Disruptive Age, is coming out in 2017. Follow his blog at Digital Tonto or on Twitter @Digital Tonto.


‘Cheerios Effect’ Forces Directly Measured for the First Time
In a finding that could be useful in designing small aquatic robots, researchers have measured the forces that cause small objects to cluster together on the surface of a liquid — a phenomenon known as the “Cheerios effect.” The researchers used a custom built apparatus to measure the forces using magnetism. Credit: Harris Lab / Brown University
There’s an interesting fluid dynamics phenomenon that happens every morning in millions of cereal bowls. When there are just a few bits of cereal left floating on top of the milk, they tend to cluster together in the middle or around the edges of the bowl, rather than dispersing across the surface.
Now a team of Brown University researchers has developed a way to measure the forces involved in this type of clustering. It’s the first time, the researchers say, that these forces have been experimentally measured in objects at the millimeter/centimeter scale. And the implications of the work go far beyond cereal bowls — the results could be useful in guiding the self-assembly of micromachines or in designing microscale robots that operate in and around water.
“There have been a lot of models describing this Cheerios effect, but it’s all been theoretical,” said Ian Ho, an undergraduate student at Brown and lead author of a paper describing the work. “Despite the fact that this is something we see every day and it’s important for things like self-assembly, no one had done any experimental measurements at this scale to validate these models. That’s what we were able to do here.”
The research was published in Physical Review Letters on December 19, 2019. Ho’s co-authors were Giuseppe Pucci, a visiting scholar at Brown, and Daniel Harris, an assistant professor in Brown’s School of Engineering.
The Cheerios effect arises from the interaction of gravity and surface tension — the tendency of molecules on the surface of a liquid to stick together, forming a thin film across the surface. Small objects like Cheerios aren’t heavy enough to break the surface tension of milk, so they float. Their weight, however, does create a small dent in the surface film. When one Cheerio dent gets close enough to another, they fall into each other, merging their dents and eventually forming clusters on the milk’s surface.
In order to test just how strongly Cheerios — and other objects in the Cheerio size and weight range — attract each other, the researchers used a custom-built apparatus that uses magnetism to measure forces. The experiment involves two Cheerio-sized plastic disks, one of which contains a small magnet, floating in a small tub of water. Electrical coils surrounding the tub produce magnetic fields, which can pull the magnetized disk away while the other is held in place. By measuring the intensity of the magnetic field at the instant the disks begin moving away from each other, the researchers could determine the amount of attractive force.
“The magnetic field gave us a non-mechanical way of applying forces to these bodies,” Harris said. “That was important because the forces we’re measuring are similar to the weight of a mosquito, so if we’re physically touching these bodies we’re going to interfere with the way they move.”
The experiments revealed that a traditional mathematical model of the interaction actually under-predicts the strength of the attraction when the disks are positioned very close together. At first, the researchers weren’t sure what was happening, until they noticed that as two disks draw closer, they start to tilt toward each other. The tilt causes the disk to push harder against the surface of the liquid, which in turn increases the force by which the liquid pushes back. That extra push results in a slightly increased attractive force between the disks.
“We realized that there was one extra condition that our model wasn’t satisfying, which was this tilt,” Harris said. “When we added that one ingredient to the model, we got much better agreement. That’s the value of going back and forth between theory and experiment.”
The findings could be useful in the design of microscale machines and robots, the researchers say. There’s interest, for example, in using small spider-like robots that can skitter across the surface of water to do environmental monitoring. This work sheds light on the kinds of forces these robots would encounter.
“If you have multiple little machines moving around or two or more legs of a robot, you need to know what forces they exert on each other,” Harris said. “It’s an interesting area of research, and the fact that that we could contribute something new to it is exciting.”
Reference: “Direct Measurement of Capillary Attraction between Floating Disks” by Ian Ho, Giuseppe Pucci and Daniel M. Harris, 19 December 2019, Physical Review Letters.
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Even though quantum computers are still in their crawling phase, computer scientists continue to push their limits. Recently, a group of scientists used a two-qubit quantum system to model the energies of a hydrogen molecule and found that using an iterative algorithm to calculate each digit of the phase shift gave very accurate results. Their system, while not directly extensible, has the potential to help map the energies of more complex molecules and could result in significant time and power savings compared to classical computers.
There are some situations, like quantum states of particles, that classical computers can only approximate, and they often do so quite poorly, with high degrees of uncertainty despite extensive computing time. For modeling quantum situations, there's no better tool than another quantum system that can be used to store and process the relevant data, as quantum computers can explore many possible states at once (though only one state can be measured as the outcome).
First, a quick rundown on quantum computers: while a regular computer processes and uses bits comprised of zeroes and ones, a quantum computer processes qubits, or bits that can store a superposition of both zero and one that will be in only one of these states when read out. In other words, when a qubit is measured, its superposition collapses to one of its available states (in this case, zero or one).
Modeling the energy levels of molecular hydrogen requires calculating the distance between the two atoms and the effect of different levels of excitation. A group of scientists designed a three-step method to handle this: encode the wave function of the molecule using qubits, simulate time evolution with quantum logic gates, and then use an iterative phase estimation algorithm to reduce the error, using the output of each trial as the input for the next. To get the energy, they calculated the phase shift of the molecule's wave function as a series of bits, and calculated one bit at a time with the qubit system.
To model a hydrogen molecule (two bonded hydrogen atoms), scientists injected two photons into an optical circuit, with each photon's polarization representing the encoding for a "control" qubit and a "register" qubit. The register represents an eigenstate, or one accepted energy configuration of the hydrogen molecule, and the control is in an equal superposition of a vertical and horizontal polarization.
The photons are then passed through a logic gate that represents an evolution of the wave function over time. The gate polarizes the control photon, forcing it to collapse into either a vertical or horizontal state. It also performs an operation on the register photon if the control comes out of the gate horizontally polarized, or leaves the register photon alone if the control becomes vertically polarized. The position of the control photon is measured and converted to a bit—0 for horizontal, and 1 for vertical. This represents one pass through the optical circuit.
The algorithm used 31 samples, or photon pairs, for each bit, and a "majority vote" was taken using all the samples—the resulting number is used as one digit in the binary expansion of the phase shift. The next iteration put all the photon pairs through the same circuit again, using the output of the first iteration as input for the second. With each new time around, the output was used to simulate a different time point in the evolution of the hydrogen molecule.
The least significant digit was always calculated first, then the next most significant, as this order allows for the best estimation of the most significant digits. The finished product looks something like 0.01001011101011100000, and varies depending on the excitation of the atoms and their distance from each other. Researchers found that they could calculate the phase shift out to 20 significant digits before the least significant digit stopped strongly favoring one value over another.
The results of the experiment mirrored very closely the energy curves of a hydrogen molecule as a function of the atomic separation, indicating that this is an excellent method for studying the energies of molecules. While the general approach to the problem, in particular the use of an iterative algorithm to estimate the phase of the wave function, proved accurate, the system that was used is only applicable to the hydrogen molecule. Simulating larger molecules requires more qubits and logic gates, which decrease the accuracy of measurements.
The precision in the hydrogen molecule system is high because the error introduced by one gate is always a constant, and can be corrected for by the classical method of the majority vote. If it were possible to look at the system after each gate, correct the error, and continue on, large systems requiring multiple logic gates would work pretty well. However, a quantum system can only be observed once it has run its course, and each logic gate roughly doubles the error each time the photons pass through it. Therefore, some new quantum correction techniques will have to be introduced before quantum computers can take on larger molecules. Despite these limitations, the work is an important demonstration of the promise of quantum computing, and shows that the techniques we already have can be put to practical use.
Nature, 2010. DOI: 10.1038/NCHEM.483


A compass needle made by a Magnetoreceptor and assisted by Cryptochromes
Here it is: In yellow, a polymer made of five molecules of the protein termed Magneto-Receptor (MagR) - five loops hosting iron. It is surrounded by cryptochrome proteins
Credit: S. Qin et al. Nature Mater. http://dx.doi.org/10.1038/nmat4484 (2015).
"Together with Cry, it forms a nanoscale ‘needle’: a rod-like core of CG8198 (MagR) polymers with an outer layer of Cry proteins that twists around the core (see 'Protein biocompass')."
"Using an electron microscope, Xie’s team saw assemblies of these rods orienting themselves in a weak magnetic field in the same way as compass needles."
"Many birds have a compass in their eyes. Their retinas are loaded with a protein called cryptochrome, which is sensitive to the Earth’s magnetic fields. It’s possible that the birds can literally see these fields, overlaid on top of their normal vision. This remarkable sense allows them to keep their bearings when no other landmarks are visible."
Following the experiments of Researcher Lauren Foley from the University of Massachusetts Medical School we can create artificial magnetic fields resembling the Earth's field and place for instance the fly food always in the south. Flies would learn to go to the south to find food. Transgenic flies that do not have cryptochromes in their retinas could not find the south. When the human gene was inserted in their genome, their capacity to find the pole with the food was restored.
Excerpts from an article by The Guardian
“The nanoscale biocompass has the tendency to align itself along geomagnetic field lines and to obtain navigation cues from a geomagnetic field,” said Xie. “We propose that any disturbance in this alignment may be captured by connected cellular machinery, which would channel information to the downstream neural system, forming the animal’s magnetic sense.”
“It has been well documented that cryptochromes, which are crucial to the compass proposed in this new paper, may harness significant quantum effects to convert the Earth’s weak magnetic field into a signal in the animal’s brain. This is a tantalising possibility since the new UK quantum technology hubs are focusing about a quarter of their £150M on sensor systems. It would be remarkable if we can learn some tricks from Mother Nature in this highly-advanced field of physics,” he added.
3 examples from The Guardian
Enzymes: "enzymes make use of a remarkable trick called quantum tunnelling to accelerate biochemical reactions. Essentially, the enzyme encourages electrons and protons to vanish from one position in a biomolecule and instantly rematerialise in another, without passing through the gap in between – a kind of quantum teleportation."
Photosynthesis: "Energy packet was not hopping haphazardly about, but performing a neat quantum trick. Instead of behaving like a localised particle travelling along a single route, it behaves quantum mechanically, like a spread-out wave, and samples all possible routes at once to find the quickest way."
European robin: "an internal chemical compass that utilises an astonishing quantum concept called entanglement, which Einstein dismissed as “spooky action at a distance”. This phenomenon describes how two separated particles can remain instantaneously connected via a weird quantum link. The current best guess is that this takes place inside a protein in the bird’s eye, where quantum entanglement makes a pair of electrons highly sensitive to the angle of orientation of the Earth’s magnetic field, allowing the bird to “see” which way it needs to fly."
Specialised/Mechanistic article Magnetoreception and the radical pair mechanism:
The discovery of magnetite (Fe3O4) in the human brain in 1992 by Dr. Joesph Kirschvink at CalTech
Using an ultrasensitive superconducting magnetometer in a clean-lab environment, we have detected the presence of ferromagnetic material in a variety of tissues from the human brain. These magnetic and high-resolution transmission electron microscopy measurements imply the presence of a minimum of 5 million single-domain crystals per gram for most tissues in the brain and greater than 100 million crystals per gram for pia and dura.
Biogenic magnetite in the human brain may account for high-field saturation effects observed in the T1 and T2 values of magnetic resonance imaging and, perhaps, for a variety of biological effects of low-frequency magnetic fields.
Another study by Dr. Joesph Kirschvink
Magnetite Minerals in the Human Brain: What Is Their Role?
Production of single-domain magnetite throughout life by sockeye salmon, Oncorhynchus nerka.
Similar results in humans


In the last section we covered the basics of qubits and introduced the concept of logical and physical qubits. In this section we will look at some of the most popular ways to create qubits and discuss their advantages. It’s important to remember that the goal is to find a method that can be scaled up into a large system, since the power of a quantum computer can grow exponentially with size. We can’t just measure the success of one method on it’s performance today, but also the challenges we might face when attempting to build a larger machine.
This implementation of qubit is seeing a lot of success, being the main focus of IBM and Google’s large universal quantum computers. These qubits use phenomena found in electric superconducting circuits to create a quantum two-state system.
Advantages: Superconducting qubits have fast gate times (faster operation time), meaning similar computations can be performed much more quickly than on other qubits (e.g. ion trap), this is important since useful computations will likely have millions of logical gates (operations). Additionally, the technology behind superconducting qubits can take advantage of existing methods and processes (such as printable circuits) that we have already spent years improving. As a result it is much easier to envisage a scalable superconducting quantum computer than with other existing methods.
Disadvantages: Superconducting qubits have fast decoherence times, meaning their ‘memory’ is very short lived and we need more error correcting qubits to compensate. Since superconducting qubits can normally only interact with the handful of qubits next to them on the device, we need extra operations to perform most algorithms. They also must be kept very cold (below 100mK, or 0.1 degrees above absolute zero) which can be expensive and inconvenient. Finally, each superconducting qubit is slightly different and must be calibrated which could cause problems on larger systems.
Fun Fact: The qubits being used in IBM’s chips are superconducting transmon qubits. ‘Transmon’ comes from plasmon qubits and the transmission line added to disperse troublesome low frequencies (the transmission line was actually dropped for a capacitor, but the name was too catchy to change!).
Ion Trap Qubits
Ion trap quantum computing is perhaps easier to understand for the average layperson than with superconducting quantum computers. Ion trap computers literally trap ions (charged atoms) using magnetic fields and hold them in place, the outermost electron orbiting the nucleus can then be put in different states and used as a qubit.
Advantages: A big feature of ion trap computers is their stability; the qubits have much longer decoherence times than those in a superconducting quantum computer. While an ion trap computer can operate at room temperature, to get the best performance the ions need to be cooled. Fortunately around 4K (four degrees above absolute zero) seems to be sufficient which is much cheaper and easier than the 0.1K needed by superconducting qubits. Finally, the connections between ion trap qubits can be reconfigured meaning each qubit can interact with each other qubit in the computer, avoiding some of the computational overhead found with superconducting chips.
Disadvantages: Ion trap computers are generally significantly slower than their superconducting counterparts, which is a big problem. While they do not need to be kept as cold, the ions do need to be in a high vacuum. The technology involved in creating ion traps is not as mature as with superconducting qubits, we will need to see large improvements in the area before we can imagine a scalable system.
Other Types of Qubits
Superconducting and Ion trap quantum computers are currently the most serious and viable attempts to creating a useful, universal quantum computer. There are other technologies capable of creating usable qubits and we cover a couple here:
Photonic qubits (made from particles of light) can theoretically be used to create a universal quantum computer, but in practice this is hard to achieve. Instead they could be good candidates for quantum key distribution. Quantum key distribution is a non-computational application of quantum information used to securely exchange cryptographic keys. Quantum key distribution is still in it’s infancy and faces the difficult problem of transporting qubits between the two parties, photons are very stable over long distances and so far seem the best candidates for the job.
Topological Qubits operate on quite a different principle to the other qubits we have seen in this article. Topological quantum computation uses anyons, (a type of particle that occurs in 2D systems) to create stabler quantum systems. Anyons can be moved around in relation to each other to affect their state. Importantly, the state is affected by the number of rotations around each other, this can create a type of braid which is where the ‘topological’ part of the name comes from. Unfortunately we can’t confirm that the type of anyon needed to create a universal quantum computer have not been experimentally confirmed yet, and this model of quantum computation will remain theoretical for the time being.


Some people want to move mountains. Kunal Das, Ph.D., assistant professor of physics, wants to move electrons.
Das is a theoretical physicist researching an area where the classical rules of physics no longer apply—the nanoscale universe of quantum physics, a submicroscopic world where particles defy common sense. In that mysterious world of the ultra-small, Das is searching for new ways to move the currents that power computers.
“When the first computers came along in the 1960s, they were huge objects which filled up an entire room and had miniscule computing power,” Das says, as he gestures to his computer in his Freeman Hall office. “How is it that today we have something this compact and with this much more power? Today, every two years computers become twice as fast and half as big.”
Computers are powered by electronic circuitry in which currents move large clusters of electrons at a time to feed a tiny computer chip. The number of electrons needed for each operation has gotten smaller with time. But within 20 years, Das says, computers will reach a point where each operation could be done by just one electron, and thus won’t be able to get any faster or any smaller.
What then? Where will technology go?
Already, scientists are experimenting with storing information not in bits, but in qubits (or quantum bits), which can potentially store much larger amount of information than traditional bits. Can a “quantumchip” be in the offing?
That’s where quantum mechanics come in.
Das has focused his research on adiabatic electron pumps, which can be used to control the flow of individual or entangled pairs of electrons in order to power quantum computers. Quantum computers, which are still in their infancy, have the potential to perform certain calculations significantly faster than any silicon-based computer.
Quantum mechanics have become very important partly because, at the qubit level, individual particles of matter play essential roles. The current that powers the computer no longer flows as a cluster of electrons, but as one electron at a time; and such motion is governed by quantum mechanics.
“In classical physics, we talk about currents flowing continuously, like water,” Das says. “At the nanoscale, your current is comprised of individual electrons, and it is discrete as opposed to continuous.”
In other words, if you were to look at water flowing through a pipe, you would discover that at the submicroscopic level it is made of molecules that are discrete from one another, like individual grains of sand.
The problem is that the super-small world of quantum mechanics is notoriously unpredictable. In fact, an electron at the quantum level has a few weird characteristics that stem from the fact that quantum mechanics is all about probabilities, not absolutes.
“An electron, from a quantum mechanical perspective, does not behave like it does in classic physics, where it always acts like a particle,” Das says. “Here, it acts like a particle some of the time and like a wave some of the time. It has wave-particle duality, and it becomes probabilistic, meaning you cannot say for sure that the electron is definitely here. It might have some probability of it being here, or some probability of it being there. That’s what makes quantum mechanics strange and confusing to the layperson.”
An adiabatic electron pumping system is complex, but Das describes it as a mechanism that manipulates the shape of the “quantum wavefunction” of an electron, by varying such things as voltage or a magnetic field at the nanoscale. Das is researching how to apply the pumping system to single electrons and also to pairs of “entangled” electrons in which one electron can affect another even when separated by vast distances.
He hopes that his research will ultimately lead to a dependable system of moving currents of electrons in a precisely controlled way without destroying their fragile quantum state, which is essential to powering quantum computers.
“Once we start using the wave nature of electrons and the probabilistic nature of quantum mechanics, we can potentially do certain computations tremendously faster,” he says.
At this point, quantum computers have not yet been built, although some experiments have been carried out. Research is being done at a frantic pace, however, as such systems would be invaluable to national security, Das says.
“All existing encryption systems are based upon the fact that we cannot crack them with the computers that we have available now,” says Das. “With a quantum mechanical algorithm, you could crack encryption methods very fast.”
There are also potential applications to teleportation, Das says, but not of the Star Trek variety—at least not yet.
What you could teleport is the state of an electron,” he says. “We could transfer those properties to a location which is far away, but not the physical object itself. So, in a sense, in quantum mechanics, you can be in two places at the same time.”


Physicists were stunned when two twisted sheets of graphene showed signs of superconductivity. Now Stanford scientists have shown that the wonder material also generates a type of magnetism once only dreamed of theoretically.
By Ker Than
Sometimes the best discoveries happen when scientists least expect it. While trying to replicate another team’s finding, Stanford physicists recently stumbled upon a novel form of magnetism, predicted but never seen before, that is generated when two honeycomb-shaped lattices of carbon are carefully stacked and rotated to a special angle.
The authors suggest the magnetism, called orbital ferromagnetism, could prove useful for certain applications, such as quantum computing. The group describes their finding in the July 25 issue of the journal Science.
“We were not aiming for magnetism. We found what may be the most exciting thing in my career to date through partially targeted and partially accidental exploration,” said study leader David Goldhaber-Gordon, a professor of physics at Stanford’s School of Humanities and Sciences. “Our discovery shows that the most interesting things turn out to be surprises sometimes.”
The Stanford researchers inadvertently made their discovery while trying to reproduce a finding that was sending shockwaves through the physics community. In early 2018, Pablo Jarillo-Herrero’s group at MIT announced that they had coaxed a stack of two subtly misaligned sheets of carbon atoms – twisted bilayer graphene – to conduct electricity without resistance, a property known as superconductivity.
The discovery was a stunning confirmation of a nearly decade-old prediction that graphene sheets rotated to a very particular angle should exhibit interesting phenomena.
When stacked and twisted, graphene forms a superlattice with a repeating interference, or moiré, pattern. “It’s like when you play two musical tones that are slightly different frequencies,” Goldhaber-Gordon said. “You’ll get a beat between the two that’s related to the difference between their frequencies. That’s similar to what you get if you stack two lattices atop each other and twist them so they’re not perfectly aligned.”
Physicists theorized that the particular superlattice formed when graphene rotated to 1.1 degrees causes the normally varied energy states of electrons in the material to collapse, creating what they call a flat band where the speed at which electrons move drops to nearly zero. Thus slowed, the motions of any one electron becomes highly dependent on those of others in its vicinity. These interactions lie at the heart of many exotic quantum states of matter.
“I thought the discovery of superconductivity in this system was amazing. It was more than anyone had a right to expect,” Goldhaber-Gordon said. “But I also felt that there was a lot more to explore and many more questions to answer, so we set out to try to reproduce the work and then see how we could build upon it.”
A series of fortunate events
While attempting to duplicate the MIT team’s results, Goldhaber-Gordon and his group introduced two seemingly unimportant changes.
First, while encapsulating the honeycomb-shaped carbon lattices in thin layers of hexagonal boron nitride, the researchers inadvertently rotated one of the protective layers into near alignment with the twisted bilayer graphene.
“It turns out that if you nearly align the boron nitride lattice with the lattice of the graphene, you dramatically change the electrical properties of the twisted bilayer graphene,” said study co-first author Aaron Sharpe, a graduate student in Goldhaber-Gordon’s lab.
Secondly, the group intentionally overshot the angle of rotation between the two graphene sheets. Instead of 1.1 degrees, they aimed for 1.17 degrees because others had recently shown that twisted graphene sheets tend to settle into smaller angles during the manufacturing process.
“We figured if we aim for 1.17 degrees, then it will go back toward 1.1 degrees, and we’ll be happy,” Goldhaber-Gordon said. “Instead, we got 1.2 degrees.”
An anomalous signal
The consequences of these small changes didn’t become apparent until the Stanford researchers began testing the properties of their twisted graphene sample. In particular, they wanted to study how its magnetic properties changed as its flat band – that collection of states where electrons slow to nearly zero – was filled or emptied of electrons.
While pumping electrons into a sample that had been cooled close to absolute zero, Sharpe detected a large electrical voltage perpendicular to the flow of the current when the flat band was three-quarters full. Known as a Hall voltage, such a voltage typically only appears in the presence of an external magnetic field – but in this case, the voltage persisted even after the external magnetic field had been switched off.
This anomalous Hall effect could only be explained if the graphene sample was generating its own internal magnetic field. Furthermore, this magnetic field couldn’t be the result of aligning the up or down spin state of electrons, as is typically the case for magnetic materials, but instead must have arisen from their coordinated orbital motions.
“To our knowledge, this is the first known example of orbital ferromagnetism in a material,” Goldhaber-Gordon said. “If the magnetism were due to spin polarization, you wouldn’t expect to see a Hall effect. We not only see a Hall effect, but a huge Hall effect.”
Strength in weakness
The researchers estimate that the magnetic field near the surface of their twisted graphene sample is about a million times weaker than that of a conventional refrigerator magnet, but this weakness could be a strength in certain scenarios, such as building memory for quantum computers.
“Our magnetic bilayer graphene can be switched on with very low power and can be read electronically very easily,” Goldhaber-Gordon said. “The fact that there’s not a large magnetic field extending outward from the material means you can pack magnetic bits very close together without worrying about interference.”
Goldhaber-Gordon’s lab isn’t done exploring twisted bilayer graphene yet. The group plans to make more samples using recently improved fabrication techniques in order to further investigate the orbital magnetism.


In a simple experiment, when a pair of flashlights is shone in a dark room such that their light beams cross each other, does one notice anything strange? The rather anticlimactic answer is maybe not. The reason for this is the individual photons that make up light merely pass each other by – similar to indifferent spirits in the night – and do not interact in any way.
However, what will happen if light particles are allowed to interact, repelling and attracting each other similar to atoms in ordinary matter? Light sabers provide one interesting, although sci-fi possibility. These are beams of light that are capable of pulling and pushing on each other, making for stunning, epic confrontations. Or, in a more likely case, two light beams could meet and combine into a single, luminous stream.
This would mean that the rules of physics may need to be tweaked to realize such optical behavior, but actually, researchers at Harvard University, MIT, and elsewhere, have now shown that photons can certainly be made to interact — a major breakthrough that could pave the way for applying photons in quantum computing, if not in light sabers.
The research team, headed by Vladan Vuletic, the Lester Wolfe Professor of Physics at MIT, and Professor Mikhail Lukin from Harvard University, published the results of the study in the Science journal. The scientists reported that they have viewed groups of three photons interacting and, in effect, binding together to create an entirely new kind of photonic matter.
During controlled experiments, the team observed that when a very weak laser beam is shone via a dense cloud of ultracold rubidium atoms, the photons stick together in triplets or pairs instead of exiting the cloud as single, arbitrarily spaced photons. This indicates that some kind of interaction — in this case, attraction — is occurring among them.
Usually, photons lack mass and can travel at 300,000 kilometers per second (the speed of light), the research team noted that the bound photons have in fact attained a fraction of an electron’s mass. The newly weighed-down light particles were also quite sluggish, and compared to normal non-interacting photons, travel about 100,000 times slower.
According to Vuletic, the results show that photons can certainly entangle, or attract, each other. If the photons can be made to interact in other different ways, they may be harnessed to perform very fast, extraordinarily complex quantum computations.
“The interaction of individual photons has been a very long dream for decades,” Vuletic says.
Co-authors of Vuletic include Sergio Cantu, Qi-Yung Liang, and Travis Nicholson from MIT, Aditya Venkatramani and Lukin of Harvard University, Alexey Gorshkov and Michael Gullans of the University of Maryland, Cheng Ching of the University of Chicago, and Jeff Thompson from Princeton University.
The MIT-Harvard Center for Ultracold Atoms is headed by Vuletic and Lukin and together they have been exploring ways – both experimental and theoretical – to promote interactions between photons. The effort finally paid off in 2013, because for the first time, the scientists observed the interaction and binding between pairs of photons, producing a whole new state of matter. In their latest study, the team wondered if interactions could occur between not just two photons, but more.
For example, you can combine oxygen molecules to form O2 and O3 (ozone), but not O4, and for some molecules you can’t form even a three-particle molecule. So it was an open question: Can you add more photons to a molecule to make bigger and bigger things?
In order to find out, the researchers used the same experimental method which they utilized to observe the interactions between two photons. In this process, a cloud of rubidium atoms is first cooled to ultracold temperatures, i.e., just a millionth of a degree above absolute zero. When the atoms are cooled, they slow down to a near standstill. The researchers then shone an extremely weak laser beam through this cloud of immobilized atoms — the laser beam was so weak that only a handful of photons were able to pass through the cloud at any single time. They then determined the photons as they exit the other side of the atom cloud.
In the latest experiment, it was observed that the photons streamed out as triplets and pairs, instead of coming out of the cloud at haphazard intervals, since single photons have nothing to do with each other.
Besides tracking the rate and number of photons, the researchers measured the photons’ phase, both before and after passing through the cloud of immobilized atoms. The phase of a photon suggests its frequency of oscillation.
“The phase tells you how strongly they’re interacting, and the larger the phase, the stronger they are bound together,” Venkatramani explains. The researchers noted that when three-photon particles simultaneously exited the atom cloud, their phase was moved compared to what it was before when there was no interaction between the photons, and was in fact three times larger than the phase shift of two-photon particles.
“This means these photons are not just each of them independently interacting, but they’re all together interacting strongly.”
The team then came up with a theory to describe what might have made the photons to interact in the first place. The researchers’ model, based on physical principles, presents the following scenario: As one photon moves via the cloud of rubidium atoms, it shortly lands on an adjoining atom prior to skipping to next atom, similar to a bee flitting from one flower to another, until it comes to the other end.
Similarly, if another photon is concurrently traveling through the cloud of rubidium atoms, it can also briefly land on a rubidium atom and form a polariton, a hybrid that is part atom and part photon. The two polaritons can then interact with each other through their atomic component. The atoms remain where they are at the edge of the cloud, whilst the photons exit, still bound together. The team noted that this same phenomenon can take place with three photons, producing an even stronger bond than the two-photon interactions.
“What was interesting was that these triplets formed at all,” Vuletic says. “It was also not known whether they would be equally, less, or more strongly bound compared with photon pairs.”
The whole interaction inside the atom cloud takes place over a millionth of a second, and this interaction activates the photons to stay bound together, even after they have exited the cloud.
“What’s neat about this is, when photons go through the medium, anything that happens in the medium, they ‘remember’ when they get out,” Cantu says.
This means that photons that have interacted with one another, in this case via an attraction between them, can be believed to be as strongly entangled, or correlated — an important property for any quantum computing bit.
Photons can travel very fast over long distances, and people have been using light to transmit information, such as in optical fibers. If photons can influence one another, then if you can entangle these photons, and we’ve done that, you can use them to distribute quantum information in an interesting and useful way.
In the future, the researchers will investigate ways to force other interactions, for example, repulsion, where photons might scatter off each other similar to billiard balls.
“It’s completely novel in the sense that we don’t even know sometimes qualitatively what to expect,” Vuletic says. “With repulsion of photons, can they be such that they form a regular pattern, like a crystal of light? Or will something else happen? It’s very uncharted territory.”
The National Science Foundation partly supported the research.


Table Of Contents
Quantum Computing is the breakthrough technology that is growing at a fast pace. Today, each passing day it sees new development and the day will not be too far when you will be able to purchase Quantum computers from the market. But, in today’s date, nothing can be said about this technology development. Read more>
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Quantum Computing & Challenges to Develop Quantum Computers
What is Quantum Computing?
The physics at microscopic levels of atoms or subatomic particles is completely different as compared at macroscopic levels. At those small scales, or at quantum levels, the concept of dual nature comes into play. Dual nature refers to the existence of both particle nature and wave nature, for example, an electron can exhibit both particle nature as well as wave nature. The branch of physics which deals at these smallest scales is termed as Quantum physics. The computation that can be done exploiting concepts of quantum physics is termed as Quantum computing. Quantum computing started with Richard Feynman and afterward many scientists contributed to the development of Quantum computing.
The computers you use nowadays use classical physics concept, i.e. the physics at macroscopic or large levels. At macroscopic levels, the physics is much simpler and the algorithms used in computers for calculations uses general physics laws – Newton laws, Maxwell equations etc. But, at the quantum level, these classical laws and equations fails and are not valid. This is because of the appearance of Planck’s constant in quantum equations and an increase of the uncertainty at microscopic levels. Now, you can imagine how difficult it is to solve quantum problems.
How do Quantum Computers Work?
In digital electronics, you must have studied bits, i.e. 0 and 1. The classical computers, that you use today are completely based on these bits for calculation and all processes or tasks completed by them. ‘0’ means the electrical signal is ‘OFF’ and ‘1’ means the electrical signal is ‘ON’. Similarly, Qubits are the quantum bits which help in quantum computing.
What are the Qubits?
Qubits are bits ‘0’, ‘1’ with a coherent superposition of 0 and 1. The superposition concept comes into play because of the wave nature at the smallest scale. This can be explained with the help of electron spin. The electron has two spins – spin up and spin down. Spin up refers to classical bit ‘0’ and spin down refers to classical bit ‘1’. But, quantum allows them another state also, i.e. superposition of 0 and 1.
Quantum computers work with Qubits but as you can see above, as the number of Qubits increases, it becomes more and more difficult to reach to the solution of a computation problem. The external environment also disturbs the system, therefore Quantum computing becomes almost impossible. The state of the computer become unpredictable due to this, which is called as Decoherence.
Also, if we try to calculate the state of one particle in a two-particle system. Consequently, the state of another particle gets affected due to interactions between the particles. This phenomenon is termed as Quantum Entanglement.
Unlike, Classical computers that we use today, we cannot manufacture Quantum computers using Transistors and Diodes. You can say this is a big problem in the manufacture of Quantum computers. But, there are other technologies which can solve this problem. One such technology is to use Quantum dots in the manufacture of Quantum computers. In Quantum dots, a single electron is trapped in between the atoms which looks like a cage of atoms.
What are the challenges in Quantum Computing & to Develop Quantum Computers?
There are several challenges in the field of Quantum computing. Also, there are many problems which need to be solved to help Quantum computers not remain confined to a few big laboratories. These are –
- Decoherence Prevention.
- Research on Quantum Algorithms that Increase the speed of Quantum Computers.
- To create quantum computers portable – In Today’s date, the size of the Quantum computers is too large that it can only be used in big laboratories.
- Quantum Error Correction.
- Designing of better Quantum circuitry.
- A search of other technologies to manufacture Quantum computers.
- Designing better processors to store more Qubits.
Do Quantum Computers Exist and Where?
Yes, Quantum Computers exist but it is only confined to big laboratories for research and development purposes. The big names in Quantum computers manufacturers are – IBM, D-Wave systems, and Google. Recently this year, in 2018, Google get a lead in the development of 72 Qubit Processor which is the best Qubit Processor till now. Previously, the highest processor that could store Qubits is 20 Qubits processor which was developed by IBM. But, now its Google’s 72 Qubit Processor which they named Bristlecone.
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A team of researchers from MIT, Google, the University of Sydney, and Cornell University present a new quantum error correcting code that requires measurements of only a few quantum bits at a time to ensure consistency between one stage of a computation and the next.
Quantum computers are largely theoretical devices that could perform some computations exponentially faster than conventional computers can. Crucial to most designs for quantum computers is quantum error correction, which helps preserve the fragile quantum states on which quantum computation depends.
The ideal quantum error correction code would correct any errors in quantum data, and it would require measurement of only a few quantum bits, or qubits, at a time. But until now, codes that could make do with limited measurements could correct only a limited number of errors — one roughly equal to the square root of the total number of qubits. So they could correct eight errors in a 64-qubit quantum computer, for instance, but not 10.
In a paper they’re presenting at the Association for Computing Machinery’s Symposium on Theory of Computing in June, researchers from MIT, Google, the University of Sydney, and Cornell University present a new code that can correct errors afflicting — almost — a specified fraction of a computer’s qubits, not just the square root of their number. And for reasonably sized quantum computers, that fraction can be arbitrarily large — although the larger it is, the more qubits the computer requires.
“There were many, many different proposals, all of which seemed to get stuck at this square-root point,” says Aram Harrow, an assistant professor of physics at MIT, who led the research. “So going above that is one of the reasons we’re excited about this work.”
Like a bit in a conventional computer, a qubit can represent 1 or 0, but it can also inhabit a state known as “quantum superposition,” where it represents 1 and 0 simultaneously. This is the reason for quantum computers’ potential advantages: A string of qubits in superposition could, in some sense, perform a huge number of computations in parallel.
Once you perform a measurement on the qubits, however, the superposition collapses, and the qubits take on definite values. The key to quantum algorithm design is manipulating the quantum state of the qubits so that when the superposition collapses, the result is (with high probability) the solution to a problem.
But the need to preserve superposition makes error correction difficult. “People thought that error correction was impossible in the ’90s,” Harrow explains. “It seemed that to figure out what the error was you had to measure, and measurement destroys your quantum information.”
The first quantum error correction code was invented in 1994 by Peter Shor, now the Morss Professor of Applied Mathematics at MIT, with an office just down the hall from Harrow’s. Shor is also responsible for the theoretical result that put quantum computing on the map, an algorithm that would enable a quantum computer to factor large numbers exponentially faster than a conventional computer can. In fact, his error-correction code was a response to skepticism about the feasibility of implementing his factoring algorithm.
Shor’s insight was that it’s possible to measure relationships between qubits without measuring the values stored by the qubits themselves. A simple error-correcting code could, for instance, instantiate a single qubit of data as three physical qubits. It’s possible to determine whether the first and second qubit have the same value, and whether the second and third qubit have the same value, without determining what that value is. If one of the qubits turns out to disagree with the other two, it can be reset to their value.
In quantum error correction, Harrow explains, “These measurement always have the form ‘Does A disagree with B?’ Except it might be, instead of A and B, A B C D E F G, a whole block of things. Those types of measurements, in a real system, can be very hard to do. That’s why it’s really desirable to reduce the number of qubits you have to measure at once.”
A quantum computation is a succession of states of quantum bits. The bits are in some state; then they’re modified, so that they assume another state; then they’re modified again; and so on. The final state represents the result of the computation.
In their paper, Harrow and his colleagues assign each state of the computation its own bank of qubits; it’s like turning the time dimension of the computation into a spatial dimension. Suppose that the state of qubit 8 at time 5 has implications for the states of both qubit 8 and qubit 11 at time 6. The researchers’ protocol performs one of those agreement measurements on all three qubits, modifying the state of any qubit that’s out of alignment with the other two.
Since the measurement doesn’t reveal the state of any of the qubits, modification of a misaligned qubit could actually introduce an error where none existed previously. But that’s by design: The purpose of the protocol is to ensure that errors spread through the qubits in a lawful way. That way, measurements made on the final state of the qubits are guaranteed to reveal relationships between qubits without revealing their values. If an error is detected, the protocol can trace it back to its origin and correct it.
It may be possible to implement the researchers’ scheme without actually duplicating banks of qubits. But, Harrow says, some redundancy in the hardware will probably be necessary to make the scheme efficient. How much redundancy remains to be seen: Certainly, if each state of a computation required its own bank of qubits, the computer might become so complex as to offset the advantages of good error correction.
But, Harrow says, “Almost all of the sparse schemes started out with not very many logical qubits, and then people figured out how to get a lot more. Usually, it’s been easier to increase the number of logical qubits than to increase the distance — the number of errors you can correct. So we’re hoping that will be the case for ours, too.”
Stephen Bartlett, a physics professor at the University of Sydney who studies quantum computing, doesn’t find the additional qubits required by Harrow and his colleagues’ scheme particularly daunting.
“It looks like a lot,” Bartlett says, “but compared with existing structures, it’s a massive reduction. So one of the highlights of this construction is that they actually got that down a lot.”
“People had all of these examples of codes that were pretty bad, limited by that square root ‘N,’” Bartlett adds. “But people try to put bounds on what may be possible, and those bounds suggested that maybe you could do way better. But we didn’t have constructive examples of getting here. And that’s what’s really got people excited. We know we can get there now, and it’s now a matter of making it a bit more practical.”
PDF Copy of the Study: Sparse Quantum Codes from Quantum Circuits
Image: Jose-Luis Olivares/MIT


Quantum Internet can be used to send messages that cannot be hacked, increase GPS accuracy and enable cloud quantum computing. For more than twenty years, dreams of creating such a quantum network have remained largely unattainable due to the difficulty of sending quantum signals over long distances without loss.
Now, researchers at Harvard and the Massachusetts Institute of Technology have found a way to fix signal loss with a prototype quantum node that can capture, store, and confuse bits of quantum information. Research is the missing link to practical quantum internet and an important step forward in the development of distant quantum networks.
“This demonstration is a conceptual breakthrough that can expand the maximum possible range of quantum networks and potentially open many new applications in a way that is impossible using any existing technologies,” said Mikhail Lukin, professor of physics named after George Fasmer Leverett and co-director of the Harvard Quantum Initiative. “This is the realization of the goal that was achieved by our quantum science and the engineering community for over two decades. "
Study published in Nature,
All types of communication technologies – from the first telegraph to the modern fiber-optic Internet – should have taken into account the fact that signals deteriorate and are lost when transmitting over long distances. The first transponders that receive and amplify signals to correct this loss were designed to amplify telegraph signals with wire fading in the mid-1800s. Two hundred years later, repeaters are an integral part of our long-distance communications infrastructure.
In a classic network, if Alice in New York wants to send Bob a message in California, the message moves from coast to coast more or less in a straight line. Along the way, the signal passes through repeaters, where it is read, amplified, and corrected for errors. The whole process is vulnerable to attacks at any time.
However, if Alice wants to send a quantum message, the process will be different. Quantum networks use quantum particles of light – individual photons – to transmit quantum states of light over long distances. These networks have a trick that classical systems do not have: entanglement.
Obfuscation – what Einstein called "eerie action at a distance" – allows bits of information to be perfectly correlated at any distance. Since quantum systems cannot be observed without change, Alice could use entanglement to tell Bob without fear of eavesdroppers. This concept is the basis for applications such as quantum cryptography – security, which is guaranteed by the laws of quantum physics.
However, long-distance quantum communication is also affected by the usual loss of photons, which is one of the main obstacles to the implementation of large-scale quantum Internet. But the same physical principle that makes quantum communication super-safe also makes it impossible to use existing classical repeaters to eliminate information loss.
How can you amplify and correct a signal if you cannot read it? The solution to this seemingly impossible task involves the so-called quantum repeater. Unlike classical repeaters, which amplify a signal through an existing network, quantum repeaters create a network of entangled particles through which a message can be transmitted.
In essence, a quantum repeater is a small specialized quantum computer. At each stage of such a network, quantum repeaters should be able to capture and process the quantum bits of quantum information to correct errors and store them long enough for the rest of network be ready. Until now, this has been impossible for two reasons: firstly, single photons are very difficult to capture. Secondly, quantum information is notoriously fragile, which makes it very difficult to process and store for long periods of time.
Lukin Laboratory, in collaboration with Marco Loncar, Professor of Electrical Engineering Tiancai Lin at the Harvard School of Engineering and Applied Sciences John A. Paulson (SEAS),
Hongkun Park, Mark Hyman Jr., professor of chemistry at Harvard School of Arts and Sciences (FAS), and Dirk Englund, associate professor of electrical engineering and computer science at the Massachusetts Institute of Technology (MIT), are working to use a system that can both perform well. tasks are silicon vacancies of color centers in diamonds.
These centers are tiny defects in the atomic structure of diamond that can absorb and emit light, causing the brilliant colors of diamond.
“Over the past few years, our laboratories have worked to understand and control individual silicon color centers, especially how to use them as quantum memory devices for single photons,” said Mihir Bhaskar, a graduate student of the Lukina group.
Researchers have integrated a separate color center into the cavity of a diamond nanotube, which limits information photons and forces them to interact with a single color center. They then placed the device in a dilution refrigerator, which reaches a temperature close to absolute zero, and sent individual photons via fiber optic cables to the refrigerator, where they were effectively captured and caught by the center of color.
A device can store quantum information in milliseconds — long enough to transmit information over thousands of kilometers. Electrodes embedded around the cavity were used to supply control signals for processing and storing information stored in memory.
“This device combines the three most important elements of a quantum repeater – long memory, the ability to efficiently capture information from photons and the way it is processed locally,” said Bart Machielse, a graduate student at the Laboratory for Nanoscale Optics. "Each of these problems was resolved separately, but not one device combined all three."
“We are currently working on expanding this study by incorporating our quantum memories into real urban fiber optic channels,” said Ralph Reading, Ph.D. in Lukin’s group. “We plan to create large networks of entangled quantum memories and explore the first applications of quantum Internet.”
“This is the first demonstration at the system level, combining the main achievements in the field of nanotechnology, photonics and quantum control, which demonstrates a clear quantum advantage in the transmission of information using quantum repeater nodes. We look forward to exploring new unique applications using these methods, ”Lukin said.
Experimental memory demonstration of enhanced quantum communication, Nature (2020). DOI: 10.1038 / s41586-020-2103-5 https://nature.com/articles/s41586-020-2103-5
Researchers Demonstrate Missing Link For Quantum Internet (2020, March 23)
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Physicists have theorized that a new type of material, called a three-dimensional (3D) topological insulator (TI), could be a good candidate from which to create qubits that will be resilient from these errors and protected from losing their quantum information. This material has both an insulating interior and metallic top and bottom surfaces that conduct electricity. The most important property of 3D topological insulators is that the conductive surfaces are predicted to be protected from the influence of the surroundings. Few studies exist that have experimentally tested how TIs behave in real life.
A new study from the University of Utah found that in fact, when the insulating layers are as thin as 16 quintuple atomic layers across, the top and bottom metallic surfaces begin to influence each other and destroy their metallic properties. The experiment demonstrates that the opposite surfaces begin influencing each other at a much thicker insulating interior than previous studies had shown, possibly approaching a rare theoretical phenomenon in which the metallic surfaces also become insulating as the interior thins out.
"Topological insulators could be an important material in future quantum computing. Our findings have uncovered a new limitation in this system", stated Vikram Deshpande, assistant professor of physics at the University of Utah and corresponding author of the study. "People working with topological insulators need to know what their limits are. It turns out that as you approach that limit, when these surfaces start 'talking' to each other, new physics shows up, which is also pretty cool by itself."
The new study published on July 16, 2019 in the journal Physics Review Letters .
Imagine a hardcover textbook as a 3D topological insulator, Vikram Deshpande said. The bulk of the book are the pages, which is an insulator layer - it can't conduct electricity. The hardcovers themselves represent the metallic surfaces. Ten years ago, physicists discovered that these surfaces could conduct electricity, and a new topological field was born.
Vikram Deshpande and his team created devices using 3D TIs by stacking five few-atom-thin layers of various materials into sloppy sandwich-like structures. The bulk core of the sandwich is the topological insulator, made from a few quintuple layers of bismuth antimony tellurium selenide (Bi2-xSbxTe3-ySey). This core is sandwiched by a few layers of boron nitride, and is topped off with two layers of graphite, above and below. The graphite works like metallic gates, essentially creating two transistors that control conductivity. Last year Vikram Deshpande led a study that showed that this topological recipe built a device that behaved like you would expect - bulk insulators that protect the metallic surfaces from the surrounding environment.
In this study, they manipulated the 3D TI devices to see how the properties changed. First, they built van der Waal heterostructures - those sloppy sandwiches - and exposed them to a magnetic field. Vikram Deshpande's team tested many at his lab at the University of Utah and first author Su Kong Chong, doctoral candidate at the U, traveled to the National High Magnetic Field Lab in Tallahassee to perform the same experiments there using one of the highest magnetic fields in the country. In the presence of the magnetic field, a checkerboard pattern emerged from the metallic surfaces, showing the pathways by which electrical current will move on the surface. The checkerboards, consisting of quantized conductivities versus voltages on the two gates, are well-defined, with the grid intersecting at neat intersection points, allowing the researchers to track any distortion on the surface.
They began with the insulator layer at 100 nanometers thick, about a thousandth of the diameter of a human hair, and progressively got thinner down to 10 nanometers. The pattern started distorting until the insulator layer was at 16 nanometers thick, when the intersection points began to break up, creating a gap that indicated that the surfaces were no longer conductive.
"Essentially, we've made something that was metallic into something insulating in that parameter space. The point of this experiment is that we can controllably change the interaction between these surfaces", stated Vikram Deshpande. "We start out with them being completely independent and metallic, and then start getting them closer and closer until they start 'talking', and when they're really close, they are essentially gapped out and become insulating."
Previous experiments in 2010 and 2012 had also observed the energy gap on the metallic surfaces as the insulating material thins out. But those studies concluded that the energy gap appeared with much thinner insulating layers - five nanometers in size. This study observed the metallic surface properties break down at much larger interior thickness, up to 16 nanometers. The other experiments used different "surface science" methods where they observed the materials through a microscope with a very sharp metallic tip to look at every atom individually or studied them with highly energetic light.
"These were extremely involved experiments which are pretty far removed from the device-creation that we are doing", stated Vikram Deshpande.
Next, Vikram Deshpande and the team will look more closely into the physics creating that energy gap on the surfaces. He predicts that these gaps can be positive or negative depending on material thickness.
Other authors who contributed to the study are Kyu Bum Han and Taylor Sparks from the University's Department of Materials Science and Engineering.


Results are first to suggest how to engineer even warmer superconductors with atom-by-atom control
A study at the Department of Energy’s SLAC National Accelerator Laboratory suggests for the first time how scientists might deliberately engineer superconductors that work at higher temperatures.
In their report, a team led by SLAC and Stanford University researchers explains why a thin layer of iron selenide superconducts — carries electricity with 100 percent efficiency — at much higher temperatures when placed atop another material, which is called STO for its main ingredients strontium, titanium and oxygen.
These findings, described today in the journal Nature, open a new chapter in the 30-year quest to develop superconductors that operate at room temperature, which could revolutionize society by making virtually everything that runs on electricity much more efficient. Although today’s high-temperature superconductors operate at much warmer temperatures than conventional superconductors do, they still work only when chilled to minus 135 degrees Celsius or below.
In the new study, the scientists concluded that natural trillion-times-per-second vibrations in the STO travel up into the iron selenide film in distinct packets, like volleys of water droplets shaken off by a wet dog. These vibrations give electrons the energy they need to pair up and superconduct at higher temperatures than they would on their own.
“Our simulations indicate that this approach – using natural vibrations in one material to boost superconductivity in another – could be used to raise the operating temperature of iron-based superconductors by at least 50 percent,” said Zhi-Xun Shen, a professor at SLAC and Stanford University and senior author of the study.
While that’s still nowhere close to room temperature, he added, “We now have the first example of a mechanism that could be used to engineer high-temperature superconductors with atom-by-atom control and make them better.”
Spying on Electrons
The study probed a happy combination of materials developed two years ago by scientists in China. They discovered that when a single layer of iron selenide film is placed atop STO, its maximum superconducting temperature shoots up from 8 degrees to nearly 77 degrees above absolute zero (minus 196 degrees Celsius).
While this was a huge and welcome leap, it would be hard to build on this advance without understanding what, exactly, was going on.
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