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Over the past century, quantum field theory has proved to be the single most sweeping and successful physical theory ever invented. It is an umbrella term that encompasses many specific quantum field theories the way shape covers specific examples like the square and the circle. The most prominent of these theories is known as the Standard Model, and it is this framework of physics that has been so successful.

It can explain at a fundamental level literally every single experiment that weve ever done, said David Tong, a physicist at the University of Cambridge.

But quantum field theory, or QFT, is indisputably incomplete. Neither physicists nor mathematicians know exactly what makes a quantum field theory a quantum field theory. They have glimpses of the full picture, but they cant yet make it out.

There are various indications that there could be a better way of thinking about QFT, said Nathan Seiberg, a physicist at the Institute for Advanced Study. It feels like its an animal you can touch from many places, but you dont quite see the whole animal.

Mathematics, which requires internal consistency and attention to every last detail, is the language that might make QFT whole. If mathematics can learn how to describe QFT with the same rigor with which it characterizes well-established mathematical objects, a more complete picture of the physical world will likely come along for the ride.

If you really understood quantum field theory in a proper mathematical way, this would give us answers to many open physics problems, perhaps even including the quantization of gravity, said Robbert Dijkgraaf, director of the Institute for Advanced Study (and a regular columnist for Quanta).

Nor is this a one-way street. For millennia, the physical world has been mathematics greatest muse. The ancient Greeks invented trigonometry to study the motion of the stars. Mathematics turned it into a discipline with definitions and rules that students now learn without any reference to the topics celestial origins. Almost 2,000 years later, Isaac Newton wanted to understand Keplers laws of planetary motion and attempted to find a rigorous way of thinking about infinitesimal change. This impulse (along with revelations from Gottfried Leibniz) birthed the field of calculus, which mathematics appropriated and improved and today could hardly exist without.

Now mathematicians want to do the same for QFT, taking the ideas, objects and techniques that physicists have developed to study fundamental particles and incorporating them into the main body of mathematics. This means defining the basic traits of QFT so that future mathematicians wont have to think about the physical context in which the theory first arose.

The rewards are likely to be great: Mathematics grows when it finds new objects to explore and new structures that capture some of the most important relationships between numbers, equations and shapes. QFT offers both.

Physics itself, as a structure, is extremely deep and often a better way to think about mathematical things were already interested in. Its just a better way to organize them, said David Ben-Zvi, a mathematician at the University of Texas, Austin.

For 40 years at least, QFT has tempted mathematicians with ideas to pursue. In recent years, theyve finally begun to understand some of the basic objects in QFT itself abstracting them from the world of particle physics and turning them into mathematical objects in their own right.

Yet its still early days in the effort.

We wont know until we get there, but its certainly my expectation that were just seeing the tip of the iceberg, said Greg Moore, a physicist at Rutgers University. If mathematicians really understood [QFT], that would lead to profound advances in mathematics.

Its common to think of the universe as being built from fundamental particles: electrons, quarks, photons and the like. But physics long ago moved beyond this view. Instead of particles, physicists now talk about things called quantum fields as the real warp and woof of reality.

These fields stretch across the space-time of the universe. They come in many varieties and fluctuate like a rolling ocean. As the fields ripple and interact with each other, particles emerge out of them and then vanish back into them, like the fleeting crests of a wave.

Particles are not objects that are there forever, said Tong. Its a dance of fields.

To understand quantum fields, its easiest to start with an ordinary, or classical, field. Imagine, for example, measuring the temperature at every point on Earths surface. Combining the infinitely many points at which you can make these measurements forms a geometric object, called a field, that packages together all this temperature information.

In general, fields emerge whenever you have some quantity that can be measured uniquely at infinitely fine resolution across a space. Youre sort of able to ask independent questions about each point of space-time, like, whats the electric field here versus over there, said Davide Gaiotto, a physicist at the Perimeter Institutefor Theoretical Physics in Waterloo, Canada.

Quantum fields come about when youre observing quantum phenomena, like the energy of an electron, at every point in space and time. But quantum fields are fundamentally different from classical ones.

While the temperature at a point on Earth is what it is, regardless of whether you measure it, electrons have no definite position until the moment you observe them. Prior to that, their positions can only be described probabilistically, by assigning values to every point in a quantum field that captures the likelihood youll find an electron there versus somewhere else. Prior to observation, electrons essentially exist nowhere and everywhere.

Most things in physics arent just objects; theyre something that lives in every point in space and time, said Dijkgraaf.

A quantum field theory comes with a set of rules called correlation functions that explain how measurements at one point in a field relate to or correlate with measurements taken at another point.

Each quantum field theory describes physics in a specific number of dimensions. Two-dimensional quantum field theories are often useful for describing the behavior of materials, like insulators; six-dimensional quantum field theories are especially relevant to string theory; and four-dimensional quantum field theories describe physics in our actual four-dimensional universe. The Standard Model is one of these; its the single most important quantum field theory because its the one that best describes the universe.

There are 12 known fundamental particles that make up the universe. Each has its own unique quantum field. To these 12 particle fields the Standard Model adds four force fields, representing the four fundamental forces: gravity, electromagnetism, the strong nuclear force and the weak nuclear force. It combines these 16 fields in a single equation that describes how they interact with each other. Through these interactions, fundamental particles are understood as fluctuations of their respective quantum fields, and the physical world emerges before our eyes.

It might sound strange, but physicists realized in the 1930s that physics based on fields, rather than particles, resolved some of their most pressing inconsistencies, ranging from issues regarding causality to the fact that particles dont live forever. It also explained what otherwise appeared to be an improbable consistency in the physical world.

All particles of the same type everywhere in the universe are the same, said Tong. If we go to the Large Hadron Collider and make a freshly minted proton, its exactly the same as one thats been traveling for 10 billion years. That deserves some explanation. QFT provides it: All protons are just fluctuations in the same underlying proton field (or, if you could look more closely, the underlying quark fields).

But the explanatory power of QFT comes at a high mathematical cost.

Quantum field theories are by far the most complicated objects in mathematics, to the point where mathematicians have no idea how to make sense of them, said Tong. Quantum field theory is mathematics that has not yet been invented by mathematicians.

What makes it so complicated for mathematicians? In a word, infinity.

When you measure a quantum field at a point, the result isnt a few numbers like coordinates and temperature. Instead, its a matrix, which is an array of numbers. And not just any matrix a big one, called an operator, with infinitely many columns and rows. This reflects how a quantum field envelops all the possibilities of a particle emerging from the field.

There are infinitely many positions that a particle can have, and this leads to the fact that the matrix that describes the measurement of position, of momentum, also has to be infinite-dimensional, said Kasia Rejzner of the University of York.

And when theories produce infinities, it calls their physical relevance into question, because infinity exists as a concept, not as anything experiments can ever measure. It also makes the theories hard to work with mathematically.

We dont like having a framework that spells out infinity. Thats why you start realizing you need a better mathematical understanding of whats going on, said Alejandra Castro, a physicist at the University of Amsterdam.

The problems with infinity get worse when physicists start thinking about how two quantum fields interact, as they might, for instance, when particle collisions are modeled at the Large Hadron Collider outside Geneva. In classical mechanics this type of calculation is easy: To model what happens when two billiard balls collide, just use the numbers specifying the momentum of each ball at the point of collision.

When two quantum fields interact, youd like to do a similar thing: multiply the infinite-dimensional operator for one field by the infinite-dimensional operator for the other at exactly the point in space-time where they meet. But this calculation multiplying two infinite-dimensional objects that are infinitely close together is difficult.

This is where things go terribly wrong, said Rejzner.

Physicists and mathematicians cant calculate using infinities, but they have developed workarounds ways of approximating quantities that dodge the problem. These workarounds yield approximate predictions, which are good enough, because experiments arent infinitely precise either.

We can do experiments and measure things to 13 decimal places and they agree to all 13 decimal places. Its the most astonishing thing in all of science, said Tong.

One workaround starts by imagining that you have a quantum field in which nothing is happening. In this setting called a free theory because its free of interactions you dont have to worry about multiplying infinite-dimensional matrices because nothings in motion and nothing ever collides. Its a situation thats easy to describe in full mathematical detail, though that description isnt worth a whole lot.

Its totally boring, because youve described a lonely field with nothing to interact with, so its a bit of an academic exercise, said Rejzner.

But you can make it more interesting. Physicists dial up the interactions, trying to maintain mathematical control of the picture as they make the interactions stronger.

This approach is called perturbative QFT, in the sense that you allow for small changes, or perturbations, in a free field. You can apply the perturbative perspective to quantum field theories that are similar to a free theory. Its also extremely useful for verifying experiments. You get amazing accuracy, amazing experimental agreement, said Rejzner.

But if you keep making the interactions stronger, the perturbative approach eventually overheats. Instead of producing increasingly accurate calculations that approach the real physical universe, it becomes less and less accurate. This suggests that while the perturbation method is a useful guide for experiments, ultimately its not the right way to try and describe the universe: Its practically useful, but theoretically shaky.

We do not know how to add everything up and get something sensible, said Gaiotto.

Another approximation scheme tries to sneak up on a full-fledged quantum field theory by other means. In theory, a quantum field contains infinitely fine-grained information. To cook up these fields, physicists start with a grid, or lattice, and restrict measurements to places where the lines of the lattice cross each other. So instead of being able to measure the quantum field everywhere, at first you can only measure it at select places a fixed distance apart.

From there, physicists enhance the resolution of the lattice, drawing the threads closer together to create a finer and finer weave. As it tightens, the number of points at which you can take measurements increases, approaching the idealized notion of a field where you can take measurements everywhere.

The distance between the points becomes very small, and such a thing becomes a continuous field, said Seiberg. In mathematical terms, they say the continuum quantum field is the limit of the tightening lattice.

Mathematicians are accustomed to working with limits and know how to establish that certain ones really exist. For example, theyve proved that the limit of the infinite sequence $latex frac{1}{2}$ +$latex frac{1}{4}$ +$latex frac{1}{8}$ +$latex frac{1}{16}$ is 1. Physicists would like to prove that quantum fields are the limit of this lattice procedure. They just dont know how.

Its not so clear how to take that limit and what it means mathematically, said Moore.

Physicists dont doubt that the tightening lattice is moving toward the idealized notion of a quantum field. The close fit between the predictions of QFT and experimental results strongly suggests thats the case.

There is no question that all these limits really exist, because the success of quantum field theory has been really stunning, said Seiberg. But having strong evidence that something is correct and proving conclusively that it is are two different things.

Its a degree of imprecision thats out of step with the other great physical theories that QFT aspires to supersede. Isaac Newtons laws of motion, quantum mechanics, Albert Einsteins theories of special and general relativity theyre all just pieces of the bigger story QFT wants to tell, but unlike QFT, they can all be written down in exact mathematical terms.

Quantum field theory emerged as an almost universal language of physical phenomena, but its in bad math shape, said Dijkgraaf. And for some physicists, thats a reason for pause.

If the full house is resting on this core concept that itself isnt understood in a mathematical way, why are you so confident this is describing the world? That sharpens the whole issue, said Dijkgraaf.

Even in this incomplete state, QFT has prompted a number of important mathematical discoveries. The general pattern of interaction has been that physicists using QFT stumble onto surprising calculations that mathematicians then try to explain.

Its an idea-generating machine, said Tong.

At a basic level, physical phenomena have a tight relationship with geometry. To take a simple example, if you set a ball in motion on a smooth surface, its trajectory will illuminate the shortest path between any two points, a property known as a geodesic. In this way, physical phenomena can detect geometric features of a shape.

Now replace the billiard ball with an electron. The electron exists probabilistically everywhere on a surface. By studying the quantum field that captures those probabilities, you can learn something about the overall nature of that surface (or manifold, to use the mathematicians term), like how many holes it has. Thats a fundamental question that mathematicians working in geometry, and the related field of topology, want to answer.

One particle even sitting there, doing nothing, will start to know about the topology of a manifold, said Tong.

In the late 1970s, physicists and mathematicians began applying this perspective to solve basic questions in geometry. By the early 1990s, Seiberg and his collaborator Edward Witten figured out how to use it to create a new mathematical tool now called the Seiberg-Witten invariants that turns quantum phenomena into an index for purely mathematical traits of a shape: Count the number of times quantum particles behave in a certain way, and youve effectively counted the number of holes in a shape.

Witten showed that quantum field theory gives completely unexpected but completely precise insights into geometrical questions, making intractable problems soluble, said Graeme Segal, a mathematician at the University of Oxford.

Another example of this exchange also occurred in the early 1990s, when physicists were doing calculations related to string theory. They performed them in two different geometric spaces based on fundamentally different mathematical rules and kept producing long sets of numbers that matched each other exactly. Mathematicians picked up the thread and elaborated it into a whole new field of inquiry, called mirror symmetry, that investigates the concurrence and many others like it.

Physics would come up with these amazing predictions, and mathematicians would try to prove them by our own means, said Ben-Zvi. The predictions were strange and wonderful, and they turned out to be pretty much always correct.

But while QFT has been successful at generating leads for mathematics to follow, its core ideas still exist almost entirely outside of mathematics. Quantum field theories are not objects that mathematicians understand well enough to use the way they can use polynomials, groups, manifolds and other pillars of the discipline (many of which also originated in physics).

For physicists, this distant relationship with math is a sign that theres a lot more they need to understand about the theory they birthed. Every other idea thats been used in physics over the past centuries had its natural place in mathematics, said Seiberg. This is clearly not the case with quantum field theory.

And for mathematicians, it seems as if the relationship between QFT and math should be deeper than the occasional interaction. Thats because quantum field theories contain many symmetries, or underlying structures, that dictate how points in different parts of a field relate to each other. These symmetries have a physical significance they embody how quantities like energy are conserved as quantum fields evolve over time. But theyre also mathematically interesting objects in their own right.

A mathematician might care about a certain symmetry, and we can put it in a physical context. It creates this beautiful bridge between these two fields, said Castro.

Mathematicians already use symmetries and other aspects of geometry to investigate everything from solutions to different types of equations to the distribution of prime numbers. Often, geometry encodes answers to questions about numbers. QFT offers mathematicians a rich new type of geometric object to play with if they can get their hands on it directly, theres no telling what theyll be able to do.

Were to some extent playing with QFT, said Dan Freed, a mathematician at the University of Texas, Austin. Weve been using QFT as an outside stimulus, but it would be nice if it were an inside stimulus.

Mathematics does not admit new subjects lightly. Many basic concepts went through long trials before they settled into their proper, canonical places in the field.

Take the real numbers all the infinitely many tick marks on the number line. It took math nearly 2,000 years of practice to agree on a way of defining them. Finally, in the 1850s, mathematicians settled on a precise three-word statement describing the real numbers as a complete ordered field. Theyre complete because they contain no gaps, theyre ordered because theres always a way of determining whether one real number is greater or less than another, and they form a field, which to mathematicians means they follow the rules of arithmetic.

Those three words are historically hard fought, said Freed.

In order to turn QFT into an inside stimulus a tool they can use for their own purposes mathematicians would like to give the same treatment to QFT they gave to the real numbers: a sharp list of characteristics that any specific quantum field theory needs to satisfy.

A lot of the work of translating parts of QFT into mathematics has come from a mathematician named Kevin Costello at the Perimeter Institute. In 2016 he coauthored a textbook that puts perturbative QFT on firm mathematical footing, including formalizing how to work with the infinite quantities that crop up as you increase the number of interactions. The work follows an earlier effort from the 2000s called algebraic quantum field theory that sought similar ends, and which Rejzner reviewed in a 2016 book. So now, while perturbative QFT still doesnt really describe the universe, mathematicians know how to deal with the physically non-sensical infinities it produces.

His contributions are extremely ingenious and insightful. He put [perturbative] theory in a nice new framework that is suitable for rigorous mathematics, said Moore.

Costello explains he wrote the book out of a desire to make perturbative quantum field theory more coherent. I just found certain physicists methods unmotivated and ad hoc. I wanted something more self-contained that a mathematician could go work with, he said.

By specifying exactly how perturbation theory works, Costello has created a basis upon which physicists and mathematicians can construct novel quantum field theories that satisfy the dictates of his perturbation approach. Its been quickly embraced by others in the field.

He certainly has a lot of young people working in that framework. [His book] has had its influence, said Freed.

Costello has also been working on defining just what a quantum field theory is. In stripped-down form, a quantum field theory requires a geometric space in which you can make observations at every point, combined with correlation functions that express how observations at different points relate to each other. Costellos work describes the properties a collection of correlation functions needs to have in order to serve as a workable basis for a quantum field theory.

The most familiar quantum field theories, like the Standard Model, contain additional features that may not be present in all quantum field theories. Quantum field theories that lack these features likely describe other, still undiscovered properties that could help physicists explain physical phenomena the Standard Model cant account for. If your idea of a quantum field theory is fixed too closely to the versions we already know about, youll have a hard time even envisioning the other, necessary possibilities.

There is a big lamppost under which you can find theories of fields [like the Standard Model], and around it is a big darkness of [quantum field theories] we dont know how to define, but we know theyre there, said Gaiotto.

Costello has illuminated some of that dark space with his definitions of quantum fields. From these definitions, hes discovered two surprising new quantum field theories. Neither describes our four-dimensional universe, but they do satisfy the core demands of a geometric space equipped with correlation functions. Their discovery through pure thought is similar to how the first shapes you might discover are ones present in the physical world, but once you have a general definition of a shape, you can think your way to examples with no physical relevance at all.

And if mathematics can determine the full space of possibilities for quantum field theories all the many different possibilities for satisfying a general definition involving correlation functions physicists can use that to find their way to the specific theories that explain the important physical questions they care most about.

I want to know the space of all QFTs because I want to know what quantum gravity is, said Castro.

Theres a long way to go. So far, all of the quantum field theories that have been described in full mathematical terms rely on various simplifications, which make them easier to work with mathematically.

One way to simplify the problem, going back decades, is to study simpler two-dimensional QFTs rather than four-dimensional ones. A team in France recently nailed down all the mathematical details of a prominent two-dimensional QFT.

Other simplifications assume quantum fields are symmetrical in ways that dont match physical reality, but that make them more tractable from a mathematical perspective. These include supersymmetric and topological QFTs.

The next, and much more difficult, step will be to remove the crutches and provide a mathematical description of a quantum field theory that better suits the physical world physicists most want to describe: the four-dimensional, continuous universe in which all interactions are possible at once.

This is [a] very embarrassing thing that we dont have a single quantum field theory we can describe in four dimensions, nonperturbatively, said Rejzner. Its a hard problem, and apparently it needs more than one or two generations of mathematicians and physicists to solve it.

But that doesnt stop mathematicians and physicists from eyeing it greedily. For mathematicians, QFT is as rich a type of object as they could hope for. Defining the characteristic properties shared by all quantum field theories will almost certainly require merging two of the pillars of mathematics: analysis, which explains how to control infinities, and geometry, which provides a language for talking about symmetry.

Its a fascinating problem just in math itself, because it combines two great ideas, said Dijkgraaf.

If mathematicians can understand QFT, theres no telling what mathematical discoveries await in its unlocking. Mathematicians defined the characteristic properties of other objects, like manifolds and groups, long ago, and those objects now permeate virtually every corner of mathematics. When they were first defined, it would have been impossible to anticipate all their mathematical ramifications. QFT holds at least as much promise for math.

I like to say the physicists dont necessarily know everything, but the physics does, said Ben-Zvi. If you ask it the right questions, it already has the phenomena mathematicians are looking for.

And for physicists, a complete mathematical description of QFT is the flip side of their fields overriding goal: a complete description of physical reality.

I feel there is one intellectual structure that covers all of it, and maybe it will encompass all of physics, said Seiberg.

Now mathematicians just have to uncover it.

See the article here:

The Mystery at the Heart of Physics That Only Math Can Solve - Quanta Magazine

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A team of physicists, including the University of Warwick, have proved that a subatomic particle can switch into its antiparticle alter-ego and back again, in a new discovery just revealed last week.

This new result shows for the first time that charm mesons can oscillate between the two states.

An extraordinarily precise measurement made by UK researchers using the LHCb experiment at CERN has provided the first evidence that charm mesons can change into their antiparticleand back again.

For more than 10 years, scientists have known that charm mesons, subatomic particles that contain a quark and an antiquark, can travel as a mixture of their particle and antiparticle states, a phenomenon called mixing. However, this new result shows for the first time that they can oscillate between the two states.

Armed with this new evidence, scientists can try to tackle some of the biggest questions in physics around how particles behave outside of the Standard Model. One being, whether these transitions are caused by unknown particles not predicted by the guiding theory.

The Large Hadron Collider tunnel. Credit: CERN

The research, submitted today to Physical Review Letters and available onarXiv, received funding from the Science and Technology Facilities Council (STFC).

Being one and the other

In the strange world of quantum physics, the charm meson can be itself and its antiparticle at once. This state, known as quantum superposition, results in two particles each with their own mass a heavier and lighter version of the particle. This superposition allows the charm meson to oscillate into its antiparticle and back again.

Using data collected during the second run of the Large Hadron Collider, researchers from the University of Oxford measured a difference in mass between the two particles of 0.00000000000000000000000000000000000001 grams or in scientific notation 110-38g. A measurement of this precision and certainty is only possible when the phenomenon is observed many times, and this is only possible due so many charm mesons being produced in LHC collisions.

As the measurement is extremely precise, the research team ensured the analysis method was even more so. To do this, the team used a novel technique originally developed by colleagues at the University of Warwick.

The LHCb experiment at CERN. Credit: CERN

There are only four types of particle in the Standard Model, the theory that explains particle physics, that can turn into their antiparticle. The mixing phenomenon was first observed in Strange mesons in the 1960s and in beauty mesons in the 1980s. Until now, the only other one of the four particles that has been seen to oscillate this way is the strange-beauty meson, a measurement made in 2006.

Professor Guy Wilkinson at University of Oxford, whose group contributed to the analysis, said:

What makes this discovery of oscillation in the charm meson particle so impressive is that, unlike the beauty mesons, the oscillation is very slow and therefore extremely difficult to measure within the time that it takes the meson to decay. This result shows the oscillations are so slow that the vast majority of particles will decay before they have a chance to oscillate. However, we are able to confirm this as a discovery because LHCb has collected so much data.

Professor Tim Gershon at University of Warwick, developer of the analytical technique used to make the measurement, said:

Charm meson particles are produced in protonproton collisions and they travel on average only a few millimeters before transforming, or decaying, into other particles. By comparing the charm meson particles that decay after traveling a short distance with those that travel a little further, we have been able to measure the key quantity that controls the speed of the charm meson oscillation into anti-charm meson the difference in mass between the heavier and lighter versions of charm meson.

This discovery of charm meson oscillation opens up a new and exciting phase of physics exploration; researchers now want to understand the oscillation process itself, potentially a major step forward in solving the mystery of matter-antimatter asymmetry. A key area to explore is whether the rate of particle-antiparticle transitions is the same as that of antiparticle-particle transitions, and specifically whether the transitions are influenced/caused by unknown particles not predicted by the Standard Model.

Dr. Mark Williams at University of Edinburgh, who convened the LHCb Charm Physics Group within which the research was performed, said:

Tiny measurements like this can tell you big things about the Universe that you didnt expect.

The result, 110-38g, crosses the five sigma level of statistical significance that is required to claim a discovery in particle physics.

Reference: Observation of the mass difference between neutral charm-meson eigenstates by LHCb collaboration: R. Aaij, C. Abelln Beteta, T. Ackernley, B. Adeva, M. Adinolfi, H. Afsharnia, C.A. Aidala, S. Aiola, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, Z. Aliouche, G. Alkhazov, P. Alvarez Cartelle, S. Amato, Y. Amhis, L. An, L. Anderlini, A. Andreianov, M. Andreotti, F. Archilli, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, B. Audurier, S. Bachmann, M. Bachmayer, J.J. Back, P. Baladron Rodriguez, V. Balagura, W. Baldini, J. Baptista Leite, R.J. Barlow, S. Barsuk, W. Barter, M. Bartolini, F. Baryshnikov, J.M. Basels, G. Bassi, B. Batsukh, A. Battig, A. Bay, M. Becker, F. Bedeschi, I. Bediaga, A. Beiter, V. Belavin, S. Belin, V. Bellee, K. Belous, I. Belov, I. Belyaev, G. Bencivenni, E. Ben-Haim, A. Berezhnoy, R. Bernet, D. Berninghoff, H.C. Bernstein, C. Bertella, A. Bertolin, C. Betancourt, F. Betti, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, M.S. Bieker, S. Bifani, P. Billoir, M. Birch, F.C.R. Bishop, A. Bitadze, A. Bizzeti, M. Bjrn, M.P. Blago, T. Blake, F. Blanc, S. Blusk, D. Bobulska, J.A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Boldyrev, A. Bondar, N. Bondar, S. Borghi, M. Borisyak, M. Borsato, J.T. Borsuk, S.A. Bouchiba, T.J.V. Bowcock, A. Boyer, C. Bozzi, M.J. Bradley et al., Submitted, Physical Review Letters.arXiv: 2106.03744

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Subatomic Particle Seen Changing to Antiparticle and Back for the First Time in Extraordinary Experiment - SciTechDaily

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Image credit: Russell Huffman

By Ryan F. Mandelbaum and Olivia Lanes

What is Quantum Computing? Most of this blogs readers are already excited about this technology after all, weve spent many hours reading textbooks and documentation trying to figure out how to write programs for real quantum chips. But many of our friends, family members, and people we randomly encounter still scratch their heads when they hear the words quantum and computer put together. We think its high time that they learn about quantum computing, too.

Partially inspired by Talia Gershons awesome WIRED video where she explains quantum computing at five different difficulty levels, we came up with some stock quantum computing explanations you can use to start spreading your excitement for quantum computing to other people in your life (or, if youre new here, use to understand quantum yourself). While were excited about this technology, we tried our best to sidestep the hype; quantum computers are exciting enough on their own, and theres no need to exaggerate how far along they are, what they can do today, or what we hope theyll do in the future.

But, no matter who youre trying to explain quantum to, theres a core understanding we think everyone should have. A quantum computer is similar to a classical computer in a lot of ways. Just like a classical computer, you store information using some physical system. You have to initialize that system, then perform some sort of operations on it (in other words, run a program), and then extract the information. It differs from classical computing in two key elements, however:

These core counterintuitive ideas underlie the fundamental operations of quantum computing. Once you understand these two pieces, the rest is a matter of how deep youd like to learn, and how quantum algorithms might provide benefits to you, your life, or the industry you work in. You should also get started using Qiskit.

Each of these explanations are based mainly on our experiences and opinions, and you might have your own tricks to help get quantum computing across feel free to tell us about them, what worked, and what didnt in the comments!

Some problems are really hard for todays computers to tackle, like designing drugs, running machine learning algorithms, and solving certain kinds of math equations. But the ability to solve those problems could help humankind tackle some of its biggest challenges. Well, quantum computers represent a new kind of computing system under development today that solves problems using an architecture that follows the most fundamental laws of nature and we hope theyll one day be able to to solve these hard problems. You can even try them out for yourself.

Hey, you know what a computer is but do you know how it works? Well basically, it thinks of everything, the YouTube videos you watch, the letters on the screen, everything, in a special kind of code. Programs and apps are basically just instructions that change the code around, leading to the results you see on the screen. But theres only so many different kinds of things that a regular computer can do with that code. A quantum computer works similarly to a regular computer, but its code looks a little different, and it can do even more things to those codes than your parents computers can. Quantum computers are really new, so theyre not better than a regular computer juuust yet but we think that one day they might be able to solve some of the biggest challenges in the world. Maybe it will even help you do your homework faster or something.

What do I do for work? Well *cracks knuckles*

So, there are some problems that people would like to solve that take even the best supercomputers a ridiculously long amount of time to run problems like simulating chemistry or breaking big numbers into smaller factors. Quantum computers might be able to tackle these problems by relying on a different set of physical laws than your computer does. Your computer is really just lots of electrical switches, called bits, that represents everything using binary code. In other words, the language your computer speaks encodes everything as long strings of 0s or 1s, while programs are mathematical operations that can change zeros to ones and vice versa. However, at even at the most fundamental level, a quantum computers code and its corresponding hardware looks differently. Quantum bits, or qubits, dont have to be binary during the calculation; they can actually exist in well-defined combinations of 0 and 1.

Its kind of like, if I was a qubit, instead of having mashed potatoes OR asparagus, I can have a third of a helping of mashed potatoes and two thirds of a helping of asparagus so long as it adds up to a whole side dish. However, once the problem ends, the quantum computers can only give answers in binary code, with some probability determining the outcome. Its like, if someone wanted to know which side dish I had, they check by closing their eyes, shoving their fork onto my plate, and reporting only the first side dish they taste, with the probabilities determined by how much of each side I had on my plate when they went in for a bite. Qubits also interact differently from regular bits. Lets say that Olivia and Ryan are both at dinner, and you only know that between them theyve eaten a helping of potatoes and a helping of asparagus, and not whose dish has what sides on it. But even if they havent spoken since dinner started, if you did the same eyes-closed fork jab you did on my plate, the sides they picked will be more correlated than the usual rules of random guessing would allow.

A direct consequence of this quantum dinner behavior is that there exist different types of algorithms for quantum computers. In fact, due to the quantum nature of the processor, scientists have already shown that at least theoretically, some quantum algorithms can be run exponentially faster than their classical counterparts. Provided that we can build the hardware, all these sorts of near-impossible problems may one day have solutions within arms reach. Anyway, thats what I do at work. Can you pass the gravy?

Editor Note: While thankfully we havent encountered a large contingency of quantum computing conspiracies, hype and tabloid coverage has led to some worrying interpretations of what quantum can and cant do some indeed bordering on conspiracy-minded thinking. But according to at least one expert, the best way to speak with conspiracy theorists isnt with facts but with empathy.

Oh, youre worried about quantum computers? Whys that? I was actually really interested in learning more about them, too, and I didnt understand them at first. What have you learned so far? Huh, thats interesting. So far, Ive learned that some research labs are working on a new kind of computer that can solve certain problems that classical computers cant. I was definitely really interested in the science behind it. See, theyre more or less just computer processors that rely on a system of bits to solve problems. However, these quantum bits can perform a richer set of mathematical operations than classical bits, which makes them better at solving certain problems. What did you read that they could do? Portals and new dimensions, huh? Thats really interesting, but no, I did some research on my own and what the media doesnt want you to know is that these computers are more business-y than science fiction-y they might one day be revolutionary for chemistry, machine learning, and other topics. But the media also doesnt want you to know that these computers are still really early in their development like, they forget their information quickly and theres a lot of work to do before theyre something to worry about. There are actually services that let you try them out and program them on your own. Now tell me more about the UFO you saw

Quantum computers are a new kind of computer processor that one day might augment your current computing resources to tackle certain challenges difficult for todays classical computers alone. Quantum processors work in tandem with classical computers as part of a cloud-based computing workflow, providing value by performing mathematical operations challenging for classical processors. While theres no device capable of executing a killer app yet, research has demonstrated that the enhanced capabilities of quantum systems could accelerate the research and development process, and provide value to certain industries in the coming years chemical and materials design, drug development, finance, and machine learning, for example. In one report, Boston Consulting Group predicted that productivity gains by end users of quantum computing, both in cost savings and revenue generation opportunities, could equal $450 billion or more annually. Many Fortune-500 companies have already begun to research and develop domain-specific thought leadership in quantum computing so as to be prepared when the field matures.

Quantum processors are kind of like a GPU in the sense that theyre designed to handle specific tasks that the CPU isnt well-suited to handle. But unlike a GPU, quantum computers work using a different kind of hardware architecture, one that allows them to perform a richer array of logical operations than just Boolean logic. These hardware requirements lead to bulky systems, so todays developers hoping to exploit quantum resources run their code over the cloud, employing both classical and quantum processing power where necessary for their program.

Quantum computers are a nascent technology, so programming them today is can be a lot like writing code in assembly language, stringing individual quantum bits together into circuits using quantum logic gates. These circuits are similar to classical computers in that their programs begin by initializing the qubits into a string of zeroes and ones, then perform operations, then return an output. However, quantum gates can also produce superpositions of strings, creating well-defined combinations of bitstrings (though you can only end up with one of these bitstrings, determined by the rules of probability, at the end of the calculation). Further operations produce entanglement and interference, linking certain qubits together and changing those probability distributions such that certain bitstrings become more likely and certain bitstrings become less likely when you measure the final result.

Given how recently quantum programming languages arose, developers have organized into open source communities like Qiskit where they maintain the code used to access quantum computers. As part of that, theyre designing and implementing quantum algorithms that can run on these devices, and creating modules designed to harness the potential power of quantum computers without having to continually program individual bits kind of like building a higher-level programming language on top of the assembly language with which we access quantum computers today. You can learn more by getting started with Qiskit here!

Quantum mechanics might be confusing, but it can still be incredibly useful, even if youre not a physicist. A computer based on the laws of quantum physics might help solve problems in chemistry, machine learning, or even solving partial differential equations.

Objects following the rules of quantum mechanics can enter states called superpostions. If an objects state is in a superposition of 0 and 1, that means that the object is in a linear combination of both values simultaneously until a measurement forces the object into one state or the other, with the probability of measuring either state based on the coefficients of each state in the linear combination. These objects can also become entangled, meaning you cannot describe one object mathematically on its own; when we perform experiments on entangled particles, we find that their properties are more correlated than classical physics would otherwise allow. We use these principles to construct sets of quantum bits, or qubits. I cant know each qubit value individually I can only create these linear combinations from states that include both qubits. But if I measure one qubit and force it to choose, lets say it ends up measuring 1, then the other qubit will take on a value highly correlated with the first value more correlated than random chance alone would allow. We use these ideas to generate interference, where certain combinations of qubit values become more likely and certain ones become less likely.

In a classical computer, computational spaces add together, because bits can exist in only one state or the other, 0 or 1. In a quantum computer, the computational space grows exponentially as you add more bits (2^n where n is the number of bits) so its easy to understand how they can become powerful computational tools. Furthermore, there are certain problems that are hard for classical computers to compute. Because quantum computers themselves rely on quantum physics, they are better able to simulate quantum mechanical phenomena, like chemical interactions and bonds. Though the devices are noisy and error prone today, researchers hope that quantum computers will be able to utilize the properties of entanglement and interference to run some algorithms faster than a classical computer can, making solutions to these hard problems finally feasible. Together, these benefits might one day allow scientists to perform various elements of their jobs faster.

Macroscopic quantum effects have long been observed in superconducting circuits. However, it wasnt until theoretical developments showing that flux and voltage can be quantized circuit QED that this idea was applied to quantum information processing.

A superconducting transmon qubit is essentially a quantized anharmonic oscillator. The circuits macro state can be described by the quantized energy levels; the ground state (0), the excited state (1), or even higher order excited states as well (2, 3, 4, etc.). But because the circuit is anharmonic the energy transitions between states 0 and 1 is different than 1 and 2, so we can isolate the bottom levels with a microwave pulse at that frequency to create a quantum bit for information processing.

In order to read-out and control the state of a transmon, we couple the qubit to either a 2D or 3D resonator (the physics is the same). The qubit and the resonator interact in such a way that when we probe the resonator with a standing microwave tone, the resonant frequency will actually shift depending on if the qubit is in the ground or excited state. This is how we can read out and interact with the qubits that make up a quantum computer.

Coupling these qubit-cavity systems together in an array and allowing them to talk to other another with 2-qubit gates (essentially more finely tuned microwave pulses) creates a quantum processor. Running specific gates in a specific order on this processor can create quantum algorithms. By leveraging the processors quantum properties of entanglement, superposition and interference, some quantum algorithms can theoretically be run significantly faster than their classical counterparts. Once we have reached the point where applying these algorithms has become useful and advantageous, we will have achieved what we call the era of quantum advantage.

Whispers: Hey there, pup, listen. I told my boss I would be able to teach you quantum computing, but you barely understand how your doggy door works. So heres what Im gonna do. Im gonna train you how to give me your left paw when I say initialize. Then youre gonna give me your right paw when I say X-gate. Then when I say Hadamard gate, youre going to hop on your hind legs and give me both paws. When I say CNOT, youre going to roll over, and when I say measure, youre going to bark. If you do this for me Ill cut some salami up into your dinner tonight.

Hey, Boss! Yeah! I finally figured out how to explain quantum computing to the dog! Yep, Ill write it all down in the blog post tonight. Wanna see?

Get started using Qiskit here!

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How Do You Explain Quantum Computing To Your Dog (And Other Important People in Your Life)? - Medium

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Quantum computing is one of those technologies that, like artificial intelligence, has been attracting the interest of investors for some time - even though few can actually explain what it involves.

The technology, put very simply, involves harnessing quantum physics - the branch of the science that seeks to describe and explain how and why objects behave and move in the way that they do - to store data or perform computations to a vastly more efficient degree than traditional computers.

Quantum computers are said to be able to operate millions of times faster than existing ones.

A number of governments around the world are pumping capital into the sector in the hope of establishing a lead in the field. They include Germany which, in June last year, announced a 2bn (1.7bn) investment into two new quantum computers.

China, meanwhile, is setting up a national laboratory for quantum information sciences.

But the technology has also been the topic of much debate in investment circles.

Supporters believe it has the potential to transform many industries and sectors, including genetic medicine, pharmacology, financial services and materials development.

Sceptics argue that its vast potential may take many years, if ever, to be realised.

Wednesday, however, brought news of a deal that suggests quantum computing may indeed be on the verge of a breakthrough that could see it being applied more widely across business and industry.

Cambridge Quantum Computing, a British business founded in 2014, announced it is to combine with the quantum solutions arm of the US industrial giant Honeywell.

The pair said the combined business would be "extremely well-positioned to lead the quantum computing industry by offering advanced, fully integrated hardware and software solutions at an unprecedented pace, scale and level of performance to large high-growth markets worldwide".

Honeywell will be the majority shareholder of the new company, with CQ's shareholders, including Ilyas Khan, its founder and chief executive, owning just over 45% of the business.

Mr Khan said that he believed a breakthrough in the quantum computing had already arrived.

He told Sky News: "I think the tipping point was probably in the last 18 months. China, the United States, the United Kingdom, of course, have major programmes and lots of countries and companies have said that they face an existential risk if they don't get quantum computing right.

"In terms of applications, things that we will use on a day to day basis, I think a good analogy is mobile phones - at the end of the 1980s, before they arrived, nobody really knew that they're going to use them and of course, when they did arrive, the markets and their usage exploded.

"I would imagine that later on this year things like cyber security, for example, will be offering unhackable keys using the quantum computer, and it will begin to be more and more useful. Maybe the more esoteric uses are probably a couple of years away, machine learning, for example, [or] material discovery."

He said the combined business would be a "global powerhouse" capable of creating and commercialising quantum solutions that address "some of humanity's greatest challenges".

British tech start-ups are often accused of selling out too early but Mr Khan, who will lead the combined business, could not be described as such.

He added: "The UK is the leader in quantum and this is the first time since the Second World War that a major technology initiative is not being driven by Silicon Valley. We are a software and an algorithm provider and the merger creates an integrated business.

"[It will be] what I would describe as an Anglo American, actually a global business. The characterisation of a sell-out, I think, is probably not one I would agree with."

Honeywell will be investing between $270m (190m) and $300m (211m) in the new venture and Mr Khan said this money would be invested, predominantly, in people.

At the start of its life, the enlarged business will be employing around 350 people, of whom 200 are scientists - more than half of them boasting doctorates in disciplines such as chemistry, physics and maths.

Mr Khan went on: "This is a business where we are in scaling and growth mode - so it's primarily people. We will probably grow quite rapidly as far as the numbers are concerned, both in the United Kingdom, and in the United States, and then a reasonable amount of that capital will be in continuing to increase the capacity of the quantum computers. We have the world's best performing computer right now - and we will be deploying that for customer usage over the course of the next few years."

Hinting at a forthcoming stock market flotation of the business, Mr Khan said there would also be a fund-raising at some point in the near future, in which outside investors would be able to buy a stake in the business.

He declined to say what valuation had been put on Cambridge Quantum under the transaction but said some numbers would be released "over the course of the next week or two".

Mr Khan went on: "This is something which is obviously something that I'm very proud of. It's a British winner. The United Kingdom is the leader in this. We are the world's leader and, of course, consequently very valuable."

That reluctance to talk specific numbers is, perhaps, understandable.

Barron's, the influential US financial publication, has already suggested that the enlarged business could be the 'Apple of quantum computing' because the deal brings together Honeywell's expertise in quantum hardware with Cambridge Quantum's expertise in software and algorithms - emulating the way Apple straddles hardware, operating systems, and software applications. Honeywell itself has said that quantum computing will one day be a trillion dollar-a-year industry.

The deal marks another twist in what has been an inspiring story.

Born in Haslingden, in Lancashire, Mr Khan's father was a bus driver and he was brought up in what he told the Lancashire Telegraph in 2009 was a "two up, two down terrace". Educated at Haslingden Grammar School and University of London School of Oriental and African Studies, he want into banking on graduating, spending 20 years of his career in Hong Kong.

He first came to public attention when, in 2009, he rescued Accrington Stanley FC and later served as its chairman for three years. He has reportedly sunk more than 2m of his own money into the club over a 20-year period.

On returning to the UK he joined the University of Cambridge's Judge Business School and chairman of the Stephen Hawking Foundation and it was a comment from the late Professor Hawking, a friend, who prompted him to start Cambridge Quantum.

He told The Quantum Daily last year: "The prompt really came from a comment that Stephen made to me in a meeting that we were attending and Stephen said 'this is for real'. This really opened my eyes."

It is just possible that those investors still sceptical about quantum computing may well have had their eyes opened, too, following this deal.

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British innovation will be key to success of merger dubbed the 'Apple of quantum computing' - Sky News

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