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That allows quantum computers to make many calculations in one pass, while digital ones have to perform each calculation separately. By speeding up computation, quantum computers could potentially solve big, complex problems in fields like chemistry and materials science that are out of reach today.

When Google researchers made their supremacy claim in 2019, they said their quantum computer performed a calculation in 3 minutes 20 seconds that would take about 10,000 years on a state-of-the-art conventional supercomputer.

The IBM researchers in the new study performed a different task, one that interests physicists. They used a quantum processor with 127 qubits to simulate the behavior of 127 atom-scale bar magnets — tiny enough to be governed by the spooky rules of quantum mechanics — in a magnetic field. That is a simple system known as the Ising model, which is often used to study magnetism.

This problem is too complex for a precise answer to be calculated even on the largest, fastest supercomputers.

On the quantum computer, the calculation took less than a thousandth of a second to complete. Each quantum calculation was unreliable — fluctuations of quantum noise inevitably intrude and induce errors — but each calculation was quick, so it could be performed repeatedly.

Indeed, for many of the calculations, additional noise was deliberately added, making the answers even more unreliable. But by varying the amount of noise, the researchers could tease out the specific characteristics of the noise and its effects at each step of the calculation.“We can amplify the noise very precisely, and then we can rerun that same circuit,” said Abhinav Kandala, the manager of quantum capabilities and demonstrations at IBM Quantum and an author of the Nature paper. “And once we have results of these different noise levels, we can extrapolate back to what the result would have been in the absence of noise.”In essence, the researchers were able to subtract the effects of noise from the unreliable quantum calculations, a process they call error mitigation.

Altogether, the computer performed the calculation 600,000 times, converging on an answer for the overall magnetization produced by the 127 bar magnets.

Although an Ising model with 127 bar magnets is too big, with far too many possible configurations, to fit in a conventional computer, classical algorithms can produce approximate answers, a technique similar to how compression in JPEG images throws away less crucial data to reduce the size of the file while preserving most of the image’s details

Certain configurations of the Ising model can be solved exactly, and both the classical and quantum algorithms agreed on the simpler examples. For more complex but solvable instances, the quantum and classical algorithms produced different answers, and it was the quantum one that was correct.

Thus, for other cases where the quantum and classical calculations diverged and no exact solutions are known, “there is reason to believe that the quantum result is more accurate,”

Mr. Anand is currently trying to add a version of error mitigation for the classical algorithm, and it is possible that could match or surpass the performance of the quantum calculations.

In the long run, quantum scientists expect that a different approach, error correction, will be able to detect and correct calculation mistakes, and that will open the door for quantum computers to speed ahead for many uses.

Error correction is already used in conventional computers and data transmission to fix garbles. But for quantum computers, error correction is likely years away, requiring better processors able to process many more qubits

“This is one of the simplest natural science problems that exists,” Dr. Gambetta said. “So it’s a good one to start with. But now the question is, how do you generalize it and go to more interesting natural science problems?”

Those might include figuring out the properties of exotic materials, accelerating drug discovery and modeling fusion reactions.

In 1972, using duct tape and spare parts in the basement on the campus of the University of California, Berkeley, Dr. Clauser and a graduate student, Stuart Freedman, who died in 2012, endeavored to perform Bell’s experiment to measure quantum entanglement. In a series of experiments, he fired thousands of light particles, or photons, in opposite directions to measure a property known as polarization, which could have only two values — up or down. The result for each detector was always a series of seemingly random ups and downs. But when the two detectors’ results were compared, the ups and downs matched in ways that neither “classical physics” nor Einstein’s laws could explain. Something weird was afoot in the universe. Entanglement seemed to be real.

in 2002, Dr. Clauser admitted that he himself had expected quantum mechanics to be wrong and Einstein to be right. “Obviously, we got the ‘wrong’ result. I had no choice but to report what we saw, you know, ‘Here’s the result.’ But it contradicts what I believed in my gut has to be true.” He added, “I hoped we would overthrow quantum mechanics. Everyone else thought, ‘John, you’re totally nuts.’”

the correlations only showed up after the measurements of the individual particles, when the physicists compared their results after the fact. Entanglement seemed real, but it could not be used to communicate information faster than the speed of light.

In 1982, Dr. Aspect and his team at the University of Paris tried to outfox Dr. Clauser’s loophole by switching the direction along which the photons’ polarizations were measured every 10 nanoseconds, while the photons were already in the air and too fast for them to communicate with each other. He too, was expecting Einstein to be right.

Quantum predictions held true, but there were still more possible loopholes in the Bell experiment that Dr. Clauser had identified

For example, the polarization directions in Dr. Aspect’s experiment had been changed in a regular and thus theoretically predictable fashion that could be sensed by the photons or detectors.

Anton Zeilinger

added even more randomness to the Bell experiment, using random number generators to change the direction of the polarization measurements while the entangled particles were in flight.

Once again, quantum mechanics beat Einstein by an overwhelming margin, closing the “locality” loophole.

as scientists have done more experiments with entangled particles, entanglement is accepted as one of main features of quantum mechanics and is being put to work in cryptology, quantum computing and an upcoming “quantum internet

One of its first successes in cryptology is messages sent using entangled pairs, which can send cryptographic keys in a secure manner — any eavesdropping will destroy the entanglement, alerting the receiver that something is wrong.

, with quantum mechanics, just because we can use it, doesn’t mean our ape brains understand it. The pioneering quantum physicist Niels Bohr once said that anyone who didn’t think quantum mechanics was outrageous hadn’t understood what was being said.

In his interview with A.I.P., Dr. Clauser said, “I confess even to this day that I still don’t understand quantum mechanics, and I’m not even sure I really know how to use it all that well. And a lot of this has to do with the fact that I still don’t understand it.”

Not only that, but the universe appears to be governed by a kind of cosmic censorship: Regions of extreme gravity—where space-time curves so sharply that Einstein’s equations malfunction and the true, quantum nature of gravity and space-time must be revealed—always hide behind the horizons of black holes.

Dyson, who helped develop quantum electrodynamics (the theory of interactions between matter and light) and is professor emeritus at the Institute for Advanced Study in Princeton, New Jersey, where he overlapped with Einstein, disagrees with the argument that quantum gravity is needed to describe the unreachable interiors of black holes. And he wonders whether detecting the hypothetical graviton might be impossible, even in principle. In that case, he argues, quantum gravity is metaphysical, rather than physics.

The ability to detect the “grin” of quantum gravity would seem to refute Dyson’s argument. It would also kill the gravitational decoherence theory, by showing that gravity and space-time do maintain quantum superpositions.

If gravity is a quantum interaction, then the answer is: It depends. Each component of the blue diamond’s superposition will experience a stronger or weaker gravitational attraction to the red diamond, depending on whether the latter is in the branch of its superposition that’s closer or farther away. And the gravity felt by each component of the red diamond’s superposition similarly depends on where the blue diamond is.

Before he died, Richard Feynman, who understood quantum theory as well as anyone, said, “I still get nervous with it...I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.” The problem is not with using the theory — making calculations, applying it to engineering tasks — but in understanding what it means. What does it tell us about the world?

From one point of view, quantum physics is just a set of formalisms, a useful tool kit. Want to make better lasers or transistors or television sets? The Schrödinger equation is your friend. The trouble starts only when you step back and ask whether the entities implied by the equation can really exist. Then you encounter problems that can be described in several familiar ways:

Wave-particle duality. Everything there is — all matter and energy, all known forces — behaves sometimes like waves, smooth and continuous, and sometimes like particles, rat-a-tat-tat. Electricity flows through wires, like a fluid, or flies through a vacuum as a volley of individual electrons. Can it be both things at once?

The uncertainty principle. Werner Heisenberg famously discovered that when you measure the position (let’s say) of an electron as precisely as you can, you find yourself more and more in the dark about its momentum. And vice versa. You can pin down one or the other but not both.

The measurement problem. Most of quantum mechanics deals with probabilities rather than certainties. A particle has a probability of appearing in a certain place. An unstable atom has a probability of decaying at a certain instant. But when a physicist goes into the laboratory and performs an experiment, there is a definite outcome. The act of measurement — observation, by someone or something — becomes an inextricable part of the theory

The strange implication is that the reality of the quantum world remains amorphous or indefinite until scientists start measuring

Other interpretations rely on “hidden variables” to account for quantities presumed to exist behind the curtain.

This is disturbing to philosophers as well as physicists. It led Einstein to say in 1952, “The theory reminds me a little of the system of delusions of an exceedingly intelligent paranoiac.”

“Figuring out what quantum physics is saying about the world has been hard,” Becker says, and this understatement motivates his book, a thorough, illuminating exploration of the most consequential controversy raging in modern science.

In a way, the Copenhagen is an anti-interpretation. “It is wrong to think that the task of physics is to find out how nature is,” Bohr said. “Physics concerns what we can say about nature.”

Nothing is definite in Bohr’s quantum world until someone observes it. Physics can help us order experience but should not be expected to provide a complete picture of reality. The popular four-word summary of the Copenhagen interpretation is: “Shut up and calculate!”

Becker sides with the worriers. He leads us through an impressive account of the rise of competing interpretations, grounding them in the human stories

He makes a convincing case that it’s wrong to imagine the Copenhagen interpretation as a single official or even coherent statement. It is, he suggests, a “strange assemblage of claims.

An American physicist, David Bohm, devised a radical alternative at midcentury, visualizing “pilot waves” that guide every particle, an attempt to eliminate the wave-particle duality.

Competing approaches to quantum foundations are called “interpretations,” and nowadays there are many. The first and still possibly foremost of these is the so-called Copenhagen interpretation.

Perhaps the most popular lately — certainly the most talked about — is the “many-worlds interpretation”: Every quantum event is a fork in the road, and one way to escape the difficulties is to imagine, mathematically speaking, that each fork creates a new universe

if you think the many-worlds idea is easily dismissed, plenty of physicists will beg to differ. They will tell you that it could explain, for example, why quantum computers (which admittedly don’t yet quite exist) could be so powerful: They would delegate the work to their alter egos in other universes.

When scientists search for meaning in quantum physics, they may be straying into a no-man’s-land between philosophy and religion. But they can’t help themselves. They’re only human.

If you were to watch me by day, you would see me sitting at my desk solving Schrödinger’s equation...exactly like my colleagues,” says Sir Anthony Leggett, a Nobel Prize winner and pioneer in superfluidity. “But occasionally at night, when the full moon is bright, I do what in the physics community is the intellectual equivalent of turning into a werewolf: I question whether quantum mechanics is the complete and ultimate truth about the physical universe.”

Quantum teleportation — what he called “spooky action at a distance” — can transfer information between locations without actually moving the physical matter that holds it.

This technology could profoundly change the way data travels from place to place. It draws on more than a century of research involving quantum mechanics, a field of physics that governs the subatomic realm and behaves unlike anything we experience in our everyday lives. Quantum teleportation not only moves data between quantum computers, but it also does so in such a way that no one can intercept it.

These entangled systems could be electrons, particles of light or other objects. In the Netherlands, Dr. Hanson and his team used what is called a nitrogen vacancy center — a tiny empty space in a synthetic diamond in which electrons can be trapped.

Traditional computers perform calculations by processing “bits” of information, with each bit holding either a 1 or a 0. By harnessing the strange behavior of quantum mechanics, a quantum bit, or qubit, can store a combination of 1 and 0 — a little like how a spinning coin holds the tantalizing possibility that it will turn up either heads or tails when it finally falls flat on the table.

Researchers believe these devices could one day speed the creation of new medicines, power advances in artificial intelligence and summarily crack the encryption that protects computers vital to national security. Across the globe, governments, academic labs, start-ups and tech giants are spending billions of dollars exploring the technology.

Although it cannot move objects from place to place, it can move information by taking advantage of a quantum property called “entanglement”: A change in the state of one quantum system instantaneously affects the state of another, distant one.

“It does not work that way today. Google knows what you are running on its servers.”

The information also cannot be intercepted. A future quantum internet, powered by quantum teleportation, could provide a new kind of encryption that is theoretically unbreakable.

quantum computing relies on the fact that subatomic particles inhabit a range of states. Different relationships among the particles may coexist, as well. Those probable states can be narrowed to determine an optimal outcome among a near-infinitude of possibilities, which allows certain types of problems to be solved rapidly.

“This is a revolution not unlike the early days of computing,” he said. “It is a transformation in the way computers are thought about.”

It could be possible, for example, to tell instantly how the millions of lines of software running a network of satellites would react to a solar burst or a pulse from a nuclear explosion — something that can now take weeks, if ever, to determine.

Mr. Brownell, who joined D-Wave in 2009, was until 2000 the chief technical officer at Goldman Sachs. “In those days, we had 50,000 servers just doing simulations” to figure out trading strategies, he said. “I’m sure there is a lot more than that now, but we’ll be able to do that with one machine, for far less money.”

If Microsoft’s work pans out, he said, the millions of possible combinations of the proteins in a human gene could be worked out “fairly easily.”

Quantum computing has been a goal of researchers for more than three decades, but it has proved remarkably difficult to achieve. The idea has been to exploit a property of matter in a quantum state known as superposition, which makes it possible for the basic elements of a quantum computer, known as qubits, to hold a vast array of values simultaneously.

There are a variety of ways scientists create the conditions needed to achieve superposition as well as a second quantum state known as entanglement, which are both necessary for quantum computing. Researchers have suspended ions in magnetic fields, trapped photons or manipulated phosphorus atoms in silicon.

In the D-Wave system, a quantum computing processor, made from a lattice of tiny superconducting wires, is chilled close to absolute zero. It is then programmed by loading a set of mathematical equations into the lattice. The processor then moves through a near-infinity of possibilities to determine the lowest energy required to form those relationships. That state, seen as the optimal outcome, is the answer.

An alternative algorithm is known that could have let the conventional computer be more competitive, or even win, by exploiting what Neven called a “bug” in D-Wave’s design. Neven said the test his group staged is still important because that shortcut won’t be available to regular computers when they compete with future quantum annealers capable of working on larger amounts of data.

“For a specific, carefully crafted proof-of-concept problem we achieve a 100-million-fold speed-up,” said Neven.

“the world’s first commercial quantum computer.” The computer is installed at NASA’s Ames Research Center in Mountain View, California, and operates on data using a superconducting chip called a quantum annealer.

Google is competing with D-Wave to make a quantum annealer that could do useful work.

Martinis is also working on quantum hardware that would not be limited to optimization problems, as annealers are.

Government and university labs, Microsoft (see “Microsoft’s Quantum Mechanics”), and IBM (see “IBM Shows Off a Quantum Computing Chip”) are also working on that technology.

“it may be several years before this research makes a difference to Google products.”

There are two problems. One is that quantum mechanics, as it is enshrined in textbooks, seems to require separate rules for how quantum objects behave when we’re not looking at them, and how they behave when they are being observed

Why are observations special? What counts as an “observation,” anyway? When exactly does it happen? Does it need to be performed by a person? Is consciousness somehow involved in the basic rules of reality?

Together these questions are known as the “measurement problem” of quantum theory.

The other problem is that we don’t agree on what it is that quantum theory actually describes, even when we’re not performing measurements.

We describe a quantum object such as an electron in terms of a “wave function,” which collects the superposition of all the possible measurement outcomes into a single mathematical object

But what is the wave function? Is it a complete and comprehensive representation of the world? Or do we need additional physical quantities to fully capture reality, as Albert Einstein and others suspected? Or does the wave function have no direct connection with reality at all, merely characterizing our personal ignorance about what we will eventually measure in our experiments?

For years, the leading journal in physics had an explicit policy that papers on the foundations of quantum mechanics were to be rejected out of hand

“If we replace ‘human judgments’ with ‘physical measurements,’” Wang and colleagues write, “and replace ‘cognitive system’ with ‘physical system,’ then these are exactly the same reasons that led physicists to develop quantum theory in the first place.”

Is nature really this weird? Or is this apparent weirdness just a reflection of our imperfect knowledge of nature?

The answer depends on how you interpret the equations of quantum mechanics, the mathematical theory that has been developed to describe the interactions of elementary particles. The success of this theory is unparalleled: Its predictions, no matter how “spooky,” have been observed and verified with stunning precision. It has also been the basis of remarkable technological advances. So it is a powerful tool. But is it also a picture of reality?

Does the wave function directly correspond to an objective, observer-independent physical reality, or does it simply represent an observer’s partial knowledge of it?

If there is an objective reality at all, the paper demonstrates, then the wave function is in fact reality-based.

What this research implies is that we are not just hearing different “stories” about the electron, one of which may be true. Rather, there is one true story, but it has many facets, seemingly in contradiction, just like in “Rashomon.” There is really no escape from the mysterious — some might say, mystical — nature of the quantum world.

We should be careful to recognize that the weirdness of the quantum world does not directly imply the same kind of weirdness in the world of everyday experience.

This is why, in fact, we are able to describe the objects around us in the language of classical physics.

I suggest that we regard the paradoxes of quantum physics as a metaphor for the unknown infinite possibilities of our own existence.

each electron somehow acts like a wave interfering with itself, as if it is simultaneously passing through both slits at once.

the electrons go back to their wavelike behavior, and the interference pattern miraculously reappears.

Instead, we see two lumps on the screen, as if the electrons, suddenly aware of being observed, decided to act like little pellets.

. For an individual particle like an electron, for example, the wave function provides information about the probabilities that the particle can be observed at particular locations, as well as the probabilities of the results of other measurements of the particle that you can make, such as measuring its momentum.

If the wave function is merely knowledge-based, then you can explain away odd quantum phenomena by saying that things appear to us this way only because our knowledge of the real state of affairs is insufficient.

If there is an objective reality at all, the paper demonstrates, then the wave function is in fact reality-based.

We should be careful to recognize that the weirdness of the quantum world does not directly imply the same kind of weirdness in the world of everyday experience. That’s because the nebulous quantum essence of individual elementary particles is known to quickly dissipate in large ensembles of particles (a phenomenon often referred to as “decoherence”).

then there is the mishandling of time. The physicist Lee Smolin's recent book, Time Reborn, links the crisis in physics with its failure to acknowledge the fundamental reality of time. Physics is predisposed to lose time because its mathematical gaze freezes change. Tensed time, the difference between a remembered or regretted past and an anticipated or feared future, is particularly elusive. This worried Einstein: in a famous conversation, he mourned the fact that the present tense, "now", lay "just outside of the realm of science".

Recent attempts to explain how the universe came out of nothing, which rely on questionable notions such as spontaneous fluctuations in a quantum vacuum, the notion of gravity as negative energy, and the inexplicable free gift of the laws of nature waiting in the wings for the moment of creation, reveal conceptual confusion beneath mathematical sophistication. They demonstrate the urgent need for a radical re-examination of the invisible frameworks within which scientific investigations are conducted.

we should reflect on how a scientific image of the world that relies on up to 10 dimensions of space and rests on ideas, such as fundamental particles, that have neither identity nor location, connects with our everyday experience. This should open up larger questions, such as the extent to which mathematical portraits capture the reality of our world – and what we mean by "reality".

a bunch of particles can share these states at the same time, effectively becoming instances of the same particle. And so: entanglement.

possible to strip away all of this indeterminateness

wave functions are very fragile, subject to a “collapse” in which all of those possibilities become just a single particle at a single point at a single time.

physicists have observed a very peculiar behavior of electrons in supercooled baths of helium. When an electron enters the bath, it acts to

two probabilities can be isolated from each other, cordoned off like quantum crime scenes

it’s possible to take a wave function and isolate it into different parts. So, if our electron has some probability of being in position (x1,y1,z1) and another probability of being in position (x2,y2,z2), those two probabilities can be isolated from each other, cordoned off like quantum crime scenes

when a macroscopic human attempts to measure a quantum mechanical system: The wave drops away and all that’s left is a boring, well-defined thing.

trapping the chance of finding the electron, not pieces of the electron

using tiny bubbles of helium as physical “traps.

repel the surrounding helium atoms, forming its own little bubble or cavity in the process.

That an electron (or other particle) can be in many places at the same time is strange enough, but the notion that those possibilities can be captured and shuttled away adds a whole new twist.

wave function isn’t a physical thing. It’s mathematics that describe a phenomenon.

The electron, upon measurement, will be in precisely one bubble.

“No one is sure what actually constitutes a measurement,”

Is consciousness required? We don’t really know.”

She became a science journalist. At first it was a lark, a way to get free press passes to conferences where she and her father could ask questions of the greatest minds in quantum mechanics, string theory and cosmology. But within a short time, as she started getting assignments, journalism became a calling, and an identity.

Tracking down the meaning of nothing — and, by extension, secrets about the origin of the universe and whether observer-independent reality exists — became the defining project of their lives. They spent hours together working on the puzzle, two dark heads bent over their physics books far into the night.

she has an epiphany — that for something to be real, it must be invariant — she flies home to share it with her father. They discuss her insight over breakfast at a neighborhood haunt, where they make a list on what they will affectionately call “the IHOP napkin.” They list all the possible “ingredients of ultimate reality,” planning to test each item for whether it is “real,” that is whether it is invariant and can exist in the absence of an observer.

their readings and interviews reveal that each item in turn is observer-dependent. Space? Observer-dependent, and therefore not real. Gravity, electromagnetism, angular momentum? No, no, and no. In the end, every putative “ingredient of ultimate reality” is eliminated, including one they hadn’t even bothered to put on the list because it seemed weird to: reality itself

What remained was an unsettling and essential insight: that “physics isn’t the machinery behind the workings of the world; physics is the machinery behind the illusion that there is a world.”

In the proposal, she clarifies how cosmology and quantum mechanics have evolved as scientists come to grips with the fact that things they had taken to be real — quantum particles, space-time, gravity, dimension — turn out to be ­observer-dependent.

Over the past hundred years, numerous experiments on elementary particles have upended the classical paradigm of a causal, deterministic universe. C