Quantum computers today are small in computational scale—the chip inside your smartphone contains billions of transistors, while the most powerful quantum computer contains a few hundred of the quantum equivalent of a transistor. They are also unreliable. If you run the same calculation over and over again, they will most likely give different answers each time.

But with their inherent ability to consider many possibilities at once, quantum computers don’t need to be very large to tackle certain thorny computational problems, and on Wednesday IBM researchers announced that they had devised a method to handle the unreliability in a way that would lead to reliable, useful answers.

“What IBM showed here is really an incredibly important step in that direction for making progress toward serious quantum algorithmic design,” said Dorit Aharonov, a professor of computer science at the Hebrew University of Jerusalem who was not involved in the research.

While researchers at Google claimed in 2019 to have achieved “quantum supremacy” — a task accomplished much faster on a quantum computer than a conventional one — IBM researchers say they have achieved something new and more useful, albeit more modestly named.

“We’re entering this phase of quantum computing that I call utility,” said Jay Gambetta, vice president of IBM Quantum. “The era of utility.”

A team of IBM researchers working for Dr. Gambetta, described their findings in a paper published Wednesday in the journal Nature.

Today’s computers are called digital or classical because they handle bits of information that are either 1 or 0, on or off. A quantum computer performs calculations on quantum bits, or qubits, that capture a more complex state of information. Just as a thought experiment by physicist Erwin Schrödinger postulated that a cat could be in a quantum state that is both dead and alive, a qubit can be both 1 and 0 simultaneously.

It enables quantum computers to do many calculations in one go, while digital ones have to perform each calculation separately. By speeding up computation, quantum computers can potentially solve large, complex problems in areas such as chemistry and materials science that are out of reach today. Quantum computers could also have a darker side by threatening privacy through algorithms that break the protections used for passwords and encrypted communications.

When Google researchers touted their supremacy in 2019, they said their quantum computer performed a calculation in 3 minutes and 20 seconds that would take about 10,000 years on an advanced conventional supercomputer.

But some other researchers, including those at IBM, rejected the claim, saying the problem was contrived. “Google’s experiment, as impressive as it was, and it was really impressive, is doing something that is not interesting for any applications,” said Dr. Aharonov, who also works as chief scientific officer for Qedma, a quantum computing company.

The Google calculation also turned out to be less impressive than it first appeared. A team of Chinese researchers was able to perform the same calculation on a non-quantum supercomputer in just over five minutes, far faster than the 10,000 years estimated by the Google team.

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 atomic-scale bar magnets—small enough to be governed by the uncanny rules of quantum mechanics—in a magnetic field. It is a simple system known as the Ising model, which is often used to study magnetism.

This problem is too complex for an exact answer to be computed 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 in quantum noise inevitably creep in and induce errors—but each calculation was fast, so it could be performed repeatedly.

For many of the calculations, additional noise was actually added, making the answers even more unreliable. But by varying the amount of noise, the researchers were able to 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 run the same circuit again,” said Abhinav Kandala, the head of quantum functions and demonstrations at IBM Quantum and author of the Nature paper. “And when we have results of these different noise levels, we can extrapolate back to what the result would have been without noise.”

Essentially, the researchers were able to subtract the effects of noise from the unreliable quantum calculations, a process they call error reduction.

“You have to get around that by inventing very clever ways to mitigate the noise,” said Dr. Aharonov. “And that’s what they do.”

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

But how good was the response?

For help, the IBM team turned to physicists at the University of California, Berkeley. Although an Ising model with 127 bar magnets is too large, with far too many possible configurations, to fit into a conventional computer, classical algorithms can produce approximate answers, a technique similar to how compression in JPEG images discards less crucial data away to reduce the size of the file while preserving most of the image’s details.

Michael Zaletel, a physics professor at Berkeley and an author for the journal Nature, said that when he started working with IBM, he thought his classical algorithms would outperform the quantum algorithms.

“It turned out a little different than I expected,” said Dr. Zaletel.

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 cases, quantum and classical algorithms produced different answers, and it was the quantum one that was correct.

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,” said Sajant Anand, a graduate student at Berkeley who did much of the work on the classical approximations.

It is not clear that quantum computation is indisputably the winner over classical techniques for the Ising model.

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

“It is not obvious that they have achieved quantum supremacy here,” said Dr. Zaletel.

In the long run, quantum researchers expect that another approach, error correction, will be able to detect and correct computational errors, opening the door for quantum computers to advance more quickly for many purposes.

Error correction is already used in conventional computers and data transmission to correct errors. But for quantum computers, error correction is likely years away, requiring better processors capable of processing many more qubits.

Error mitigation, the IBM researchers believe, is a temporary solution that can be used now for increasingly complex problems beyond the Ising model.

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

These may include figuring out the properties of exotic materials, speeding up drug discovery, and modeling fusion reactions.

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