Quantum computers today have a small computational reach, 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 do the same calculation over and over, they will most likely produce different answers each time.

But with their inherent ability to consider many possibilities at once, quantum computers don’t have to be very large to tackle some tricky computational problems, and IBM researchers announced on Wednesday that they had devised a method for dealing with unreliability in a way that would to reliable and helpful answers.

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

While Google researchers in 2019 claimed to have achieved quantum supremacy, a task performed much faster on a quantum computer than a conventional one, IBM researchers say they have achieved something new and more useful, albeit with a more modest name.

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 scientists working for Dr. Gambetta described their findings in a paper published Wednesday in the journal Nature.

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

This allows quantum computers to perform many calculations in one step, while digital ones must perform each calculation separately. By speeding up computation, quantum computers could potentially solve large, complex problems in fields like chemistry and materials science that are out of reach today. Quantum computers could also have a dark side by threatening privacy through algorithms that break the protections used for passwords and encrypted communications.

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

But some other researchers, including those at IBM, have dismissed the claim, saying the problem was contrived. Google’s experiment, as impressive as it was, and it was very impressive, is doing something that is of no interest to any application, said Dr. Aharonov, who also works as chief strategy officer at Qedma, a computer company quantum.

Google’s 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, much faster than the 10,000 years estimated by the Google team.

The IBM researchers in the new study did a different task, one that interests physicists. They used a quantum processor with 127 qubits to simulate the behavior of 127 atomic-scale rod magnets small enough to be governed by the spectral rules of quantum mechanics in a magnetic field. This is a simple system known as an Ising model, which is often used to study magnetism.

This problem is too complex to calculate an accurate answer even on the largest and fastest supercomputers.

On the quantum computer, the calculation took less than a millisecond to complete. Every quantum calculation was made up of unreliable fluctuations in quantum noise that inevitably got in the way and led to errors, but every calculation was rapid, so it could be done repeatedly.

Indeed, for many of the calculations, extra noise was deliberately added, making the answers even more unreliable. But by varying the amount of noise, the researchers were able to derive the specific characteristics of the noise and its effects at each stage of the calculation.

We can amplify the noise very precisely and then we can rerun the same circuit, said Abhinav Kandala, head of quantum capabilities and demonstrations at IBM Quantum and author of the Nature paper. And once we get the results of these different noise levels, we can extrapolate what the result would have been in the absence of noise.

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

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

Altogether, the computer performed the calculation 600,000 times, converging on one answer for the overall magnetization produced by the 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 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 strips away less crucial data to reduce the file size while preserving most of the image details.

Michael Zaletel, a physics professor at Berkeley and author of the Nature paper, said when he first started working with IBM, he thought its classical algorithms would perform better than quantum ones.

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

Some configurations of the Ising model can be solved exactly, and both the classical and quantum algorithms agree on the simplest examples. For more complex but solvable instances, quantum and classical algorithms yielded 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, said Sajant Anand, a Berkeley graduate student who has done much of the work on classical calculus approximations.

It is unclear whether quantum computing is the indisputable winner over classical techniques for the Ising model.

Mr. Anand is currently trying to implement an error-mitigation version of the classical algorithm, and it is possible that it could match or exceed the performance of quantum computations.

It’s not obvious that they’ve achieved quantum supremacy here, Dr. Zaletel said.

In the long run, quantum scientists expect that a different approach, error correction, will be able to detect and correct computational errors and that it will open the door for quantum computers to accelerate many uses.

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

Error mitigation, the IBM scientists believe, is an interim solution that can be used now for increasingly complex problems beyond the Ising model.

This is one of the simplest natural science problems ever, said Dr. Gambetta. So that’s a good starting point. But now the question is: how to generalize it and move on to more interesting natural science problems?

These could include understanding the properties of exotic materials, accelerating drug discovery and modeling fusion reactions.

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