Today, quantum computers are small in scale—the chip in 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 again, you will most likely get different answers each time.

But with their intrinsic ability to consider many possibilities simultaneously, quantum computers don’t have to be very large to solve certain thorny computational problems, and on Wednesday IBM researchers announced they have developed a method to deal with the unreliability in one way would lead to reliable, useful answers.

“What IBM has shown here is really an amazingly important step in the direction of making strides toward serious quantum algorithmic design,” said Dorit Aharonov, a professor of computer science at the Hebrew University of Jerusalem, who was not involved with the research.

While researchers at Google claimed in 2019 they’d achieved “quantum supremacy” — a task done much more quickly on a quantum computer than on a traditional computer — researchers at IBM say they’ve achieved something new and more useful, albeit with a more modest name.

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

A team of IBM scientists working for Dr. Gambetta described their findings in an article published Wednesday in the journal Nature.

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

This allows quantum computers to perform many calculations in one go, while digital computers have to perform each calculation individually. By accelerating computation, quantum computers could potentially solve large, complex problems in fields like chemistry and materials science that are unattainable today. Quantum computing could also have a dark side, compromising privacy with algorithms that break protections for passwords and encrypted communications.

When Google researchers made their claim of primacy in 2019, they said 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.

However, some other researchers, including those from IBM, dismissed the claim, saying the problem was fabricated. “Google’s experiment, as impressive as it was, and it was really impressive, does something that isn’t interesting for any application,” said Dr. Aharonov, who also works as the scientific director of Qedma, a quantum computing company.

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 the Google team had estimated.

The IBM researchers in the new study performed a different task of interest to physicists. They used a 127-qubit quantum processor to simulate the behavior of 127 atomic-scale bar magnets — tiny enough to obey the spooky rules of quantum mechanics — in a magnetic field. This is a simple system called the Ising model, which is often used to study magnetism.

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

On the quantum computer, the calculation took less than a thousandth of a second. Each quantum calculation was unreliable—fluctuations in quantum noise inevitably interfere and introduce errors—but each calculation was fast, allowing it to be performed repeatedly.

In fact, extra noise was intentionally added to many calculations, making the answers even less reliable. However, by varying the amount of noise, the researchers were able to determine the specific properties of the noise and its effects at each step of the calculation.

“We can amplify the noise very precisely and then run the same circuit again,” said Abhinav Kandala, manager of quantum capabilities and demonstrations at IBM Quantum and author of the Nature article. “And once we have results on these different noise levels, we can calculate back to what would have been the result without the noise.”

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

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

In all, the computer ran the calculation 600,000 times, arriving at a result for the total magnetization generated by the 127 bar magnets.

But how good was the answer?

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 and with far too many possible configurations to fit in a conventional computer, classical algorithms can provide approximate answers, a technique similar to compression in JPEG images containing less important data discards to reduce the size of the file while preserving most of the image details.

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

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

Certain configurations of the Ising model can be solved exactly, and for the simpler examples, both the classical and quantum algorithms agreed. For more complex but solvable cases, the quantum algorithm and the classical algorithm gave different answers, and it was the quantum algorithm that was correct.

For other cases where quantum and classical calculations differ 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 it has done the classical approximations.

It is not clear whether quantum computing is the undeniable winner over classical techniques for the Ising model.

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

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

In the long term, quantum scientists expect that another approach, error correction, will be able to detect and correct computational errors and that this will open the door to many applications for quantum computers.

In conventional computers and data transmission, error correction is already used to fix corruption. But for quantum computers, error correction will likely be years away, requiring better processors that can handle many more qubits.

IBM scientists believe that error mitigation is a temporary solution that can now be used for increasingly complex problems outside of the Ising model.

“This is one of the simplest scientific problems there is,” said Dr. Gambetta. “So it’s a good start. But now the question is: how to generalize it and move on to more interesting scientific problems?”

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