• *Physical* 17, 13

Researchers have used quantum computers to solve difficult physics problems. But claims of a quantum “advantage” must wait as ever-improving algorithms boost the performance of classical computers.

Quantum computers have great potential as tools for performing complex calculations. But exactly when their abilities will surpass those of their classical counterparts is an ongoing debate. Recently, a 127-qubit quantum computer was used to calculate the dynamics of a series of small magnets, or spins, a problem that would take an unfathomable amount of time to solve exactly with a classical computer. [1]. The team behind the feat demonstrated that their quantum calculation was more accurate than non-exact classical simulations using state-of-the-art approximation methods. But these methods represented only a small handful of those available to classical computing researchers. Now Joseph Tindall and his colleagues at the Flatiron Institute in New York show that a classical computer using an algorithm based on the so-called tensor network can produce very precise solutions to the spin problem with relative ease. [2]. The results show that the field of classical computing still has many tricks up its sleeve, making it difficult to predict when the field of quantum computing will gain the upper hand.

Quantum computers have made huge leaps in performance, leading to natural comparisons with classical computers. In 2019, Google’s 53-qubit Sycamore quantum computer took 200 seconds to perform a specific calculation that was predicted to take 10,000 years with a classical computer, leading researchers to claim their system had a quantum advantage. [3]. Other groups immediately responded to the claim, pointing out several ways they could speed up classical methods, reducing the supposed advantage of Google’s quantum technique (see Viewpoint: Imperfections Reduce Simulation Cost of Quantum Computers). “Quantum computing isn’t the only thing that’s getting better,” says Tindall. “Classical methods are also improving and have been for decades.”

Researchers are now avoiding the direct rivalry between quantum and classical, focusing instead on where quantum computers can be useful. “There’s this unfortunate emphasis on trying to immediately show an advantage,” says IBM quantum computing expert Abhinav Kandala. Instead of an advantage, he says the first thing to show is “utility,” which is defined as a quantum computer providing a precise solution to a problem that is beyond exact classical calculus. Achieving utility has been a challenge, given that quantum computers are currently noisy and error-prone. Kandala and his colleagues demonstrated quantum utility in the summer of last year by using IBM’s 127-qubit Eagle quantum computer to solve a common type of physics problem based on the so-called Ising model. [1].

The Ising model refers to a collection of spins that interact with each other, affecting their mutual alignment. The Ising model is often used by condensed matter physicists to study magnetic phenomena in materials, but it becomes increasingly difficult to solve Ising-based problems as the number of spins increases. Focusing on a specific spin system, Kandala and his colleagues used their quantum computer to determine quantities such as the system’s overall spin alignment or magnetization. They then developed a noise mitigation strategy to extrapolate the predictions to zero-error solutions, which they compared to exact solutions that were available for certain values of the input variables. Through this comparison, the researchers showed that their quantum calculations were more accurate than predictions obtained from classical simulations performed by team members at the University of California, Berkeley, on a supercomputer.

News of this demonstration of quantum utility spread quickly. “It was a big deal,” says Tindall. But after analyzing the result, he and his colleagues wondered if the IBM team had perhaps underestimated the capabilities of classical methods in their precision comparison. Tindall’s team now reports an improved classical simulation method that better compares to the quantum one used by Kandala’s team.

The new classical method uses tensor networks: series of data sets connected through links. Physicists have long used tensor networks to study many-body quantum systems, such as electrons in a superconductor or atoms in a molecule. Networks allow them to compress the enormous amounts of information contained in a complete description of the wave function of that system. “A tensor network is essentially like a zip file for the wave function,” says Tindall.

Tindall and his colleagues designed a “zip file” that simulates the 127 qubits of the IBM computer. To fully represent the wave function of these qubits you would need 2^{127}≈ 10^{38} numbers, which in bytes would be billions and billions of times more data than that stored in all the computers in the world. The researchers reduced the amount of data needed to less than a billion numbers by assuming that some of the wave function information (specifically some of the information about quantum entanglement between qubits) could be neglected.

Applying their network to the Ising model problem, Tindall and his colleagues solved the problem on a classical computer with greater precision than obtained using a quantum computer. Tindall notes that Kandala and his colleagues also performed tensor network calculations as part of their classical comparison. But he says the network they chose was not explicitly designed to have the same geometry as their computer. Making a different decision meant that Tindall and his colleagues didn’t need a supercomputer to run their tests. “You could run some of the simulations on a mobile phone,” he says.

Tindall and his colleagues “have successfully applied a novel classical algorithm to a timely problem that is relevant to a large part of the physics community,” says Michael Lubasch, a scientist at quantum computing company Quantinuum. But Lubasch emphasizes that the classical algorithm the team used is designed to work on a particular problem in the Ising model. Researchers can’t use this algorithm to simulate all the calculations a quantum computer can perform, he says.

Kandala is not surprised that a classical method met the requirements of his quantum computing. “This was exactly the kind of response we were hoping for,” he says. He calls the back-and-forth between the quantum and classical computing communities a “symbiotic relationship,” in which the two sides challenge each other by developing increasingly sophisticated computing methods. “Hopefully we can work together to solve the difficult problems that will take us from profit to advantage,” he says. Tindall imagines that such a problem will eventually appear, but he has not committed to a time frame for that appearance. “It could be a long time from now,” he says.

–Michael Schirber

Michael Schirber is corresponding editor of *Physics Magazine* based in Lyon, France.

## References

- and. Kim
*et al.*“Evidence for the usefulness of quantum computing before fault tolerance”, Nature**618**500 (2023). - J. Tindall
*et al.*“IBM’s Eagle experiment’s efficient simulation of a tensor network kicked off the Ising experiment,” quantum PRX**5**010308 (2024). - F.Arute
*et al.*“Quantum supremacy using a programmable superconducting processor”, Nature**574**505 (2019).

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