• *Physics* 17, 13

Scientists have harnessed quantum computers to resolve complex physics issues. However, reports of a quantum “advantage” must be put on hold as steadily enhancing algorithms improve the functionality of classical computers.

Quantum computers have an abundance of potential for conducting intricate calculations. However, the timing of when their capabilities will outdo those of their classical equivalents is an ongoing matter of contention. A 127-qubit quantum computer was recently used to compute the dynamics of an array of tiny magnets, or spins—the sort of problem that would take an unimaginably long time to accurately solve using a classical computer [1]. The team behind this accomplishment demonstrated that their quantum computation was more precise than nonexact classical simulations employing cutting-edge approximation methods. However, it should be noted that these methods represent a mere fraction of the multitude of options available to researchers in the field of classical computing. Meanwhile Joseph Tindall and his colleagues at the Flatiron Institute in New York reveal that a classical computer employing an algorithm based on a tensor network can easily produce highly accurate solutions to the spin problem [2]. These findings demonstrate that classical computers are still equipped with numerous capabilities, making it difficult to predict when quantum computers will gain an upper hand.

Quantum computers have made remarkable strides in performance, inviting natural comparisons with classical computers. In 2019, Google’s 53-qubit Sycamore quantum computer took 200 seconds to execute a specific computation that was projected to require 10,000 years with a classical computer, leading researchers to declare that their system enjoyed a quantum advantage [3]. Other groups swiftly refuted this claim, pointing out various methods by which they could expedite classical techniques, thereby decreasing the supposed advantage of Google’s quantum method. “Quantum computing is not the only thing that’s improving,” Tindall says. “Classical methods are also improving and have been improving for decades.”

Researchers are now steering clear of a direct quantum–classical rivalry, instead concentrating on where quantum computers can demonstrate their usefulness. IBM quantum-computing specialist Abhinav Kandala emphasizes the unfortunate emphasis on immediately attempting to reveal an advantage. He asserts that the primary thing to demonstrate should be “utility,” which refers to a quantum computer delivering an accurate solution to a problem that lies beyond exact classical computation. Achieving utility has been tough, given that today’s quantum computers are noisy and susceptible to errors. Kandala and his colleagues exhibited quantum utility last summer using IBM’s 127-qubit Eagle to solve a common type of physics problem based on the Ising model [1].

The Ising model relates to a collection of spins that interact with one another, affecting their mutual alignment. Physicists who specialize in condensed matter frequently turn to the Ising model to explore magnetic phenomena in materials, although it becomes increasingly difficult to solve Ising-based problems as the number of spins rises. Focusing on a specific spin system, Kandala and his colleagues employed their quantum computer to determine quantities such as the overall spin orientation, or magnetization. They then developed a noise-mitigation strategy to extrapolate the predictions to zero-error solutions, which were compared to exact solutions available for certain input variables. Through this comparison, the researchers exhibited that their quantum computations were more accurate than predictions derived from classical simulations carried out by team members from the University of California, Berkeley, using a supercomputer.

News of this quantum-utility demonstration spread rapidly. “It was a significant development,” said Tindall. However, after examining the results, he and his colleagues wondered if the IBM team had perhaps underestimated the capabilities of classical methods when contrasting their accuracy. Tindall’s team now divulges an enhanced classical simulation technique that aligns more closely with the quantum method used by Kandala’s team.

The novel classical method utilizes tensor networks—series of data arrays linked together. Physicists have long employed tensor networks to study quantum systems involving many particles, such as the electrons in a superconductor or the atoms in a molecule. The networks enable them to compress the astronomical amounts of information encapsulated in a comprehensive description of the wave function of such a system. “A tensor network is essentially the equivalent of a zip file for the wave function,” according to Tindall.

Tindall and his colleagues formulated a “zip file” simulating the 127 qubits in IBM’s computer. Fully depicting the wave function of these qubits would necessitate around 10^{38} numbers, which in bytes would amount to trillions of times more data than that stored on all the world’s computers. The researchers minimized the amount of data needed to less than about a billion numbers by making an assumption that some of the wave function’s information—specifically details concerning quantum entanglement between qubits—could be omitted.

Using their network to address the Ising-model problem, Tindall and his colleagues solved the problem on a classical computer with greater accuracy than was achieved using the quantum method. Tindall highlights that Kandala and his colleagues also executed tensor-network computations as part of their classical comparison. However, he asserts that they selected a different network design that wasn’t explicitly intended to have the same architecture as their computer. Opting for a different design meant that Tindall and his colleagues were not compelled to utilize a supercomputer to execute their trials. “You could run some of the simulations on a mobile phone,” he adds.

Tindall and his colleagues have successfully applied an innovative classical algorithm to a timely problem that pertains to a large section of the physics community, according to Michael Lubasch, a scientist at the quantum-computing company Quantinuum. However, Lubasch stipulates that the classical algorithm the team utilized is tailored to operate for a specific Ising-model problem. He asserts that such an algorithm cannot be used to replicate all computations that a quantum computer can perform.

Kandala isn’t surprised that a classical method has matched the standard set by their quantum computation. “This was precisely the type of response we were anticipating,” he says. He depicts the dynamic interplay between the quantum- and classical-computing communities as 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 challenging issues that will propel us from utility to advantage,” he concludes. Tindall acknowledges that there will likely emerge such a problem eventually, but he refrains from setting a timeline for its emergence. “It could be a considerable length of time,” he confides.

–Michael Schirber

Michael Schirber is a Corresponding Editor for *Physics Magazine* based in Lyon, France.

## References

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

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