# Simulations using a quantum computer show the current limits of the technology

Physics 15, 175

Quantum circuits still cannot outperform classical circuits when simulating molecules.

Quantum computers promise to directly simulate systems governed by quantum principles, such as molecules or materials, since quantum bits themselves are quantum objects. Recent experiments have demonstrated the power of these devices when performing carefully chosen tasks. But a new study shows that for problems of real interest, like calculating the energy states of a cluster of atoms, quantum simulations are no more accurate than those of classical computers. [1]. The results offer a benchmark for judging how close quantum computers are to becoming useful tools for chemists and materials scientists.

Richard Feynman proposed the idea of ​​quantum computers in 1982, suggesting that they could be used to calculate the properties of quantum matter. Today, quantum processors are available with several hundred quantum bits (qubits), and some can, in principle, represent quantum states impossible to encode in a classical device. The 53-qubit Sycamore processor developed by Google has demonstrated the potential to perform calculations in days that would take several millennia on current conventional computers [2]. But this “quantum advantage” is only obtained for certain computational tasks that exploit the strengths of these devices. How well do these quantum computers fare in the day-to-day challenges that researchers who study molecules and materials really want to solve?

Garnet Chan of the California Institute of Technology and his colleagues attempted to answer this question by performing simulations of a molecule and a material using a 53-qubit Google processor called Weber, based on Sycamore. “We didn’t expect to learn anything new in chemistry, given the complexity of these systems and the quality of classical algorithms,” Chan says. “The goal was to understand the performance of Sycamore hardware for a physically relevant circuit class with a physically relevant pass metric.”

The team selected two problems of current interest, without any consideration as to their suitability for a quantum circuit. The first consists in calculating the energy states of a group of 8 iron (Fe) and sulfur (S) atoms present in the catalytic core of the enzyme nitrogenase. This enzyme breaks strong bonds in nitrogen molecules as the first step in an important biological process called nitrogen fixation. Understanding the chemistry of this process could be useful in developing artificial nitrogen-fixing catalysts for the chemical industry.

Second, the team sought to infer the collective behavior of magnetic spins in the crystalline material alpha-ruthenium trichloride ( -RuCl3), which is thought to adopt an exotic quantum phase called the low-temperature spin liquid [3]. The study of these states is part of the larger project to explore quantum phenomena in materials.

The ground electronic states and low energy excitations of the two systems are determined by how the electron spins of the atoms interact with each other. These spins could be encoded into single qubits and their interactions simulated by coupling the qubits into circuits that mirror the structures of the two systems.

One of the main obstacles to accurate quantum simulations is noise – random errors both in the switching of the “gates” that perform quantum logic operations and in the reading of their output states. These errors accumulate and limit the number of gate operations a computation can perform before noise dominates. The researchers found that simulations with more than 300 gates were overwhelmed with noise. But the more complex the system, the more doors are needed. The Fe-S cluster, for example, has long-range interactions between spins; To be accurately represented, such interactions require many gates.

Due to these challenges, simulations on the Weber chip were rather limited. For example, the simulations provided predictions for the energy spectra of the Fe-S cluster and the heat capacity of -RuCl3 reasonably well, but only if the simulated systems weren’t too big. For -RuCl3 the team was only able to obtain significant results for a very small 6-atom piece of the crystal lattice; if they increased the size to just 10 atoms, the noise would overwhelm the output. And constraints on gate operations meant that only about a fifth of Weber’s quantum resources could be used for computation. However, Chan and his colleagues were able to increase this usage to half the resources when they moved to simulating a model system better suited to Weber’s specific circuit architecture.

Chan says it’s hard to see quantum circuits performing much better for problems like this until there are better ways to reduce noise or correct errors. (The schemes developed so far do not provide full quantum error correction.)

“These results are state-of-the-art and show the challenges in terms of future device performance,” says Alán Aspuru-Guzik of the University of Toronto, an expert in the use of quantum computing in chemistry. and the materials. But capabilities have steadily increased since the first quantum computers of the 2000s, as evidenced by this new work, he says. Peter Love, a quantum simulation specialist at Tufts University, Massachusetts, is optimistic about the results. “These results are both exciting and intimidating,” he says. “Compared to our expectations in 2005, they are absolutely incredible, but they also show how much work lies ahead of us.”

–Philip Ball

Philip Ball is a freelance science writer in London. His latest book is modern myths (University of Chicago Press, 2021).

## References

1. RN Tazhigulov et al.“Simulating Models of Difficult Correlated Molecules and Materials on the Sycamore Quantum Processor,” Quantum PRX 3040318 (2022).
2. F. Arrival et al.“Quantum Supremacy Using a Programmable Superconducting Processor,” Nature 574505 (2019).
3. H.Li et al.“Giant Phonon Anomalies in Kitaev’s Near Quantum Spin Liquid ${\text{RuCl}}_{3}$“, Nat. Common. 123513 (2021).

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