# Quantum computer simulations show the limits of current technology

&ball; Physics 15, 175

Quantum circuits are still unable to outperform conventional circuits when simulating particles.

Quantum computers promise direct simulations of systems governed by quantum principles, such as particles or matter, because quantum qubits themselves are quantum things. Recent experiments have demonstrated the power of these devices when performing carefully selected tasks. But a new study shows that for real-world problems, like calculating the energy states of a group of atoms, quantum simulations are no more accurate than those of classical computers. [1]. The results provide 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, noting that they could be used to calculate the properties of quantum matter. Today, quantum processors are available with several hundred quantum bits (qubits), some of which can, in principle, represent quantum states that would be impossible to encode in a classical device. The 53 kilobyte Sycamore processor developed by Google has shown its ability to perform calculations in days that could take thousands of years on conventional computers today [2]. But this “quantum advantage” is only achieved for certain computational tasks that play a role in the power of these devices. How well do quantum computers tackle the kinds of everyday challenges that researchers who study molecules and materials actually want to solve?

Garnet Chan of the California Institute of Technology and his colleagues attempted to answer this question by running simulations of a molecule and matter using a 53-kilobit Google processor called Weber, based on Sycamore. “We didn’t expect to learn anything chemically new, given the complexity of these systems and the quality of the classical algorithms,” Chan said. “The goal was to understand how well Sycamore devices perform for a class of circuits that are physically relevant to a physically relevant measure of success. »

The team chose two currently important problems, without any consideration of their relevance to the quantum circuit. The first consists in calculating the energy states of a group of 8 atoms of iron (Fe) and sulfur (S) 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 can be useful in the development of synthetic nitrogen fixation catalysts for the chemical industry.

Second, the team sought to infer the collective behavior of ferromagnets in the crystalline material α-ruthenium trichloride (

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-RuCl3), which is thought to adopt a particular quantum phase called spin fluid at lower temperatures [3]. The study of such 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 can be encoded into single qubits and their interactions simulated by coupling 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 the computation can perform before noise dominates. The researchers found that simulations of more than 300 gates were overshadowed by noise. But the more complex the system, the more doors are needed. The Fe-S group, for example, contains long-range interactions between rings; To be accurately represented, such interactions require many gates.

Due to these challenges, simulations on the Weber chip have been somewhat limited. For example, the simulations provided predictions of the energy spectra of the Fe–S group and the heat capacity of

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-RuCl3 Reasonably good – but only if the simulated systems are not too large. for

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-RuCl3 The team was only able to obtain significant results for a very small 6-atom piece of the crystal lattice; If they only increased the size to 10 atoms, the noise would overwhelm the output. And the limitations of gate operations mean that only about a fifth of Weber’s quantum resources can be used for computation. However, Chan and his colleagues could increase this resource usage by half when they move to model system simulations more suited to specific Weber circuit architectures.

Chan says it’s hard to see quantum circuits doing better at solving problems like this until there are better ways to reduce noise or correct errors. (Graphs developed so far do not allow full quantum error correction.)

“These results are state-of-the-art and show the challenges for device performance in the future,” says Alán Aspuru-Guzik of the University of Toronto, who specializes in the use of quantum computing. . in chemistry and 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 in Massachusetts, is optimistic about the results. “These discoveries are exciting and frightening at the same time,” he says. “Compared to our 2005 forecast, this is quite surprising, but it also shows how much work we still have to do. »

–Philip Paul

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.Simulation of models of difficult interconnected molecules and materials on a Sycamore quantum processor. Quantum PRX 3040318 (2022).
2. F. Arot et al.Quantum supremacy using a programmable superconducting processor. temper nature 574505 (2019).
3. H.Li et al.Giant phonon anomalies in near Kitaev quantum spin fluid
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» nat. common. 1 23513 (2021).

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