Computational power of one- and two-dimensional dual-unitary quantum circuits

Ryotaro Suzuki1,2, Kosuke Mitarai1,3,4, and Keisuke Fujii1,3,5

1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin 14195, Germany
3Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Osaka 560-8531, Japan
4JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
5Center for Emergent Matter Science, RIKEN, Wako Saitama 351-0198, Japan

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Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes universal quantum computation different from classical computers. In this work, we propose a novel family of classically simulatable circuits by making use of dual-unitary quantum circuits (DUQCs), which have been recently investigated as exactly solvable models of non-equilibrium physics, and we characterize their computational power. Specifically, we investigate the computational complexity of the problem of calculating local expectation values and the sampling problem of one-dimensional DUQCs, and we generalize them to two spatial dimensions. We reveal that a local expectation value of a DUQC is classically simulatable at an early time, which is linear in a system length. In contrast, in a late time, they can perform universal quantum computation, and the problem becomes a BQP-complete problem. Moreover, classical simulation of sampling from a DUQC turns out to be hard.

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