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

TL;DR

This paper investigates the computational capabilities of dual-unitary quantum circuits, showing they are classically simulatable at early times but become universal quantum computers at later times, with sampling also being hard.

Contribution

It introduces a new family of classically simulatable circuits based on dual-unitary quantum circuits and characterizes their transition to universal quantum computation.

Findings

Early-time local expectation values are classically simulatable.

Late-time behavior enables universal quantum computation.

Sampling from these circuits is computationally hard.

Abstract

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.