A colossal advantage: 3D-local noisy shallow quantum circuits defeat unbounded fan-in classical circuits

TL;DR

This paper demonstrates a quantum advantage where 3D-local noisy shallow quantum circuits can solve certain problems reliably, outperforming classical AC0 circuits of similar size, even under noise and locality constraints, paving the way for experimental validation.

Contribution

It introduces a problem solvable by noisy 3D-local quantum circuits that surpasses classical AC0 circuits, overcoming previous limitations related to noise and locality.

Findings

Quantum circuits solve the problem with high probability despite noise.

Classical AC0 circuits of subexponential size fail on random instances.

The approach is suitable for experimental realization.

Abstract

We present a computational problem with the following properties: (i) Every instance can be solved with near-certainty by a constant-depth quantum circuit using only nearest-neighbor gates in 3D even when its implementation is corrupted by noise. (ii) Any constant-depth classical circuit composed of unbounded fan-in AND, OR, as well as NOT gates, i.e., an AC0-circuit, of size smaller than a certain subexponential, fails to solve a uniformly random instance with probability greater than a certain constant. Such an advantage against unbounded fan-in classical circuits was previously only known in the noise-free case or without locality constraints. We overcome these limitations, proposing a quantum advantage demonstration amenable to experimental realizations. Subexponential circuit-complexity lower bounds have traditionally been referred to as exponential. We use the term colossal since our fault-tolerant 3D architecture resembles a certain Roman monument.