Quantum advantage with noisy shallow circuits in 3D

TL;DR

This paper demonstrates a quantum advantage in solving certain relation problems using shallow, local quantum circuits in 1D and 3D, even with noise, outperforming classical circuits of the same depth.

Contribution

It extends quantum advantage results to 1D local circuits and introduces a noise-tolerant quantum advantage in 3D using surface codes.

Findings

Quantum advantage persists in 1D local circuits.

Noisy 3D quantum circuits outperform classical counterparts.

Surface code enables single-shot logical state preparation.

Abstract

Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any classical constant depth circuit composed of bounded fan-in gates. Here we provide two extensions of this result. Firstly, we show that a separation in computational power persists even when the constant-depth quantum circuit is restricted to geometrically local gates in one dimension. The corresponding quantum algorithm is the simplest we know of which achieves a quantum advantage of this type. It may also be more practical for future implementations. Our second, main result, is that a separation persists even if the shallow quantum circuit is corrupted by noise. We construct a relation problem which can be solved with near certainty using a noisy constant-depth quantum circuit composed of geometrically local gates in three dimensions, provided the noise rate is below a certain constant threshold value. On the other hand, the problem cannot be solved with high probability by a noise-free classical circuit of constant depth. A key component of the proof is a quantum error-correcting code which admits constant-depth logical Clifford gates and single-shot logical state preparation. We show that the surface code meets these criteria. To this end, we provide a protocol for single-shot logical state preparation in the surface code which may be of independent interest.