Complexity of Local Quantum Circuits under Nonunital Noise

TL;DR

This paper demonstrates that local quantum circuits affected by nonunital noise can perform universal computation without mid-circuit measurements, challenging previous limitations and showing nearly noiseless dynamics are computationally hard to simulate.

Contribution

It extends the understanding of quantum circuit complexity by showing nonunital noise allows deep, error-corrected local circuits without measurements, unlike unital noise scenarios.

Findings

Nonunital noise enables error correction in local circuits without measurements.

Local quantum dynamics with weak nonunital noise are computationally universal.

Quantifies how nonunital noise affects the contraction properties of local random circuits.

Abstract

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as depolarizing noise. Building on the idea of the "quantum refrigerator" [Ben-Or, Gottesman and Hassidim (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension $d\geq 1$, can correct errors without mid-circuit measurements and extend computation to any depth, with only polylogarithmic overhead in the depth and the number of qubits. This implies that local quantum dynamics subjected to sufficiently weak nonunital noise is computationally universal and nearly as hard to simulate as noiseless dynamics. Additionally, we quantify the contraction property of local random circuits in the presence of nonunital noise.