Complexity of Local Quantum Circuits under Nonunital Noise

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless midcircuit 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 [Quantum refrigerator, arXiv1301.1995 (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi><a:mo>≥</a:mo><a:mspace width="0.2em"/><a:mn>1</a:mn></a:math>, can correct errors without midcircuit 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 are 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.