Fault-tolerant quantum memory using low-depth random circuit codes

Published

January 10, 2025

Author(s)

Jon Nelson, Gregory Bentsen, Steven Flammia, Michael Gullans

Abstract

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood decoder for depolarizing noise similar to work in Darmawan et al. [1]. As in [1], we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a tropical tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is sub-optimal.

Citation

Physical Review Research

Volume

7

Issue

1

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevResearch.7.013040

Local Download

Keywords

quantum error correction, quantum computing, statistical mechanics

Citation

Nelson, J. , Bentsen, G. , Flammia, S. and Gullans, M. (2025), Fault-tolerant quantum memory using low-depth random circuit codes, Physical Review Research, [online], https://doi.org/10.1103/PhysRevResearch.7.013040, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=957035 (Accessed October 20, 2025)