



01860nas a2200145   4500008004100000245007100041210006900112260001500181520139900196100001601595700002101611700002401632700002101656856003701677       2023                        eng d00aFault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes0 aFaultTolerant Quantum Memory using LowDepth Random Circuit Codes  c11/29/20233 a<p>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 by Darmawan et al. As in their work, 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 so-called &#39;&#39;tropical&#39;&#39; 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.</p>1 aNelson, Jon1 aBentsen, Gregory1 aFlammia, Steven, T.1 aGullans, Michael  uhttps://arxiv.org/abs/2311.17985