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Paper 1

Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes

Jon Nelson, Gregory Bentsen, Steven T. Flammia, Michael J. Gullans

Year

2023

Journal

arXiv preprint

DOI

arXiv:2311.17985

arXiv

2311.17985

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 ''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.

Open paper

Paper 2

Subwavelength vacuum lattices and atom-atom interactions in photonic crystals

A. González-Tudela, C. -L. Hung, D. E. Chang, J. I. Cirac, H. J. Kimble

Year

2014

Journal

arXiv preprint

DOI

arXiv:1407.7336

arXiv

1407.7336

We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large and strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation

Open paper