Decoding quantum errors with subspace expansions

Jarrod R. McClean (), Zhang Jiang, Nicholas C. Rubin, Ryan Babbush and Hartmut Neven
Additional contact information
Jarrod R. McClean: Google Inc.
Zhang Jiang: Google Inc.
Nicholas C. Rubin: Google Inc.
Ryan Babbush: Google Inc.
Hartmut Neven: Google Inc.

Nature Communications, 2020, vol. 11, issue 1, 1-9

Abstract: Abstract With rapid developments in quantum hardware comes a push towards the first practical applications. While fully fault-tolerant quantum computers are not yet realized, there may exist intermediate forms of error correction that enable practical applications. In this work, we consider the idea of post-processing error decoders using existing quantum codes, which mitigate errors on logical qubits using post-processing without explicit syndrome measurements or additional qubits beyond the encoding overhead. This greatly simplifies the experimental exploration of quantum codes on real, near-term devices, removing the need for locality of syndromes or fast feed-forward. We develop the theory of the method and demonstrate it on an example with the perfect [[5, 1, 3]] code, which exhibits a pseudo-threshold of p ≈ 0.50 under a single qubit depolarizing channel applied to all qubits. We also provide a demonstration of improved performance on an unencoded hydrogen molecule.

Date: 2020
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DOI: 10.1038/s41467-020-14341-w

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