Classical product code constructions for quantum Calderbank-Shor-Steane codes

Author:

Ostrev Dimiter1,Orsucci Davide1,Lázaro Francisco1,Matuz Balazs1

Affiliation:

1. Institute of Communications and Navigation, German Aerospace Center (DLR), 82234 Weßling, Germany

Abstract

Several notions of code products are known in quantum error correction, such as hypergraph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which is a natural generalization of classical product codes to quantum codes: starting from a set of component Calderbank-Shor-Steane (CSS) codes, a larger CSS code is obtained where both X parity checks and Z parity checks are associated to classical product codes. We deduce several properties of product CSS codes from the properties of the component codes, including bounds to the code distance, and show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors. We then specialize to the case of single-parity-check (SPC) product codes which in the classical domain are a common choice for constructing product codes. Logical error rate simulations of a SPC 3-fold product CSS code having parameters [[512,174,8]] are shown under both a maximum likelihood decoder for the erasure channel and belief propagation decoding for depolarizing noise. We compare the results with other codes of comparable length and dimension, including a code from the family of asymptotically good Tanner codes. We observe that our reference product CSS code outperforms all the other examined codes.

Funder

Project Error Correction for Quantum Information Processing (EQUIP), QuantERA II Programme, European Union’s Horizon 2020 research and innovation programme

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

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