Robust Syndrome Extraction via BCH Encoding

• URL: http://arxiv.org/abs/2311.16044v1
• Date: Mon, 27 Nov 2023 18:09:10 GMT
• Title: Robust Syndrome Extraction via BCH Encoding
• Authors: Eren Guttentag, Andrew Nemec, and Kenneth R. Brown
• Abstract summary: Quantum data-syndrome (QDS) codes protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS code is to choose a syndrome measurement code, a block code that encodes the syndrome of the underlying quantum code by defining additional stabilizer measurements. We show that these codes require $O(tlogell)$ extra measurements, where $ell$ is the number of stabilizer generators of the quantum code and $t$ is the number of errors corrected by the BCH code.
• Score: 4.123763595394021
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS code is to choose a syndrome measurement code, a classical block code that encodes the syndrome of the underlying quantum code by defining additional stabilizer measurements. We propose the use of primitive narrow-sense BCH codes as syndrome measurement codes. We show that these codes asymptotically require $O(t\log\ell)$ extra measurements, where $\ell$ is the number of stabilizer generators of the quantum code and $t$ is the number of errors corrected by the BCH code. Previously, the best known general method of constructing QDS codes out of quantum codes requires $O(t^3\log\ell)$ extra measurements. As the number of additional syndrome measurements is a reasonable metric for the amount of additional time a general QDS code requires, we conclude that our construction protects against the same number of syndrome errors with significantly less time overhead.

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