Ability of stabilizer quantum error correction to protect itself from its own imperfection

The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it accordingly. However, hardware that performs quantum error correction itself is inevitably imperfect in practice. Here, we show that stabilizer codes possess a built-in capability of correcting errors not only on quantum information but also on faulty syndromes extracted by themselves. Shor's syndrome extraction for fault-tolerant quantum computation is naturally improved. This opens a path to realizing the potential of stabilizer quantum error correction hidden within an innocent looking choice of generators and stabilizer operators that have been deemed redundant.Comment: 9 pages, 3 tables, final accepted version for publication in Physical Review A (v2: improved main theorem, slightly expanded each section, reformatted for readability, v3: corrected an error and typos in the proof of Theorem 2, v4: edited language

Correction of Data and Syndrome Errors by Stabilizer Codes

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea of quantum data-syndrome (DS) codes that are capable of correcting both data qubits and syndrome bits errors. We study fundamental properties of quantum DS codes and provide several CSS-type code constructions of quantum DS codes.Comment: 2 figures. This is a short version of our full paper (in preparation

Quantum convolutional data-syndrome codes

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.Comment: Abstract submitted for The 20th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2019

Single-shot decoding of good quantum LDPC codes

Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Z\'emor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.Comment: 35 pages, 3 figure