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arXiv · 2208.00581

Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three

Pei-Hao Liou·Ching-Yi Lai
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Abstract

To perform achieve fault-tolerant quantum computation, one can use flagged syndrome extraction with fewer ancilla qubits. However, it suffers from long circuit depth if one stabilizer is measured at a time. Previously, Reichardt showed that it is possible to measure multiple stabilizers with at most one shared flag qubit for certain small quantum codes. In this paper, we propose a procedure for general Calderbank-Shor-Steane codes of distance three so that multiple $Z$-stabilizers ($X$-stabilizers) can be fault-tolerantly measured in parallel with one shared flag qubit. We simulate the memory and computation pseudo-thresholds for various code schemes. In particular, our parallel scheme based on Shor's nine-qubit code performs better than known seven- and nine-qubit schemes in the literature.

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Pei-Hao Liou, Ching-Yi Lai. 2023-02-17. Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three. https://doi.org/10.1103/physreva.107.022614

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