Parallel syndrome extraction with shared flag qubits for CSS codes of distance three

• URL: http://arxiv.org/abs/2208.00581v1
• Date: Mon, 1 Aug 2022 03:06:54 GMT
• Title: Parallel syndrome extraction with shared flag qubits for CSS codes of distance three
• Authors: Pei-Hao Liou, Ching-Yi Lai
• Abstract summary: It is possible to measure multiple stabilizers in parallel with at most one shared flag qubit for certain small quantum codes. We propose a procedure for general CSS codes of distance three so that multiple $Z$-stabilizers ($X$-stabilizers) can be fault-tolerantly measured in parallel with one shared flag qubit.
• Score: 3.1219977244201056
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 in parallel with at most one shared flag qubit for certain small quantum codes. In this paper, we propose a procedure for general CSS 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 nine-qubit schemes in the literature when the memory error rate is high.

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