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Parallel syndrome extraction with shared flag qubits for CSS codes of distance three | | Pei-Hao Liou
; Ching-Yi Lai
; | | Date: |
1 Aug 2022 | | 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. | | Source: | arXiv, 2208.00581 | | Services: | Forum | Review | PDF | Favorites | |
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