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Fault-tolerance thresholds for code conversion schemes with quantum Reed-Muller codes
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DOI：10.1088/2058-9565/abb027.png)
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Abstract
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Code concatenation and conversion are two prominent methods to realize universal fault-tolerant quantum computation without the need for magic state distillation. In this paper, we analyze three quantum Reed-Muller (QRM) codes of different code lengths under code conversion schemes, and compare them with the 105-qubit concatenated code on optimized encoding circuits. The depolarizing error thresholds for the 7-, 15-, and 31-qubit QRM codes turn out to be 1.19 x 10(-3), 5.40 x 10(-4)and 2.41 x 10(-6) respectively, all of three compared unfavorably with the improved result of 1.52 x 10(-3)for the 105-qubit code, which indicates a relatively small error-suppression capability and strict precision requirements for hardware equipment when using the code conversion scheme. While for resource requirements, code conversion schemes show obvious advantages. For the seven-qubit QRM code, the required qubit and gate overheads for level-3 gates to achieve the target logical error rate of 10(-15) are roughly 4 orders of magnitude smaller than those for the 105-qubit code.
Keywords:
universal quantum computation
fault-tolerant code conversion
universal concatenated code
depolarizing threshold value
resource overhead
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