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Quantum Physics
Title: Low-overhead quantum computing with the color code
(Submitted on 19 Jan 2022 (v1), last revised 9 Apr 2024 (this version, v2))
Abstract: Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the rich structure of the color-code phase to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, our approach yields about a $3\times$ improvement in the space-time overhead, obtained from a combination of a $1.5\times$ improvement in spatial overhead together with a $2\times$ speedup due to the parallelisation of commuting logical measurements. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10\% at a physical error rate of $10^{-3}$ and by 50\% at $10^{-4}$.
Submission history
From: Benjamin Brown [view email][v1] Wed, 19 Jan 2022 19:00:02 GMT (1123kb,D)
[v2] Tue, 9 Apr 2024 07:10:53 GMT (1573kb,D)
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