Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

Physical Review Letters
Aleksander KubicaKrysta M Svore

Abstract

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_{3DCC}^{(1)}≃1.9% and p_{3DCC}^{(2)}≃27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

References

Aug 1, 1996·Physical Review. a·A R Calderbank, P W Shor
Aug 1, 1986·Physical Review. B, Condensed Matter·M S ChallaK Binder
Feb 1, 1991·Physical Review. B, Condensed Matter·J Lee, J M Kosterlitz
Mar 16, 1992·Physical Review Letters·C Borgs, R Kotecký
Jul 20, 2001·Physical Review Letters·A HoneckerP Pujol
Dec 13, 2006·Physical Review Letters·H Bombin, M A Martin-Delgado
Apr 28, 2009·Physical Review Letters·Bryan Eastin, Emanuel Knill
Oct 2, 2009·Physical Review Letters·Helmut G KatzgraberM A Martin-Delgado
Jul 30, 2016·Nature Communications·Benjamin J BrownDan E Browne

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Citations

Aug 7, 2019·Physical Review Letters·Aleksander Kubica, John Preskill
Apr 18, 2020·Physical Review Letters·David K TuckettBenjamin J Brown
Jan 23, 2021·Scientific Reports·Michael VasmerAleksander Kubica

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