Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code

We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford) \(\overline{CCZ}\) between three 2D surface codes in time linear in...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Scruby, T R, Browne, D E, Webster, P, Vasmer, M
Format: Article
Language:English
Subjects:
Building codes
Codes
Decoding
Error analysis
Error detection
Optimization
Online Access:Get full text
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Summary:We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford) \(\overline{CCZ}\) between three 2D surface codes in time linear in the code distance. We present a fully detailed set of bounded-height lattice slices through the 3D codes which retain the code distance and measurement-error detecting properties of the full 3D code and admit a dimension-jumping process which expands from/collapses to 2D surface codes supported on the boundaries of each slice. At each timestep of the procedure the slices agree on a common set of overlapping qubits on which \(CCZ\) should be applied. We use these slices to simulate the performance of a simple JIT decoder against stochastic \(X\) and measurement errors and find evidence for a threshold \(p_c \sim 0.1\%\) in all three codes. We expect that this threshold could be improved by optimisation of the decoder.
ISSN:2331-8422
DOI:10.48550/arxiv.2012.08536