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

• URL: http://arxiv.org/abs/2012.08536v3
• Date: Fri, 20 May 2022 02:18:02 GMT
• Title: Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
• Authors: T. R. Scruby, D. E. Browne, P. Webster, M. Vasmer
• Abstract summary: We develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes. We find evidence for a threshold $p_c sim 0.1%$ in all three codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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