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

T. R. Scruby; D. E. Browne; P. Webster; M. Vasmer

doi:10.22331/q-2022-05-24-721

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

T. R. Scruby^1,2, D. E. Browne², P. Webster³, and M. Vasmer^4,5

¹Okinawa Institute of Science and Technology, Okinawa, 904-0495, Japan
²Dept. of Physics and Astronomy, University College London, London, WC1E 6BT, UK
³Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
⁴Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
⁵Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Published:	2022-05-24, volume 6, page 721
Eprint:	arXiv:2012.08536v3
Doi:	https://doi.org/10.22331/q-2022-05-24-721
Citation:	Quantum 6, 721 (2022).

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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.

Featured image: 3D spacetime (left) and 2D space (right) diagrams illustrating the relative motion of the three codes during the logical gate. Each of the three 2D codes sweeps out a 3D surface code over time and the cubic region where all three of these codes intersect supports a transversal $\overline{CCZ}$.

For an animated illustration of 3D spacetime diagram click here.

► BibTeX data

@article{Scruby2022numerical,
  doi = {10.22331/q-2022-05-24-721},
  url = {https://doi.org/10.22331/q-2022-05-24-721},
  title = {Numerical {I}mplementation of {J}ust-{I}n-{T}ime {D}ecoding in {N}ovel {L}attice {S}lices {T}hrough the {T}hree-{D}imensional {S}urface {C}ode},
  author = {Scruby, T. R. and Browne, D. E. and Webster, P. and Vasmer, M.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {721},
  month = may,
  year = {2022}
}

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[1] Suhas Vittal, Poulami Das, and Moinuddin Qureshi, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[2] Thomas R. Scruby, Michael Vasmer, and Dan E. Browne, "Non-Pauli errors in the three-dimensional surface code", Physical Review Research 4 4, 043052 (2022).

[3] Michael E. Beverland, Aleksander Kubica, and Krysta M. Svore, "Cost of Universality: A Comparative Study of the Overhead of State Distillation and Code Switching with Color Codes", PRX Quantum 2 2, 020341 (2021).

[4] Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D. Bartlett, "Universal Fault-Tolerant Quantum Computing with Stabiliser Codes", arXiv:2012.05260, (2020).

[5] Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D. Bartlett, "Universal fault-tolerant quantum computing with stabilizer codes", Physical Review Research 4 1, 013092 (2022).

[6] Thomas R. Scruby, Michael Vasmer, and Dan E. Browne, "Non-Pauli Errors in the Three-Dimensional Surface Code", arXiv:2202.05746, (2022).

[7] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

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