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