Higgott, O;
Wilson, M;
Hefford, J;
Dborin, J;
Hanif, F;
Burton, S;
Browne, DE;
(2021)
Optimal local unitary encoding circuits for the surface code.
Quantum
, 5
, Article 517. 10.22331/q-2021-08-05-517.
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Abstract
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi {et al.} [7] showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size L, however the most efficient known method for encoding an unknown state, introduced by Dennis {et al.} [18], has O(L^{2}) time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly 2L time steps to encode an unknown state in a distance L planar code. We further show how an O(L) complexity local unitary encoder for the toric code can be found by enforcing locality in the O(log L) -depth non-local renormalisation encoder. We relate these techniques by providing an O(L) local unitary circuit to convert between a toric code and a planar code, and also provide optimal encoders for the rectangular, rotated and 3D surface codes. Furthermore, we show how our encoding circuit for the planar code can be used to prepare fermionic states in the compact mapping, a recently introduced fermion to qubit mapping that has a stabiliser structure similar to that of the surface code and is particularly efficient for simulating the Fermi-Hubbard model.
| Type: | Article |
|---|---|
| Title: | Optimal local unitary encoding circuits for the surface code |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.22331/q-2021-08-05-517 |
| Publisher version: | https://doi.org/10.22331/q-2021-08-05-517 |
| Language: | English |
| Additional information: | © Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (https://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10133193 |
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