Burton, S;
Browne, D;
(2021)
Limitations on Transversal Gates for Hypergraph Product Codes.
IEEE Transactions on Information Theory
10.1109/TIT.2021.3131043.
(In press).
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Abstract
In a fault tolerant quantum computer, quantum codes are expected to serve the conflicting purposes of protecting quantum information while also allowing that information to be manipulated by fault-tolerant gates. We introduce a new technique for placing limitations on such gates, and apply this technique to a class of quantum codes known as hypergraph product codes contained within the vertical sector. These codes are constructed from input which is a pair of classical linear codes, and generalize the Kitaev surface code which is the hypergraph product of classical repetition codes. We provide a necessary condition on these input codes, under which the resulting hypergraph product code has transversal gates limited to the Clifford group.We conjecture that this condition is satisfied by all [n, k, d] Gallagher codes with d ≥ 3 and k ≤ n/2. This work is a generalization of an argument due to Bravyi and König, and we also conjecture this is a refinement of the recent notion of disjointness due to Jochym-O’Connor et. al.
| Type: | Article |
|---|---|
| Title: | Limitations on Transversal Gates for Hypergraph Product Codes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIT.2021.3131043 |
| Publisher version: | https://doi.org/10.1109/TIT.2021.3131043 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Logic gates, Qubit, Product codes, Tensors, Quantum mechanics, Switches, Lattices |
| 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/10140865 |
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