Limitations on transversal gates for hypergraph product codes
Simon Burton, Dan Browne
TL;DR
This paper investigates the limitations of transversal gates in hypergraph product quantum codes, showing they are restricted to the Clifford group, thus constraining their fault-tolerant quantum computing capabilities.
Contribution
It extends the understanding of logical operator structures in hypergraph product codes and generalizes previous arguments to establish gate restrictions.
Findings
Transversal gates in these codes are limited to the Clifford group.
The analysis applies to hypergraph product codes restricted to the vertical sector.
The work generalizes an argument by Bravyi and K"onig.
Abstract
We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertical sector. By generalizing an argument of Bravyi and K\"onig, we find that transversal gates for these codes must be restricted to the Clifford group.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography