Fault-tolerant gates on hypergraph product codes

TL;DR

This paper introduces a method to perform universal Clifford gates on hypergraph product quantum codes using code deformation, enabling efficient logical operations within a single code block.

Contribution

It generalizes punctures and wormhole defects for hypergraph product codes, allowing universal gate implementation without multiple code blocks.

Findings

Clifford gates can be performed via code deformation on hypergraph product codes.

Universal quantum computation is achievable within a single code block.

The method reduces the need for many separate code blocks for logical gates.

Abstract

Hypergraph product codes are a class of quantum low density parity check (LDPC) codes discovered by Tillich and Z\'emor. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold. With these features, they asymptotically offer a smaller overhead compared to topological codes. However, existing techniques to perform logical gates in hypergraph product codes require many separate code blocks, so only becomes effective with a very large number of logical qubits. Here, we demonstrate how to perform Clifford gates on this class of codes using code deformation. To this end, we generalize punctures and wormhole defects, the latter introduced in a companion paper. Together with state injection, we can perform a universal set of gates within a single block of the class of hypergraph product codes.