Non-local resources for error correction in quantum LDPC codes

TL;DR

This paper explores integrating non-local resources via cavity-mediated gates into quantum LDPC codes, improving fault-tolerance thresholds and proposing an architectural layout for efficient stabilizer measurement.

Contribution

It introduces a method to incorporate non-local resources into quantum LDPC codes using cavity-mediated gates, enhancing fault-tolerance and circuit parallelization.

Findings

Thresholds of 0.84%-0.60% for hypergraph product codes

Pseudo-thresholds of 0.3%-0.4% for lifted product codes

Cavity cooperativities in the range 10^4-10^6

Abstract

Quantum low density parity check (qLDPC) codes are an attractive alternative to the surface code due to their relatively high code rate and distance. However, unlike the surface code which has simple, geometrically local, stabilizer checks, high performing qLDPC codes have non-local stabilizers that are challenging to measure. Recent advancements have shown how to deterministically perform high-fidelity, cavity mediated many-body gates, enabling the encoding and decoding of non-local GHZ states. We integrate this non-local resource into the DiVincenzo-Aliferis method of fault-tolerant stabilizer measurement for quantum hypergraph product and lifted product codes. Using circuit-level noise simulations, including the noise optimized cavity mediated gate, we find promising thresholds of $0.84 \%-0.60 \%$ for the hypergraph product code and psuedo-threshold of $0.3\%-0.4\%$ for the lifted product codes, with cavity cooperativities in the range $C\sim 10^4-10^6$. We propose a compatible tri-layer architectural layout for scheduling stabilizer measurements, enhancing circuit parallelizability.