Toward a 2D Local Implementation of Quantum LDPC Codes

TL;DR

This paper proposes a 2D local implementation of quantum LDPC codes using a bilayer architecture and a specialized syndrome measurement protocol, reducing overhead while maintaining low logical error rates.

Contribution

It introduces a novel error correction protocol for 2D local gates that leverages bivariate bicycle qLDPC codes and parallel syndrome measurement to improve efficiency.

Findings

Logical error rates comparable to surface codes

Reduced physical qubit requirements

Effective syndrome measurement via local operations and classical communication

Abstract

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes which affects code performance and ease of physical realization. For device architectures restricted to 2D local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate bicycle qLDPC codes and show that they are well suited for a parallel syndrome measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes bivariate bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits.