Toward a 2D Local Implementation of Quantum Low-Density Parity-Check Codes

Journal Article · 09 January 2025 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.6.010306 · OSTI ID:2498406

Berthusen, Noah ; Devulapalli, Dhruv ; Schoute, Eddie ; Childs, Andrew M. ; Gullans, Michael J. ; Gorshkov, Alexey V. ; Gottesman, Daniel

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (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. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019040; SC0020312; SC0024220
• OSTI ID: 2498406
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 1 Vol. 6; ISSN 2691-3399; ISSN PQRUAG
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English