Networked Realization of Quantum LDPC Codes

2026-04-27

AI Summary

This work addresses the practical challenges of deploying high-performance quantum low-density parity-check (QLDPC) codes, which are hindered by long-range connectivity and frequent qubit movement induced by nonlocal stabilizers. The study presents the first implementation and evaluation of bivariate bicycle codes in a networked architecture: codewords are distributed across multiple nodes via balanced minimum-cut partitioning of the X-Z joint Tanner graph, inter-node stabilizer measurements are executed using Bell-pair-mediated remote CNOT gates, and error correction performance is assessed under circuit-level noise with the BP-OSD decoding algorithm. Results demonstrate that the proposed scheme maintains strong error-correction capability across varying Bell-pair fidelities, closely approaching the performance of monolithic implementations, thereby confirming the feasibility and promise of non-geometrically local QLDPC codes in distributed quantum computing.

Abstract

Quantum low-density parity-check (QLDPC) codes with good parameters are promising candidates for low-overhead fault-tolerant quantum computing, but their non-local stabilizers require long-range connectivity and frequent qubit movement, introducing practical challenges. Prior work has studied the networked implementation of topological codes, where each node only holds one or a few qubits of the entire code, and demonstrated competitive performance under practical constraints such as the quality of network-provided entanglement. However, since these codes are already geometrically local, such a networked setting might not be essential. In this work, we propose and study the networked implementation of better QLDPC codes, specifically bivariate bicycle codes due to their similarity to surface codes and the controlled amount of long-range connections in their stabilizers. We begin by recreating networked surface codes in Stim, with one code qubit per node, and provide additional insights into their circuit-level noise performance. We then extend this approach to bipartitions of bivariate bicycle codes, using balanced min-cut partitioning on their combined X-Z Tanner graph to identify optimal qubit splits. For stabilizers spanning nodes, we implement teleported CNOTs and vary the Bell pair fidelity enabling these gates. Through circuit-level noise simulations with BP-OSD decoding, we provide the first insights into networked realizations of these codes and compare their performance with monolithic implementations. We conclude by outlining advantages, limitations, and future directions.

Problem

• Quantum LDPC codes
• networked implementation
• long-range connectivity
• qubit movement
• fault-tolerant quantum computing

Innovation

• networked quantum computing
• QLDPC codes
• bivariate bicycle codes
• teleported CNOT
• circuit-level noise simulation