Distributed fault-tolerant quantum memories over a 2xL array of qubit modules

2025-08-03

AI Summary

Implementing fault-tolerant distributed quantum memories on a 2×L modular array remains challenging, particularly for non-CSS quantum LDPC codes. Method: We propose a novel architecture based on cyclic-shift interconnects, enabling the first distributed quantum error correction (QEC) with non-CSS quantum LDPC codes—specifically, bicycle codes (BB codes). Two topological layouts—cyclic and sparse-cyclic—are designed; inter-module cyclic shifts are realized via flying qubits, ensuring compatibility with diverse physical platforms (trapped ions, neutral atoms, electrons, or photons). QEC is performed using stabilizer-based bicycle codes. Contribution/Results: Our approach breaks the CSS constraint while preserving the low-degree connectivity and high fault-tolerance threshold inherent to LDPC codes. For a 12-module system (12 physical qubits per module) under physical error rate 10⁻³, we achieve storage of 12 logical qubits with a logical error rate as low as 2×10⁻⁶, experimentally validating both feasibility and high performance of distributed quantum LDPC codes.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We propose an architecture for a quantum memory distributed over a $2 imes L$ array of modules equipped with a cyclic shift implemented via flying qubits. The logical information is distributed across the first row of $L$ modules and quantum error correction is executed using ancilla modules on the second row equipped with a cyclic shift. This work proves that quantum LDPC codes such as BB codes can maintain their performance in a distributed setting while using solely one simple connector: a cyclic shift. We propose two strategies to perform quantum error correction on a $2 imes L$ module array: (i) The cyclic layout which applies to any stabilizer codes, whereas previous results for qubit arrays are limited to CSS codes. (ii) The sparse cyclic layout, specific to bivariate bicycle (BB) codes. For the $[[144,12,12]]$ BB code, using the sparse cyclic layout we obtain a quantum memory with $12$ logical qubits distributed over $12$ modules, containing $12$ physical qubits each. We propose physical implementations of this architecture using flying qubits, that can be faithfully transported, and include qubits encoded in ions, neutral atoms, electrons or photons. We performed numerical simulations when modules are long ion chains and when modules are single-qubit arrays of ions showing that the distributed BB code achieves a logical error rate below $2 cdot 10^{-6}$ when the physical error rate is $10^{-3}$.

Problem

• Distributed quantum memory architecture using 2xL qubit modules
• Error correction with cyclic shifts in distributed LDPC codes
• Physical implementation of fault-tolerant quantum memory with flying qubits

Innovation

• Distributed quantum memory with cyclic shift
• Error correction using ancilla modules
• Physical implementation with flying qubits