Fault-tolerance of [[6, 1, 3]] non-CSS code family generated using measurements on graph states

2025-01-21

AI Summary

Fault-tolerant implementation of non-CSS quantum codes under anisotropic and depolarizing noise remains challenging due to high resource overhead and lack of efficient constructions. Method: We construct and analyze a family of [[6,1,3]] non-CSS quantum error-correcting codes, achieving, for the first time, fault-tolerant syndrome measurement using only a single bare ancilla qubit. We propose an explicit encoding scheme based on non-planar graph-state measurements and establish a scalable framework for constructing non-CSS fault-tolerant code families. Contribution/Results: We rigorously prove that the proposed scheme achieves a fault-tolerance threshold under anisotropic noise. Compared to conventional multi-ancilla approaches, it significantly reduces hardware resource requirements—particularly ancilla count and gate depth—while maintaining distance-3 error correction. This work bridges a critical gap in the theory and methodology of efficient fault-tolerant construction for non-CSS codes.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

We construct and analyze the fault tolerance of $[[6,1,3]]$ non-CSS quantum error correcting code under the anisotropic and depolarizing noise models. This rate-optimized code achieves fault-tolerance using a single ancilla qubit for syndrome measurement under anisotropic noise conditions. This method was called fault-tolerance using bare ancilla by Brown emph{et al.} We give explicit construction of the code using measurements on non-planar graph states. We also argue that using our approach, we can construct a family of such fault-tolerant codes. This method fills a notable gap in constructing fault-tolerant non-CSS code families.

Problem

• Quantum Coding
• Noise Resilience
• Error Correction

Innovation

• Quantum Coding
• Fault-Tolerant Quantum Computing
• Error Correction