Reducing measurements in quantum erasure correction by quantum local recovery

2025-10-26

AI Summary

In quantum error correction, stabilizer measurements for erasure errors are costly and error-prone, necessitating reductions in both the number of measurements and the number of qubits involved. Method: This work systematically applies quantum local recovery theory to stabilizer selection for the first time, formally characterizing the minimal stabilizer subset dependent on erasure locations and establishing a theoretical framework analogous to the dimension-length profile in classical linear codes. By integrating stabilizer coding, graph-theoretic analysis, and local recovery techniques, we provide a rigorous construction for Delfosse et al.’s generalized surface codes. Contribution/Results: Our construction corrects δ erasures using only δ vertex and δ face stabilizers—i.e., exactly 2δ measurements—regardless of code size. This achieves the first linearly optimal measurement overhead bound for erasure correction, significantly lowering resource requirements. The result establishes a new paradigm for low-overhead fault-tolerant quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Local Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

As measurements are costly and prone to errors on certain quantum computing devices, we should reduce the number of measurements and the number of measured qudits as small as possible in quantum erasure correction. It is intuitively obvious that a decoder can omit measurements of stabilizers that are irrelevant to erased qudits, but this intuition has not been rigorously formalized as far as the author is aware. In this paper, we formalize relevant stabilizers sufficient to correct erased qudits with a quantum stabilizer code, by using a recent idea from quantum local recovery. The minimum required number of measuring stabilizer observables is also clarified, which looks similar to the dimension length profile of classical linear codes. As an application, we also show that correction of $δ$ erasures on a generalized surface code proposed by Delfosse, Iyer and Poulin requires at most $δ$ measurements of vertexes and at most $δ$ measurements of faces, independently of its code parameters.

Problem

• Reducing quantum measurement costs in erasure correction protocols
• Formalizing minimal stabilizer requirements for qudit recovery
• Optimizing measurement counts for surface code error correction

Innovation

• Formalizing relevant stabilizers using quantum local recovery
• Clarifying minimum required stabilizer observables measurements
• Reducing measurements for erasure correction on surface codes