Efficient Verification of Stabilizer Code Subspaces with Local Measurements

Abstract We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace verification and explore several practically significant stabilizer code subspaces. First, we present two efficient verification strategies for general stabilizer code subspaces, using measurements of their stabilizer generators and stabilizer groups, respectively. Then, building on the observation that certain tests can be conducted in parallel due to specific structural properties of the subspace, we propose a coloring strategy tailored to graph code subspaces and an XZ strategy for Calderbank-Shor-Steane (CSS) code subspaces. Compared to stabilizer-based strategies, these new strategies require significantly fewer measurement settings and consume fewer state copies, achieving near-global optimality. Notably, all the strategies employ a limited number of Pauli measurements, are non-adaptive, and work for mixed states, enabling efficient experimental certification of whether quantum states remain within the target code subspace in noisy quantum computers. This work presents the first systematic study of efficient verification of stabilizer code subspaces with local measurements.