A Diary of a Faulty Logical Qubit: Logical Gate Set Tomography

The quantum characterization, verification, and validation (QCVV) toolbox assesses processor performance by analyzing their qubits and logic operations. One can construct a comprehensive model of quantum processor operations via tomographic reconstruction methods, using data from many individual experiments designed to probe the operations. In particular, gate set tomography (GST) infers process matrices for the full gate set using data from structured quantum programs. As platforms move beyond the NISQ regime toward fault-tolerant, error-corrected machines with thousands of qubits, exhaustive characterization at the physical-qubit level becomes impractical. A natural alternative is to characterize logical qubits to reduce experimental and computational overhead. Several logical-level methods exist—e.g., logical randomized benchmarking and logical process tomography—but they are either incomplete in their characterization or rely on strong assumptions about state-preparation-and-measurement (SPAM). We investigate logical gate set tomography (LoGST) as a route to comprehensive logical-level characterization. Our work overall examines the performance of LoGST on logical qubits encoded with five-qubit and seven-qubit quantum error-correcting codes. As a first step, we investigate the effects of physical pauli stochastic noise on logical qubits encoded with the five-qubit error-correcting code.