Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction

In advanced quantum processors, quantum operations are increasingly processed along multiple insequence measurements that result in classical data and affect the rest of the computation. Because of the information gain of classical measurements, nonunitary dynamical processes can affect the system, which common quantum channel descriptions fail to describe faithfully. Quantum measurements are correctly treated by so-called quantum instruments, capturing both classical outputs and postmeasurement quantum states. Here we present a general recipe for characterizing quantum instruments and demonstrate its experimental implementation and analysis. Thereby the full dynamics of a quantum instrument can be captured, exhibiting details of the quantum dynamics that would be overlooked with standard techniques. For illustration, we apply our characterization technique to a quantum instrument used for the detection of qubit loss and leakage, which was recently implemented as a building block in a quantum error-correction (QEC) experiment [Nature 585, 207 (2020)]. Our analysis reveals unexpected and in-depth information about the failure modes of the implementation of the quantum instrument. We then numerically study the implications of these experimental failure modes on QEC performance, when the instrument is employed as a building block in QEC protocols on a logical qubit. Our results highlight the importance of careful characterization and modeling of failure modes in quantum instruments, as compared to simplistic hardware-agnostic phenomenological noise models, which fail to predict the undesired behavior of faulty quantum instruments. The presented methods and results are directly applicable to generic quantum instruments and will be beneficial to many complex and high-precision applications.