Good models for noisy mid-circuit measurements

Quantum measurement, or readout, is traditionally the last step in a quantum circuit (program) that gets run on a quantum computer. But qubits can also be measured — sometimes repeatedly — in the middle of a quantum circuit. These mid-circuit measurements are critical for quantum error correction, and are now being implemented in a growing range of testbed quantum processors. Like all quantum logic operations, they're not perfect. And when they fail, they can fail in novel ways that don't afflict circuit-terminating measurements (e.g., failing to fully collapse the quantum state). Mid-circuit measurements can be modeled by quantum instruments — a particular kind of quantum channel — but like process matrices, instruments don't lend themselves to intuition. Here, we construct new models and metrics for errors in mid-circuit measurements, inspired by the error generator representation of errors in logic gates, and show how to use these models for better characterization and simulation of realistic errors in mid-circuit measurements.