Learning noisy mid-circuit measurement as an instrument: SPAM-robust identification and benchmarking of RESET protocols

Mid-circuit measurement (MCM) is essential for reset, feedforward, and error correction, but real devices mix readout mistakes with measurement-induced back-action in correlated ways. We present a platform-agnostic framework that treats a single-qubit MCM as a general "instrument" and shows how to learn its full error behavior directly from recorded outcome strings, without assuming a separation between readout and back-action and without relying on state-preparation and measurement (SPAM) accuracy. Using short sequences of outcomes, we provide two practical identification methods: a compact spectral/Hankel approach and a low-order invariant method. We then compare two protocols: (A) verify with repeated measurements and keep only all-zero sequences, and (B) repeated RESETs implemented as measure-and-flip. We derive their steady-state fidelities, convergence speeds, and fidelity–yield trade-offs. Starting from a twirled, maximally mixed prior, our analysis gives closed-form predictions that guide when repeated verification helps, when repeated RESETs are superior, and how correlated errors change both. We outline an experimental procedure on superconducting qubits with full outcome logging to validate identifiability and to benchmark and optimize RESET under realistic noise.