SPAM-robust learnability of quantum dynamics

Abstract

Accurate characterization of quantum dynamics is essential for the calibration and control of quantum devices. Unknown state preparation and measurement (SPAM) errors, however, introduce gauge ambiguities that limit what can be learned. A central question is therefore which properties are learnable despite SPAM errors, and whether physical structure in the dynamics can restrict these ambiguities and expand the set of learnable properties. In this work, we address both questions within a unified framework for quantum channels and continuous-time evolution. First, for general quantum channels and Lindbladian dynamics, we use the cycle structure of a generalized pattern-transfer graph to fully characterize all learnable parameter combinations and show achievability by constructing explicit SPAM-robust learning protocols, establishing a baseline where continuous gauge freedom prevents many individual parameters from being identified. Second, we show that coherent structure drastically restricts this gauge ambiguity, reducing continuous gauge freedom to discrete or even trivial choices. This restriction manifests across both discrete- and continuous-time settings, including purely Hamiltonian evolution, noisy quantum channels close to a target unitary, and Lindbladian dynamics close to a target Hamiltonian. In particular, when the dynamics preserves or remains close to a coherent Hamiltonian form, all coherent coefficients and broad classes of dissipative error parameters become individually learnable. These results establish a systematic route to exploiting physical structure for SPAM-robust characterization, providing a foundation for the reliable calibration and control of quantum devices.