Convergence analysis for autonomous adaptive learning applied to quantum architectures

We present a formal analysis and convergence proofs for an autonomous adaptive learning algorithm useful for the tuneup and stabilization of quantum computing architectures. We focus on the specific application of spatial noise mapping in a "spectator" qubit paradigm, in which these qubits act as sensors to provide information useful for decoherence mitigation on proximal data qubits. In earlier work, the authors introduced and experimentally demonstrated this framework, Noise Mapping for Quantum Architectures (NMQA), as applied in autonomous adaptive scheduling of sensor-qubit measurements across multi-qubit architectures. This methodology has several unique features: a classical measurement model that incorporates discretized single-qubit projective measurements, and a two-layered particle filtering structure to facilitate adaptive information sharing between qubits in small spatial regions. In this work, we formalize the NMQA problem definition and build direct links to conventional non-linear filtering theory. Taking into account NMQA's departure from existing literature, we show that NMQA satisfies axioms of theorems for asymptotic convergence in specific parameter regimes. Outside of these parameter regimes, we augment our theoretical analysis with numerical studies to estimate rates of convergence for NMQA. We find that these numerical estimates match our theoretical expectations for a variety of physical configurations. Our work ensures that the methodology encapsulated by NMQA permits comparative analysis with existing filtering techniques in the literature, while highlighting unique directions for future automation of quantum computer tuneup, calibration, and stabilization.