Robust Quantum Algorithmic Binary Decision-Making on Displacement Signals

A relevant signal in the quantum domain may manifest as a displacement or a phase shift operator in the bosonic phase space. For a real parameter β embedded in such a displacement operator, the task of determining if βin \[β_-th, β_+th\] for real asymmetric thresholds \(β_-th ne -β_+th\) is a binary decision problem. We propose a framework based on generalized quantum signal processing interferometry (GQSPI) on hybrid qubit-bosonic oscillator systems that addresses this parameter detection problem by recasting the practical task of active binary hypothesis testing on quantum systems to that of a polynomial approximation. We achieve a small decision error probability p_err on the order of O\(frac{1}{d}log{(d\)}), with d as the circuit depth. We analyze the protocol when (i) β is a deterministic parameter, and (ii) when β is drawn randomly from a known prior distribution. The performance of the sensing protocol under dephasing noise is also shown to be robust. We further extend our protocol from two thresholds to more general multi-threshold cases as well. Overall, the proposed framework enables decision-making over arbitrary thresholds for any general displacement signal in a single or a few shots.