Shallow-Depth Variational Quantum Hypothesis Testing

The task of discriminating between two known quantum channels is a well known binary hypothesis testing task. We present a variational quantum algorithm with a parameterized state preparation and two-outcome positive operator valued measure (POVM) which defines the acceptance criteria for the hypothesis test. Both the state preparation and measurement are simultaneously optimized using success probability of single-shot discrimination as an objective function which can be calculated using localized measurements. Under constrained signal mode photon number quantum illumination we match the performance of known optimal 2-mode probes by simulating a bosonic circuit. Our results show that variational algorithms can prepare optimal states for binary hypothesis testing with resource constraints.