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Quantum state discrimination is a central task in many quantum computingsettings where one wishes to identify what quantum state they are holding. Weintroduce a framework that generalizes many of its variants and present ahybrid quantum-classical algorithm based on semidefinite programming tocalculate the maximum reward when the states are pure and have efficientcircuits. To this end, we study the (not necessarily linearly independent) purestate case and reduce the standard SDP problem size from $2^n L$ to $N L$ where$n$ is the number of qubits, $N$ is the number of states, and $L$ is the numberof possible guesses (typically $L = N$). As an application, we givenow-possible algorithms for the quantum change point identification problemwhich asks, given a sequence of quantum states, determine the time steps whenthe quantum states changed. With our reductions, we are able to solve SDPs forproblem sizes of up to $220$ qubits in about $8$ hours and we also giveheuristics which speed up the computations.

A generalized framework for quantum state discrimination, hybrid algorithms, and the quantum change point problem