  Quantum state discrimination is a central task in many quantum computing
settings where one wishes to identify what quantum state they are holding. We
introduce a framework that generalizes many of its variants and present a
hybrid quantum-classical algorithm based on semidefinite programming to
calculate the maximum reward when the states are pure and have efficient
circuits. To this end, we study the (not necessarily linearly independent) pure
state 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 number
of possible guesses (typically $L = N$). As an application, we give
now-possible algorithms for the quantum change point identification problem
which asks, given a sequence of quantum states, determine the time steps when
the quantum states changed. With our reductions, we are able to solve SDPs for
problem sizes of up to $220$ qubits in about $8$ hours and we also give
heuristics which speed up the computations.
