A matrix-encoding variational quantum algorithm computes eigenvalues and generalized eigenvalues by measuring an ancilla to extract a loss function and its derivatives for classical gradient optimization, with circuit depth O(N squared log N).
Grover, A fast quantum mechanical algorithm for database search, STOC, in 96: Proceedings 28th Annual ACM Symposium on the Theory of Computation
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Matrix encoding method in variational algorithm of calculating eigenvalues and generalized eigenvalues
A matrix-encoding variational quantum algorithm computes eigenvalues and generalized eigenvalues by measuring an ancilla to extract a loss function and its derivatives for classical gradient optimization, with circuit depth O(N squared log N).