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).
Deutsch, Quantum theory, the Church-turing principle and the universal quantum computer, Proc.R
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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).