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).
Suzuki, Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems, Commun
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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).