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A square-root speedup for finding the smallest eigenvalue
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DOI：10.1088/2058-9565/ad6a36.png)
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We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines quantum phase estimation and quantum amplitude estimation to achieve a quadratic speedup with respect to the best classical algorithm in terms of matrix dimensionality, i.e. (O)over tilde(N/epsilon)( 9) black-box queries to an oracle encoding the matrix, where N is the matrix dimension and epsilon is the desired precision. In contrast, the best classical algorithm for the same task requires Omega(N)polylog(1/epsilon) queries. In addition, this algorithm allows the user to select any constant success probability. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix's low-energy subspace. We implement simulations of both algorithms and demonstrate their application to problems in quantum chemistry and materials science.
Keyword:
quantum algorithm
quantum information
ground state
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