Papers › A square-root speedup for finding the smallest eigenvalue
A square-root speedup for finding the smallest eigenvalue
Alex Kerzner, Vlad Gheorghiu, Michele Mosca, Thomas Guilbaud, Federico Carminati, Fabio Fracas, Luca Dellantonio
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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(√(N)/ϵ) black-box queries to an oracle encoding the matrix, where N is the matrix dimension and ϵ is the desired precision. In contrast, the best classical algorithm for the same task requires Ω(N)polylog(1/ϵ) 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.
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