Alex Kerzner, Vlad Gheorghiu, Michele Mosca, Thomas Guilbaud, Federico Carminati, Fabio Fracas and Luca Dellantonio
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引用次数: 0
Abstract
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. 9black-box queries to an oracle encoding the matrix, where N is the matrix dimension and ɛ is the desired precision. In contrast, the best classical algorithm for the same task requires 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.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.