Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory

• URL: http://arxiv.org/abs/2110.05708v2
• Date: Wed, 29 Jun 2022 19:08:24 GMT
• Title: Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory
• Authors: Mohsen Bagherimehrab, Yuval R. Sanders, Dominic W. Berry, Gavin K. Brennen, Barry C. Sanders
• Abstract summary: We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory. Our algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms -- Fourier-based and wavelet-based -- to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized-QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer.

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