Algorithmic quantum-state generation for quantum simulation of a quantum field theory*

We establish two quasilinear quantum algorithms, one Fourier-based and the other wavelet-based, for generating an approximation for the ground state of a quantum field theory (QFT).

Our quantum algorithms deliver a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcome the ground-state-generation bottleneck of the prior approach and are optimal up to polylogarithmic factors. Specifically, our quantum algorithms generate the ground state of a free massive scalar-bosonic QFT with gate complexity quasilinear in the number of discretized-QFT modes. We show that the wavelet-based algorithm is advantageous over the Fourier-based algorithms for QFTs with a broken translational invariance and generating states beyond the free-field ground state. 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 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.

This work is available at https://arxiv.org/abs/2110.05708.