Nearly Optimal Quantum Algorithm for Generating the Ground State of a Free Quantum Field Theory

• Published in: PRX quantum 2022-06, Vol.3 (2), p.020364, Article 020364
• Main Authors: Bagherimehrab, Mohsen, Sanders, Yuval R., Berry, Dominic W., Brennen, Gavin K., Sanders, Barry C.
• Format: Article
• Language: English
• ISSN: 2691-3399; 2691-3399
• DOI: 10.1103/PRXQuantum.3.020364

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 superquadratic 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.