4.6 Article

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

期刊

PRX QUANTUM
卷 3, 期 2, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PRXQuantum.3.020364

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资金

  1. Government of Alberta
  2. Natural Sciences and Engineering Research Council of Canada (NSERC)
  3. Australian Research Council [DP190102633, DP210101367, DP200100950]
  4. ARC [DP200102152]
  5. Google Quantum AI
  6. Australian Research Council [DP200102152, DP200100950] Funding Source: Australian Research Council

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We propose a quasilinear quantum algorithm for generating an approximation of the ground state of a quantum field theory. Our algorithm achieves a superquadratic speedup over existing methods for ground-state generation and overcomes the bottleneck in the previous approach. We present two quantum algorithms, Fourier-based and wavelet-based, for generating the ground state of a free massive scalar bosonic quantum field theory with quasilinear gate complexity.
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.

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