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

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.

arXiv commentThis version is identical in content to the published version. Presentation improved and figure 11 added. ( 73 pages, 15 figures, 2 tables)

References in corpus (28)

• Quantum algorithms: an overview
• Quantum random access memory
• Quantum Algorithms for Quantum Field Theories
• Cloud Quantum Computing of an Atomic Nucleus
• Efficient Simulation of Quantum Systems by Quantum Computers
• Creating superpositions that correspond to efficiently integrable probability distributions
• Simulating lattice gauge theories on a quantum computer
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Quantum algorithms and the finite element method
• Digitization of Scalar Fields for Quantum Computing
• High-precision quantum algorithms for partial differential equations
• Quantum Algorithm for Simulating the Wave Equation
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Black-box quantum state preparation without arithmetic
• Quantum Computing for Neutrino-nucleus Scattering
• Rodeo Algorithm for Quantum Computing
• BQP-completeness of Scattering in Scalar Quantum Field Theory
• Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Multi-scale quantum simulation of quantum field theory using wavelets
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• Wavefunction preparation and resampling using a quantum computer
• Quantum circuit for the fast Fourier transform
• Wavelets in Field Theory
• Projected Cooling Algorithm for Quantum Computation
• Bounds on determinants of perturbed diagonal matrices
• Projective Cooling for the transverse Ising model
• Asymptotically Efficient Quantum Karatsuba Multiplication

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• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis