Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory

Abstract

In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using $O\left({\epsilon }^{-3.23\dots }\right)$ gates, which is much faster than previous known results, namely $O\left({\epsilon }^{-8-o\left(1\right)}\right)$. Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

23 pages

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases
• Sequential Generation of Matrix-Product States in Cavity QED
• Quantum Algorithms for Fermionic Quantum Field Theories
• Structure of entanglement in regulated Lorentz invariant field theories

Cited by in corpus (31)

• Quantum Simulation for High Energy Physics
• Review on novel methods for lattice gauge theories
• Digitization of Scalar Fields for Quantum Computing
• General Methods for Digital Quantum Simulation of Gauge Theories
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Quantum simulation of scattering in the quantum Ising model
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Primitive Quantum Gates for Dihedral Gauge Theories
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Quantum Computing for Quantum Tunnelling
• Quantum simulation of quantum field theories as quantum chemistry
• Lattice Renormalization of Quantum Simulations
• Toward simulating Superstring/M-theory on a quantum computer
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Quantum Simulation of the N flavor Gross-Neveu Model
• Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
• Topological chiral currents in the Gross-Neveu model extension
• Variational adiabatic transport of tensor networks
• Benchmarking quantum computers for real-time evolution of a $(1+1)$ field theory with error mitigation
• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Identification of a natural fieldlike entanglement resource in trapped-ion chains
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Digital Quantum Simulation of Hadronization in Yang-Mills Theory
• Error Interference in Quantum Simulation
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Shearing approach to gauge-invariant Trotterization