Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
arXiv:2405.10416 · doi:10.1103/PRXQuantum.5.040347
Abstract
We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find up to 25 orders of magnitude reduction in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first principles quantum simulation of chemistry.
References in corpus (73)
- Simulated Quantum Computation of Molecular Energies
- Exactly massless quarks on the lattice
- A Method for Simulating Chiral Fermions on the Lattice
- Hamiltonian Simulation by Qubitization
- Quantum algorithms for quantum chemistry and quantum materials science
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- A Theory of Trotter Error
- Simulation of Electronic Structure Hamiltonians Using Quantum Computers
- Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
- Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
- Quantum Simulation for High Energy Physics
- Gate count estimates for performing quantum chemistry on small quantum computers
- Even more efficient quantum computations of chemistry through tensor hypercontraction
- Halving the cost of quantum addition
- A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
- Low Depth Quantum Simulation of Electronic Structure
- Simulating lattice gauge theories on a quantum computer
- Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
- A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
- A Formulation of Lattice Gauge Theories for Quantum Simulations
- Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
- Mapping local Hamiltonians of fermions to local Hamiltonians of spins
- Near-optimal ground state preparation
- Digitization of Scalar Fields for Quantum Computing
- Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
- Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
- General Methods for Digital Quantum Simulation of Gauge Theories
- Resource-efficient digital quantum simulation of -level systems for photonic, vibrational, and spin- Hamiltonians
- Digital lattice gauge theories
- Quantum Algorithms for Simulating the Lattice Schwinger Model
- Finite-density lattice QCD and sign problem: current status and open problems
- Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
- Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
- Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
- Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers
- Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
- Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
- Quantum Simulating Nature's Fundamental Fields
- Quantum algorithm for simulating real time evolution of lattice Hamiltonians
- Exploiting locality in quantum computation for quantum chemistry
- Digital quantum simulation of lattice gauge theories in three spatial dimensions
- Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
- Time-dependent Hamiltonian simulation with -norm scaling
- BQP-completeness of Scattering in Scalar Quantum Field Theory
- Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
- Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
- Digital quantum computation of fermion-boson interacting systems
- Hamiltonian simulation in the low-energy subspace
- Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
- Removing Staggered Fermionic Matter in and Lattice Gauge Theories
- Eliminating fermionic matter fields in lattice gauge theories
- Provably accurate simulation of gauge theories and bosonic systems
- Toward scalable simulations of Lattice Gauge Theories on quantum computers
- Nearly tight Trotterization of interacting electrons
- Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
- Fermion-qudit quantum processors for simulating lattice gauge theories with matter
- Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
- General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
- Quantum simulation of gauge theory via orbifold lattice
- Improved Hamiltonians for Quantum Simulations
- Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
- Variational quantum eigensolvers for sparse Hamiltonians
- Fault-tolerant quantum simulation of materials using Bloch orbitals
- Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
- Pre-equilibrium stopping and charge capture in proton-irradiated aluminum sheets
- Quantum computation of stopping power for inertial fusion target design
- Primitive Quantum Gates for an SU(3) Discrete Subgroup:
- Nearly-optimal state preparation for quantum simulations of lattice gauge theories
- Qubitization strategies for bosonic field theories
- Nuclear scattering via quantum computing
- Quantifying -gate-count improvements for ground-state-energy estimation with near-optimal state preparation
- Multi-nucleon structure and dynamics via quantum computing
- Estimating truncation effects of quantum bosonic systems using sampling algorithms
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- Efficient Quantum Simulation of QCD Jets on the Light Front
- Block encoding bosons by signal processing
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- Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
- Field digitization scaling in a symmetric model
- Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
- Creation of Wave Packets for Quantum Chromodynamics on Quantum Computers
- Quantum computational resources for lattice QCD in the strong-coupling limit