How many quantum gates do gauge theories require?

Abstract

We discuss the implementation of lattice gauge theories on digital quantum computers, focusing primarily on the number of quantum gates required to simulate their time evolution. We find that to compile quantum circuits, using available state-of-the-art methods with our own augmentations, the cost of a single time step of an elementary plaquette is beyond what is reasonably practical in the current era of quantum hardware. However, we observe that such costs are highly sensitive to the truncation scheme used to derive different Hamiltonian formulations of non-Abelian gauge theories, emphasizing the need for low-dimensional truncations of such models in the same universality class as the desired theories.

arXiv comment14 pages of RevTeX, 7 figures

References in corpus (31)

• Array Programming with NumPy
• Improved Simulation of Stabilizer Circuits
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Simulating lattice gauge theories on a quantum computer
• 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
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• General Methods for Digital Quantum Simulation of Gauge Theories
• Digital lattice gauge theories
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Gluon Field Digitization for Quantum Computers
• Towards Quantum Simulating QCD
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Sigma models on quantum computers
• Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory
• Qubit regularization of asymptotic freedom
• A qubit regularization of the $O(3)$ sigma model
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• From the $SU(2)$ Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagomé Lattice: Phase Transition and Fractionalized Flux Strings
• Universality of a truncated sigma-model

Cited by in corpus (20)

• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer
• Nonstabilizerness in U(1) lattice gauge theory
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Qubitization strategies for bosonic field theories
• Fuzzy gauge theory for quantum computers
• Simulating ${\mathbb{Z}}_2$ Lattice Gauge Theory with the Variational Quantum Thermalizer
• Randomized measurement protocols for lattice gauge theories
• Quantum mean estimation for lattice field theory
• Quantum Gate Sets for Lattice QCD in the strong coupling limit: $N_f=1$
• Toward nuclear physics from lattice QCD on quantum computers
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Reducing circuit depth with qubitwise diagonalization
• ${\mathbb{Z}}_3$ lattice gauge theory as a toy model for dense QCD
• Trotter error and gate complexity of the SYK and sparse SYK models
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Quantum computational resources for lattice QCD in the strong-coupling limit