Simulating 2D lattice gauge theories on a qudit quantum computer

Abstract

Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in $d$ different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

References in corpus (55)

• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Quantum Chemistry in the Age of Quantum Computing
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Logical quantum processor based on reconfigurable atom arrays
• Multidimensional quantum entanglement with large-scale integrated optics
• FLAG Review 2019
• Quantum optimization using variational algorithms on near-term quantum devices
• FLAG Review 2021
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Qudits and high-dimensional quantum computing
• Simulating Lattice Gauge Theories within Quantum Technologies
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• A universal qudit quantum processor with trapped ions
• Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm
• Quantum Simulation for High Energy Physics
• Lattice gauge theories simulations in the quantum information era
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Review on novel methods for lattice gauge theories
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Digital lattice gauge theories
• Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor
• Qutrit randomized benchmarking
• Approaches to the sign problem in lattice field theory
• 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
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Gluon Field Digitization for Quantum Computers
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• BQP-completeness of Scattering in Scalar Quantum Field Theory
• SU(2) lattice gauge theory on a quantum annealer
• Analog Quantum Simulation of (1+1)D Lattice QED with Trapped Ions
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Analog quantum simulation of chemical dynamics
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• A fast fault-tolerant decoder for qubit and qudit surface codes
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Review on Quantum Computing for Lattice Field Theory
• Quantum computation and simulation with vibrational modes of trapped ions
• Demonstration of logical qubits and repeated error correction with better-than-physical error rates
• Adaptive estimation of quantum observables
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
• Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing
• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Doppler-free, Multi-wavelength Acousto-optic deflector for two-photon addressing arrays of Rb atoms in a Quantum Information Processor
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density
• Variational quantum state preparation via quantum data buses

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• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
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• (2+1)D quantum electrodynamics at finite density on a quantum computer
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• Blind quantum computing with different qudit resource state architectures
• Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
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• Entanglement swapping for partially entangled qudits and the role of quantum complementarity