Improved Hamiltonians for Quantum Simulations

Abstract

Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved discretization errors will reduce quantum resources, i.e. require $\gtrsim 2^d$ fewer qubits in quantum simulations for lattices with $d$ spatial dimensions. In this work, we consider $\mathcal{O}(a^2)$-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. An explicit demonstration for ${\mathbb{Z}}_2$ gauge theory is presented including exploratory tests using the ibm_perth device.

arXiv comment5 pages, 5 figures, matched to journal version

References in corpus (56)

• Prescription for experimental determination of the dynamics of a quantum black box
• Hamiltonian Simulation by Qubitization
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Efficient variational quantum simulator incorporating active error minimisation
• Noise tailoring for scalable quantum computation via randomized compiling
• Practical Quantum Error Mitigation for Near-Future Applications
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• A random compiler for fast Hamiltonian simulation
• 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
• Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
• Characterizing large-scale quantum computers via cycle benchmarking
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Lattice QCD on Small Computers
• 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
• 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 resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Simulation of Nonequilibrium Dynamics on a Quantum Computer
• Adaptive Variational Quantum Dynamics Simulations
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Parton Physics on a Quantum Computer
• BQP-completeness of Scattering in Scalar Quantum Field Theory
• Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization
• Gluon Field Digitization via Group Space Decimation for Quantum Computers
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• A qubit regularization of the $O(3)$ sigma model
• Quantum algorithms for transport coefficients in gauge theories
• Primitive Quantum Gates for Dihedral Gauge Theories
• Framework for simulating gauge theories with dipolar spin systems
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Quantum Simulation of Light-Front Parton Correlators
• Lattice Renormalization of Quantum Simulations
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits
• Redesigning Lattice QCD
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Improved Lattice Gauge Field Hamiltonian
• Lattice QCD in curved spacetimes
• State preparation and measurement in a quantum simulation of the O(3) sigma model
• Schwinger pair production and string breaking in non-Abelian gauge theory from real-time lattice improved Hamiltonians
• Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
• State-dependent error bound for digital quantum simulation of driven systems
• Direct Improvement of Hamiltonian Lattice Gauge Theory
• On construction of projection operators
• Lattice Gauge Theory for a Quantum Computer

Cited by in corpus (29)

• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Gauge Theory Couplings on Anisotropic Lattices
• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Towards the real-time evolution of gauge-invariant ${\mathbb{Z}}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Detect anomalous quartic gauge couplings at muon colliders with quantum kernel k-means
• Quantum mean estimation for lattice field theory
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Quantum simulation of the phase transition of the massive Thirring model
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• A quantum machine learning classifier to search for new physics
• Digit quantum simulation of a fermion field in an expanding universe
• Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
• Real-space blocking of qubit variables on parallel lattice gauge theory links for quantum simulation