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.

5 pages, 5 figures, matched to journal version

References in corpus (9)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Digital lattice gauge theories
• Towards Quantum Simulating QCD
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Lattice QCD in curved spacetimes
• State-dependent error bound for digital quantum simulation of driven systems
• Lattice Gauge Theory for a Quantum Computer

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• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Gauge Theory Couplings on Anisotropic Lattices
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
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• 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
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• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Quantum simulation of the phase transition of the massive Thirring model
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• Quantum simulation of quantum mechanical system with spatial noncommutativity
• A quantum machine learning classifier to search for new physics
• Real-space blocking of qubit variables on parallel lattice gauge theory links for quantum simulation
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
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• 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