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

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Cited by in corpus (29)

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• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
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• Gauge Theory Couplings on Anisotropic Lattices
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• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
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• 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
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