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Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
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abstract
The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $d+1$-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of "normalized" ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $d=3$. The LSH formalism makes little use of structures specific to SU(2) and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).
Forward citations
Cited by 8 Pith papers
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Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers
Quantum hardware simulation of SU(2) lattice gauge thermalization matches classical extrapolations up to 101 plaquettes after error mitigation, establishing feasibility for chaotic quantum field systems.
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Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations
A qudit-based circuit for SU(2) lattice gauge theory on a cube, with improved decompositions for uniformly-controlled rotations and new elementary-gate resource estimates.
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Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
Gauss's law constraints in jmax=1/2 SU(2) lattice gauge theory are converted into stabilizer codes that correct single-qubit errors using about 9N or 12N physical qubits per N plaquettes.
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Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
Exact diagonalization shows 1+1D SU(2) lattice gauge theory with dynamical fermions satisfies ETH, including for non-local string operators that display a memory peak.
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Quantum computation of hadron scattering in a lattice gauge theory
On a trapped-ion quantum computer, the authors prepared multiple meson wave packets and simulated their early-time collisions in a 1+1D Z2 lattice gauge theory.
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Dynamics of entanglement entropy for a locally monitored lattice gauge theory
Local projective measurements of electric flux and mass density in a 1+1D Z2 gauge theory yield size-independent late-time entanglement saturation, indicating no measurement-induced phase transition in the no-click limit.
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Effects of monitoring on entanglement dynamics for $1+1$D $\mathbb Z_2$ lattice gauge theory
In the no-click limit, both local and non-local monitoring of a 1+1D Z2 lattice gauge theory produce late-time entanglement saturation values that are independent of system size, giving no evidence of a measurement-in...
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Observation of Robust and Coherent Non-Abelian Hadron Dynamics on Noisy Quantum Processors
A 60-site SU(2) lattice gauge theory was run on 120 qubits, but the implemented dynamics approximate to non-interacting fermion hopping, and the abstract's claimed breathing-mode frequency is not extracted anywhere.
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