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Simulating lattice gauge theories on a quantum computer

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arxiv quant-ph/0510027 v1 pith:XOEYZ6LX submitted 2005-10-04 quant-ph

Tim Byrnes , Yoshihisa Yamamoto This is my paper · ORCID
classification quant-ph
keywords latticegaugetheoriescomputerhamiltoniannumberquantumexamine
verification ladder T0 review T1 audit T2 compute T3 formal

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We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.

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Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universal framework with exponential speedup for the quantum simulation of quantum field theories including QCD

    quant-ph 2025-06 conditional novelty 8.0 of 10

    Fermion extensions of the orbifold-lattice simulation framework achieve O(L^d) gates per Trotter step for QCD-like theories without oracles.

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    Deforms SU(2)_k Yang-Mills theory via quantum groups to enable finite d-dimensional gauge links, restores unitarity with gauge-variant completions, and reports O(d^5) upper bounds on generalized-controlled-X gates plu...

  5. Ether of Orbifolds

    hep-lat 2026-03 accept novelty 6.0 of 10

    Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.

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    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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    The Kogut-Susskind Hamiltonian is recovered from the orbifold lattice Hamiltonian in the infinite scalar mass limit, with numerical confirmation for SU(2) and SU(3) Yang-Mills theory in 2+1 dimensions.

  9. Quantum computation of hadron scattering in a lattice gauge theory

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    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.

  10. Parton Physics on a Quantum Computer

    hep-lat 2019-08 conditional novelty 6.0 of 10

    A quantum-computer algorithm is proposed for computing parton distribution functions and hadronic tensors, with a Thirring-model demonstration and QCD resource estimates that favor extracting PDFs by fitting the hadro...

  11. Quantum Simulation of Gauge Theories for Particle and Nuclear Physics

    hep-lat 2026-05 unverdicted novelty 3.0 of 10

    The talk summarizes the quantum simulation program for lattice gauge theories, covering target problems in dense matter, algorithmic strategies, recent progress, and remaining challenges.

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