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arXiv:2606.21563

SU(2) gauge theory with fermions on a semi-simple cubic lattice

Randy Lewis, Shidsa Pourbakhsh, Arnab Pradhan, Lance Siquioco

hep-latquant-phSubmitted Jun 19, 2026• Announced Jun 22, 2026• 0 citations
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Abstract

A practical Hamiltonian approach to lattice gauge theories would provide access to several important areas of phenomenology that have been beyond the reach of conventional lattice methods. Quantum computers seem to be a natural platform for this approach. With near-term quantum computers in mind, our work considers a three-dimensional spatial lattice that can host fermions and non-Abelian gauge fields while needing fewer qubits than a simple cubic lattice. Specifically, the semi-simple cubic (ssc) lattice is obtained by removing half of the gauge links from a standard cubic lattice in such a way that every vertex becomes trivalent, which streamlines the handling of Gauss's law. The ssc lattice is topologically equivalent to the triamond lattice but, because the gauge links at each vertex span all three directions, the ssc lattice can accommodate a local fermion derivative. The case of staggered fermions with SU(2) gauge fields is presented here.

Comments
13 pages, 7 figures

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A practical Hamiltonian approach to lattice gauge theories would provide access to several important areas of phenomenology that have been beyond the reach of conventional lattice methods. Quantum computers seem to be a natural platform for this approach. With near-term quantum computers in mind, our work considers a three-dimensional spatial lattice that can host fermions and non-Abelian gauge fields while needing fewer qubits than a simple cubic lattice. Specifically, the semi-simple cubic (ssc) lattice is obtained by removing half of the gauge links from a standard cubic lattice in such a way that every vertex becomes trivalent, which streamlines the handling of Gauss's law. The ssc lattice is topologically equivalent to the triamond lattice but, because the gauge links at each vertex span all three directions, the ssc lattice can accommodate a local fermion derivative. The case of staggered fermions with SU(2) gauge fields is presented here.
Quantum simulation provides a promising framework for studying non-perturbative phenomena in lattice gauge theories that are difficult to access using classical computational methods. In particular, classical Monte Carlo approaches suffer from the sign problem, limiting their applicability to real-time dynamics and finite-density regimes. Quantum computers, by directly encoding quantum dynamics, offer a natural pathway to overcoming these limitations. In this thesis, we study quantum simulations of a truncated SU(2) lattice gauge theory using a Hamiltonian formulation, representing an important non-Abelian step toward quantum chromodynamics. We focus on three-dimensional gauge-theory simulations in the noisy intermediate-scale quantum (NISQ) era, where limited qubit resources pose a significant challenge. To address this, we introduce the triamond lattice, a three-dimensional lattice geometry that enforces local gauge invariance while providing an economical encoding of gauge degrees of freedom, thereby reducing qubit overhead compared to conventional lattice constructions. We derive the corresponding Hamiltonian, construct physical gauge-invariant states, and implement quantum simulations using quantum imaginary time evolution to prepare ground states, alongside real-time evolution methods to study dynamical behavior. Error-mitigation techniques are employed to extract reliable physical observables from noisy quantum hardware. Our results demonstrate that the triamond lattice enables resource-efficient three-dimensional quantum gauge simulations and represents a practical step toward scalable quantum simulations of non-perturbative gauge theories.
Abstract Lattice gauge theory should be able to address significant new scientific questions when implemented on quantum computers. In practice, error-mitigation techniques have already allowed encouraging progress on small lattices. In this work we focus on a truncated version of SU(2) gauge theory, which is a familiar non-Abelian step toward quantum chromodynamics. First, we demonstrate effective error mitigation for imaginary time evolution on a lattice having two square plaquettes, obtaining the ground state using an IBM quantum computer and observing that this would have been impossible without error mitigation. Then we propose the triamond lattice as an expedient approach to lattice gauge theories in three spatial dimensions and we derive the Hamiltonian. Finally, error-mitigated imaginary time evolution is applied to the three-dimensional triamond unit cell, and its ground state is obtained from an IBM quantum computer. Future work will want to relax the truncation on the gauge fields, and the triamond lattice is increasingly valuable for such studies.
The development of quantum technology and the advent of quantum computation have renewed interest in Hamiltonian formulations of lattice gauge theories. In contrast to Euclidean Monte Carlo calculations, Hamiltonian simulation requires a direct representation of the physical Hilbert space, an efficient treatment of enforcing Gauss' law as constraints, and a formulation of real-time dynamics in terms of degrees of freedom that can be encoded on quantum or quantum-inspired classical platforms. The starting point corresponds to finding a suitable basis for Hamiltonian lattice gauge theories. The existing literature focuses on several complementary approaches: electric basis, magnetic basis, gauge-fixed, quantum-link, qubit-regularised, finite-group, and orbifold formulations. This article primarily focuses on the prepotential and loop--string--hadron formulations, where non-Abelian Gauss laws are solved locally and the dynamics is written directly in terms of gauge-invariant loop, string and hadron excitations. The discussion covers the SU(2) and SU(3) constructions in one spatial dimension, the role of residual Abelian Gauss laws, and the extension to higher dimensions through point splitting. We conclude by highlighting its direct applications: eliminating redundant gauge degrees of freedom makes exact diagonalisation and tensor network calculations feasible for studying real-time dynamics, provides insights into thermalisation properties, enables mapping of physical degrees of freedom onto analog and digital quantum hardware, and enables quantum simulation of dynamics.
We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux jmax=1/2j_{\rm max}=1/2jmax​=1/2, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half of the vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.
Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.
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