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arXiv:2501.13383 · Physical review. B./Physical review. B

Native three-body interactions in a superconducting lattice gauge quantum simulator

Jamal Busnaina, Zheng Shi, Jesús M. Alcaine-Cuervo, Chun Yang, Ibrahim Nsanzineza, E. Rico, Christopher M. Wilson

Published Sep 22, 2025• 5 citations
arXivHTMLPDF

Abstract

While universal quantum computers remain under development, analog quantum simulators offer a powerful alternative for understanding complex systems in condensed matter, chemistry, and high-energy physics. One compelling application is the characterization of real-time lattice gauge theories (LGTs). LGTs are nonperturbative tools, utilizing discretized space-time to describe gauge-invariant models. They hold immense potential for understanding fundamental physics but require enforcing local constraints analogous to electromagnetism's Gauss's law. These constraints, which arise from gauge symmetries and dictate the form of the interaction between matter and gauge fields, are a significant challenge for simulators to enforce. Implementing these constraints at the hardware level in analog simulations is crucial. This requires realizing multibody interactions between matter and gauge-field elements, enabling them to evolve together while suppressing unwanted two-body interactions that violate the gauge symmetry. In this paper, we propose and implement a parametrically activated three-qubit interaction within a circuit quantum electrodynamics architecture. We experimentally demonstrate a minimal $\text{U}(1)$ spin-$\frac{1}{2}$ model with a time evolution that intrinsically satisfies Gauss's law in the system. This design serves as the foundational block for simulating LGTs on a superconducting photonic lattice.

DOI
10.1103/6prx-zmdz

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A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.

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While universal quantum computers remain under development, analog quantum simulators offer a powerful alternative for understanding complex systems in condensed matter, chemistry, and high-energy physics. One compelling application is the characterization of real-time lattice gauge theories (LGTs). LGTs are nonperturbative tools, utilizing discretized space-time to describe gauge-invariant models. They hold immense potential for understanding fundamental physics but require enforcing local constraints analogous to electromagnetism's Gauss's law. These constraints, which arise from gauge symmetries and dictate the form of the interaction between matter and gauge fields, are a significant challenge for simulators to enforce. Implementing these constraints at the hardware level in analog simulations is crucial. This requires realizing multibody interactions between matter and gauge-field elements, enabling them to evolve together while suppressing unwanted two-body interactions that violate the gauge symmetry. In this paper, we propose and implement a parametrically activated three-qubit interaction within a circuit quantum electrodynamics architecture. We experimentally demonstrate a minimal U(1)\text{U}(1)U(1) spin-12\frac{1}{2}21​ model with a time evolution that intrinsically satisfies Gauss's law in the system. This design serves as the foundational block for simulating LGTs on a superconducting photonic lattice.
Gauge invariance is central to modern physics and underpins quantum simulations of lattice gauge theories (LGTs). Existing quantum simulation approaches employ Gauss's law either to energetically suppress gauge-violating processes in analog platforms or to detect and discard gauge-violating outcomes in digital devices. Here we introduce a third paradigm, in which Gauss's law is used to dynamically generate the gauge theory itself from a substantially simpler Hamiltonian. Starting from a readily programmable three-body XXX model, we employ experimentally efficient single-qubit U(1) gauge symmetry-generator terms that induce the dynamics of a U(1) LGT. We implement this approach using 101 qubits on a 156-qubit IBM quantum processor and observe real-time dynamics in quantitative agreement with the target LGT while reducing the entangling-gate depth per Trotter step by a factor of five compared with a direct implementation. Our results establish gauge protection as a resource for Hamiltonian engineering rather than merely symmetry preservation, opening a scalable resource-efficient route towards digital quantum simulations of increasingly complex gauge theories in higher spatial dimensions.
Measurement-based quantum simulation (MBQS)---a recently proposed architecture for simulating lattice gauge theories---implements Hamiltonian dynamics by consuming a model-specific entangled resource state with adaptive mid-circuit measurements, rather than by a gate-based circuit. The local constraints in lattice gauge theories are mirrored by the higher-form symmetries of the resource state. Here we report, to our knowledge, the first experimental realization of MBQS of real-time dynamics in the (2+1)(2+1)(2+1)-dimensional Z2\mathbb{Z}_2Z2​ gauge theory using the Quantinuum System Model H2 trapped-ion processor. We observe coherent evolution of gauge-invariant observables on 2×22\times22×2 and 3×33\times33×3 spatial lattices, consuming virtual three-dimensional cluster states of 200 and 288 resource-state qubits that are generated from instantaneous blocks of 48 and 54 qubits within the 56-qubit register by measurement, reset, and re-entanglement. The measurement record that drives the evolution simultaneously provides one-form-symmetry syndromes at no additional cost, enabling postselection that strongly suppresses observed Gauss-law violations and improves aggregate agreement with ideal Trotterized dynamics. Our results demonstrate that MBQS is a viable, symmetry-aware architecture for simulating lattice field theories on present-day hardware.
Photonic Analog Quantum Simulation of (1+1)-Dimensional U(1)U(1)U(1) Lattice Gauge Theory with Dynamical Matter
We propose a photonic scheme for analog quantum simulation of a U(1)U(1)U(1) Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.
Abstract The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss’s law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3–6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7, 8, realized mappings onto effective models to integrate out either matter or electric fields9–12, or were limited to very small systems13–16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter–gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss’s law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.
We propose a superconducting-circuit architecture that realizes a compact U(1) lattice gauge theory using the intrinsic infinite-dimensional Hilbert space of phase and charge variables. The gauge and matter fields are encoded directly in the degrees of freedom of the rotor variables associated with the circuit nodes, and Gauss's law emerges exactly from the conservation of local charge, without auxiliary stabilizers, penalty terms, or Hilbert-space truncation. A minimal gauge-matter coupling arises microscopically from Josephson nonlinearities, whereas the magnetic plaquette interaction is generated perturbatively via virtual matter excitations. Numerical diagonalization confirms the emergence of compact electrodynamics and coherent vortex excitations, underscoring the need for large local Hilbert spaces in the continuum regime. The required circuit parameters are within the current experimental capabilities. Our results establish superconducting circuits as a scalable, continuous-variable platform for analog quantum simulation of non-perturbative gauge dynamics.
A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.