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arXiv:2607.04040

Quantum simulation of gauge theories on dynamical spacetimes via Floquet-induced matrix models

Samuel Buckley-Bonanno, Noah Eckstein, Susanne F. Yelin

quant-phSubmitted Jul 4, 2026• Announced Jul 7, 2026• 0 citations
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Abstract

Quantum simulations of gauge theories are typically built on spatial lattices, an approach that has enabled major progress at the cost of requiring fixed background geometries and obscuring the treatment of curved and dynamical spacetimes. Large-$N$ matrix models offer an alternative, encoding spacetime geometry and gauge fields in the commutation structure of a set of Hermitian matrices, with the classical continuum emerging smoothly at large matrix dimensions. Here we introduce a Floquet framework that makes these models directly accessible to programmable quantum platforms. We show that Euclidean path integral weights of a Yang-Mills matrix models are reproduced, at leading order in the coupling, by the ensemble-averaged fidelities of Haar-random states evolved under periodic sequences of matrix operators. The observables for the simulated matrix model can then be accessed through established randomized benchmarking protocols in terms of the Loschmidt echo. The encoding requires exponentially fewer qubits than canonically quantized approaches. Numerically, we validate the fidelity-weight correspondence, demonstrate parallelized quantum circuits that sample the path-integral measure, and identify the deconfinement transition of an $SU(2)$ gauge field on both flat and expanding cosmological backgrounds. By avoiding a fixed spacetime lattice, the framework preserves continuous symmetries and unitarity on dynamical geometries, opening quantum simulation to field and spacetime dynamics beyond the reach of conventional lattice methods.

Comments
12 pages with 6 figures, with an additional 6 pages of appendices and 2 additional figures, as well as 12 pages of supplementary info

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Quantum simulations of gauge theories are typically built on spatial lattices, an approach that has enabled major progress at the cost of requiring fixed background geometries and obscuring the treatment of curved and dynamical spacetimes. Large-NNN matrix models offer an alternative, encoding spacetime geometry and gauge fields in the commutation structure of a set of Hermitian matrices, with the classical continuum emerging smoothly at large matrix dimensions. Here we introduce a Floquet framework that makes these models directly accessible to programmable quantum platforms. We show that Euclidean path integral weights of a Yang-Mills matrix models are reproduced, at leading order in the coupling, by the ensemble-averaged fidelities of Haar-random states evolved under periodic sequences of matrix operators. The observables for the simulated matrix model can then be accessed through established randomized benchmarking protocols in terms of the Loschmidt echo. The encoding requires exponentially fewer qubits than canonically quantized approaches. Numerically, we validate the fidelity-weight correspondence, demonstrate parallelized quantum circuits that sample the path-integral measure, and identify the deconfinement transition of an SU(2)SU(2)SU(2) gauge field on both flat and expanding cosmological backgrounds. By avoiding a fixed spacetime lattice, the framework preserves continuous symmetries and unitarity on dynamical geometries, opening quantum simulation to field and spacetime dynamics beyond the reach of conventional lattice methods.
Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU(NNN) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.
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Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach, clarifying that physical states need not be represented solely by gauge singlets. Both singlet and non-singlet representations are valid, with distinct practical trade-offs, which we elucidate using analogies to BRST quantization. We demonstrate these principles within a complete quantum simulation framework based on the orbifold lattice, which enables explicit and efficient circuit constructions relevant to real-world QCD. For singlet-based approaches, we introduce a Haar-averaging projection implemented via linear combinations of unitaries, and analyze its cost and truncation errors. We also introduce an efficient simulation protocol with an additional term to the Hamiltonian that eliminates non-singlet states from the low-energy spectrum. Beyond the singlet-approach, we show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations. This non-singlet approach is proven to be both universal and efficient. Working in temporal gauge, we provide explicit mappings of lattice Yang-Mills dynamics to Pauli-string Hamiltonians suitable for Trotterization. Classical simulations of small systems validate convergence criteria and quantify truncation and Trotter errors, showing concrete resource estimates and scalable circuit recipes for SU(N)(N)(N) gauge theories. Our framework provides both conceptual clarity and practical tools toward quantum advantage in simulating non-Abelian gauge theories.
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Quantum simulation of lattice gauge theories offers a path to first-principles calculations of real-time dynamics and finite-density phenomena that are inaccessible to classical Euclidean Monte Carlo methods. Realizing this potential requires a pipeline of controlled approximations---lattice discretization, truncation, digitization, state preparation, time evolution, measurement, and continuum extrapolation---each contributing errors and computational costs. General algorithmic asymptotic complexity arguments capture only part of the cost picture: the practical resources required for end-to-end simulation depend on numerical pre-factors, the cost of the subroutines that various algorithms call, and structural features of the lattice theory, all of which the asymptotic scaling leaves unspecified. This thesis develops contributions that aim to make such dependencies explicit and quantitative. We begin with a rigorous analysis of the asymptotic gate complexity of product formulas and Quantum Signal Processing (QSP) for the time evolution of general classes of lattice Hamiltonians, identifying the parameter regimes in which each method is favorable and estimating the associated pre-factors numerically. Since the cost of QSP-based simulation is dominated (in regimes of practical interest) by the block-encoding subroutine it calls, we also develop several novel block-encoding constructions tailored to bosonic lattice field theories and show that signal-processing techniques can be repurposed as highly efficient block-encoding subroutines. We then turn to the problem of truncating the Kogut--Susskind electric-field Hilbert space. Existing error bounds rely on energy-conservation arguments and require the truncation to grow with simulation time. By exploiting Hilbert space fragmentation we derive the tightest error bounds known to date: they decay factorially in the truncation parameter and are independent of simulation time. We validate them numerically for U(1) pure gauge theory and the Schwinger model. Finally, we address the continuum limit in the presence of approximate time evolution. For product formulas, we show that Trotter errors correspond to irrelevant operators that vanish in the continuum limit, which yields a renormalization trajectory independent of the Trotter step size. More generally, we introduce the Statistically-Bounded Time Evolution (SBTE) protocol, an algorithm-independent framework that treats approximation errors as a systematic uncertainty to be driven below the working statistical precision. This decouples the continuum-limit prescription from the choice of time-evolution algorithm and provides a basis for end-to-end cost comparisons across simulation methods.