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arXiv:2611.00201

Quantum simulation of real-time Yukawa dynamics with qubits and qumodes

Jack Y. Araz, Jeffrey Forshaw, Ross Jenkinson

quant-phhep-lathep-phSubmitted Oct 30, 2026• Announced Nov 3, 2026
arXivHTMLPDF

Abstract

Real-time quantum simulation of field theories offers access to scattering and decay dynamics, circumventing the limitations of Euclidean lattice methods. However, representing bosonic fields on qubits requires a finite-dimensional approximation and can entail costly multi-qubit operations. Hybrid qubit-qumode architectures avoid this by encoding bosonic fields directly in oscillators. We formulate scattering in the (1+1)-dimensional Yukawa theory for such a device, with staggered fermions on qubits and the scalar on qumodes. Trapped ions are a natural candidate, with the fermions on the internal states of the ions and the scalar on their collective motion, so that the Yukawa coupling becomes a native spin-dependent displacement. Emulating the device with tensor networks, we study the decay of a single scalar particle and fermion-antifermion scattering around the resonance region, using observables that can be measured on the device natively. We compare the results with those obtained using lattice perturbation theory. The emulation is able to resolve corrections beyond the Dyson summation of the one-loop self-energy.

Comments
10 pages, 6 figures

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Real-time quantum simulation of field theories offers access to scattering and decay dynamics, circumventing the limitations of Euclidean lattice methods. However, representing bosonic fields on qubits requires a finite-dimensional approximation and can entail costly multi-qubit operations. Hybrid qubit-qumode architectures avoid this by encoding bosonic fields directly in oscillators. We formulate scattering in the (1+1)-dimensional Yukawa theory for such a device, with staggered fermions on qubits and the scalar on qumodes. Trapped ions are a natural candidate, with the fermions on the internal states of the ions and the scalar on their collective motion, so that the Yukawa coupling becomes a native spin-dependent displacement. Emulating the device with tensor networks, we study the decay of a single scalar particle and fermion-antifermion scattering around the resonance region, using observables that can be measured on the device natively. We compare the results with those obtained using lattice perturbation theory. The emulation is able to resolve corrections beyond the Dyson summation of the one-loop self-energy.
Resonant scattering links particle interactions to the formation and decay of unstable excitations. We develop a hybrid quantum-computing framework to study these dynamics through fermion--antifermion collisions. Our formulation of (1+1)(1+1)(1+1)-dimensional Yukawa theory encodes fermions in qubits and the scalar field in qumodes. We identify the operations needed for a photonic implementation and benchmark the dynamics with tensor-network simulations. Near resonance, we resolve the build-up of a localised scalar excitation and the subsequent partial return of energy to the fermions. Enhanced entanglement accompanies this exchange. Time-dependent correlator measurements reproduce the analytically predicted decay rate to a few percent precision, with energy scans exhibiting a resonance peak consistent with packet-averaged Breit--Wigner behaviour. These results establish a concrete scattering benchmark for hybrid quantum computers and demonstrate how local real-time observables can probe particle-resonance dynamics.
Trapped-ion, neutral-atom, and circuit QED quantum computers naturally enable coupled qubit-boson simulations. Boson-fermion interactions arise in quantum field theory, where renormalization is required to obtain finite results. We study one of the simplest examples of a coupled fermion-boson system, the static Yukawa model, on the QSCOUT trapped-ion system. We use similarity renormalization to express the same physics in terms of effective particles described by different values of the renormalization parameter sss. This enables us to map data taken in the window of bosonic occupancy that is experimentally accessible to larger occupancies of distinct effective particles. We use this to study strongly coupled, high-occupancy regimes despite limited readout ranges. Using a trapped-ion qubit-boson device on Sandia National Laboratories' QSCOUT platform, we demonstrate the time evolution of the static Yukawa model.
Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.
A bstract We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions. In this approach, fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic modes whose canonical quadratures capture the electric and vector-potential components of the theory. To reconcile the non-compact phase space of the qumodes with the compact U(1) gauge symmetry, we introduce and compare two complementary constraint-enforcement strategies: (i) a squeezing-based projection that confines qumode states to the unit circle through an effective modification of the inner product, and (ii) a method that dynamically enforces compactness via a penalty Hamiltonian term. We construct the corresponding hybrid Hamiltonian, derive its decomposition into experimentally accessible qubit-qumode gates, and analyze its spectrum in the analytically tractable single-plaquette limit. The hybrid formulation reproduces the correct gauge-invariant dynamics and provides a scalable route toward simulating Abelian lattice gauge theories coupled to fermionic matter on near-term hybrid quantum architectures. Ground-state preparation and convergence are demonstrated using a continuous-variable extension of the Quantum Imaginary Time Evolution (QITE) algorithm, establishing a general framework for hybrid discrete-continuous quantum simulations of lattice gauge theories.
Abstract Quantum field theories describe a variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here we report an experimental realization of a quantum simulation of fermion–antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and non-perturbative quantum electrodynamics. The simulated model exhibits prototypical features in quantum field theory including particle pair creation and annihilation, as well as self-energy interactions. These are experimentally observed by manipulating four internal levels of a 171Yb+ trapped ion, where we encode the fermionic modes, and two motional degrees of freedom that simulate the bosonic modes. Our experiment establishes an avenue towards the efficient implementation of field modes, which may prove useful in studies of quantum field theories including non-perturbative regimes.
We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions. In this approach, fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic modes whose canonical quadratures capture the electric and vector-potential components of the theory. To reconcile the non-compact phase space of the qumodes with the compact U(1) gauge symmetry, we introduce and compare two complementary constraint-enforcement strategies: (i) a squeezing-based projection that confines qumode states to the unit circle through an effective modification of the inner product, and (ii) a method that dynamically enforces compactness via a penalty Hamiltonian term. We construct the corresponding hybrid Hamiltonian, derive its decomposition into experimentally accessible qubit-qumode gates, and analyze its spectrum in the analytically tractable single-plaquette limit. The hybrid formulation reproduces the correct gauge-invariant dynamics and provides a scalable route toward simulating Abelian lattice gauge theories coupled to fermionic matter on near-term hybrid quantum architectures. Ground-state preparation and convergence are demonstrated using a continuous-variable extension of the Quantum Imaginary Time Evolution (QITE) algorithm, establishing a general framework for hybrid discrete-continuous quantum simulations of lattice gauge theories.