Quantum field theory dynamics on a spin–phonon quantum computer

Nature Physics (2026) Cite this article Simulating the non-equilibrium dynamics of quantum field theories in nature is generally intractable with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields using quantum computers typically requires a boson-to-qubit encoding that can be resource-intensive. Furthermore, these encodings necessarily involve a truncation of the infinite-dimensional Hilbert space, introducing errors that grow with energy and time. Here we adopt an alternative approach that combines a qubit-based quantum computer with an active bosonic register that offers qubit, bosonic and mixed qubit–boson quantum gates. We use a hybrid analogue–digital trapped-ion quantum computer in which qubits are encoded in the internal states of the ions as well as the bosons in the ions’ motional states. Specifically, we simulate the non-equilibrium dynamics of a (1 + 1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions. These dynamics populate high-bosonic-field excitations starting from an empty state, and the experimental results effectively capture such high-occupation states. By removing the need for a large qubit overhead and avoiding truncation errors, our simulation approaches the regime in which classical methods become challenging. 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We acknowledge the University of Maryland supercomputing resources (http://hpcc.umd.edu) made available for computations of this work.This material is based on work supported by the US Department of Energy (DoE), Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator Award, via award number DE-FOA-0002253 (N.M.L., A.T.T., N.H.N., X.L. and A.M.G.). We acknowledge support from the DoE, Office of Science, Early Career Award, via award numbers DE-SC0020271 (Z.D. and S.V.K.) and DE-SC0024504 (N.M.L.). We acknowledge support from the National Science Foundation’s Quantum Leap Challenge Institute on Robust Quantum Simulation via award number OMA-2120757 (Z.D., V.V., N.M.L. and N.H.N.). We further acknowledge support from the DoE, Office of Science, Office of Nuclear Physics, via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science (award number DE-SC0023710; Z.D. and V.V.). We further acknowledge support from the DoE, Office of Science, Office of Nuclear Physics, via award number DE-SC0026067 (Z.D. and V.V.). Z.D. further acknowledges support from the DoE, Office of Science, Office of Advanced Scientific Computing Research (ASCR), program in Accelerated Research in Quantum Computing, Fundamental Algorithmic Research toward Quantum Utility (FARQu). Z.D., S.V.K. and V.V. are grateful to the Department of Physics, Maryland Center for Fundamental Physics, and College of Computer, Mathematical, and Natural Sciences at the University of Maryland, College Park, for their support. S.V.K. further acknowledges support by the DoE, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) (award number DE-SC0020970), and by the DoE QuantISED program through the theory consortium ‘Intersections of QIS and Theoretical Particle Physics’ at Fermilab (Fermilab subcontract number 666484). S.V.K. would also like to thank the Department of Physics and the College of Arts and Sciences at the University of Washington for their support. Additional support is acknowledged from the National Science Foundation Software-Tailored Architecture for Quantum Co-Design (STAQ) Award, via award number PHY-2325080 (N.M.L.). We further acknowledge early support from the DoE, Office of Science, Office of Nuclear Physics, via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science (award number DE-SC0021143; Z.D., N.M.L. and N.H.N.).These authors contributed equally: Saurabh V. Kadam, Vinay Vikramaditya.These authors jointly supervised this work: Zohreh Davoudi, Alaina M. Green, Norbert M. Linke.Joint Quantum Institute, University of Maryland, College Park, MD, USAAnton T. Than, Nhung H. Nguyen, Xingxin Liu & Alaina M. GreenDepartment of Physics, University of Maryland, College Park, MD, USAAnton T. Than, Vinay Vikramaditya, Nhung H. Nguyen, Xingxin Liu, Zohreh Davoudi, Alaina M. Green & Norbert M. LinkeNational Quantum Laboratory (QLab), University of Maryland, College Park, MD, USAAnton T. Than, Vinay Vikramaditya, Xingxin Liu, Zohreh Davoudi, Alaina M. Green & Norbert M. LinkeInQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA, USASaurabh V. KadamJoint Center for Quantum Information and Computer Science, College Park, MD, USAVinay Vikramaditya & Zohreh DavoudiQuantinuum, Broomfield, CO, USANhung H. NguyenDuke Quantum Center and Department of Physics, Duke University, Durham, NC, USANorbert M. LinkeSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarZ.D., A.M.G., N.M.L. and A.T.T. designed the research, including the algorithms and experimental workflow. A.T.T. set up the experiment, took the experimental data and analysed them. N.H.N. performed the early gate implementations and benchmarks. X.L. assisted A.T.T. in taking the data. V.V. and A.T.T. transpiled the model Hamiltonian into quantum circuits. S.V.K., V.V. and A.T.T. performed the classical simulations of the real-time dynamics. V.V. performed the noise simulations to supplement the gate calibrations. A.M.G. and N.M.L. supervised the experimental work, whereas Z.D. supervised the theoretical work. Z.D., A.M.G. and N.M.L. coordinated the collaboration. All authors contributed to the paper.Correspondence to Anton T. Than.N.M.L. is the chief technology officer of TAMOS Inc. The other authors declare no competing interests.Nature Physics thanks Panyu Hou and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a, Chain of three ions held in a blade trap. Coherent operations are performed using a Raman transition with two counterpropagating beams. One beam is split and focused onto separate ions, allowing for phase, frequency and amplitude control of the pulses sent to individual qubits. b, To implement the term for the fermion–boson coupling, a simultaneous red and blue resonant sideband operation is applied to each ion. ωm denotes the mth mode frequency and ω0 is the qubit frequency. c, This operation on an initial state \(| 0\left.\right\rangle | 0\left.\right\rangle\) results in an entangled state \(\frac{1}{\sqrt{2}}(| -\left.\right\rangle | -\alpha \left.\right\rangle +| +\left.\right\rangle | \alpha \left.\right\rangle )\), where the first ket is the spin state and the second ket is the motional coherent state with displacement parameters ±α.Phonon measurement for N = 4 and mode 2 at t = 3, needed to produce the plots in Fig. 4g. a, One qubit is chosen to probe the motional mode. The probability of this qubit being in \(| 1\left.\right\rangle\) is plotted (solid circles) as a function of red sideband pulse time, with error bars representing one s.e.m. The solid line is the result of fitting equation (33) to the experimental data. b, Fit to equation (33) yields the probability that each Fock state was occupied at t = 3. The experimental error bars represent one s.e.m. and are a result of bootstrapping.Source dataSupplementary Figs. 1–4, Sections I–III and Discussion.Data for Supplementary Figs. 1 and 4.Statistical source data.Statistical source data.Statistical source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsThan, A.T., Kadam, S.V., Vikramaditya, V. et al. Quantum field theory dynamics on a spin–phonon quantum computer. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03402-4Download citationReceived: 18 September 2025Accepted: 02 July 2026Published: 25 September 2026Version of record: 25 September 2026DOI: https://doi.org/10.1038/s41567-026-03402-4Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative