Truncation uncertainties for accurate quantum simulations of lattice gauge theories
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AbstractThe encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut–Susskind limit. In the electric basis, Hilbert space fragmentation has recently been shown to limit the excitation of large electric fields. Here, we leverage this to develop a formalism for estimating the size of truncation errors in the electric basis. Generically, the truncation error falls off as a factorial of the field truncation. Examples of this formalism are applied to the Schwinger model and a pure U(1) lattice gauge theory. For reasonable choices of parameters, we improve on previous error estimates by a factor of $10^{306}$.Popular summaryQuantum computers are expected to simulate the real time dynamics of the theories that describe the strong nuclear force, a task that classical computers cannot perform at scale. To run such a simulation, the gauge fields that carry the force must be stored in a finite number of qubits. However, a gauge field can in principle hold an unbounded amount of electric flux, so only a finite range of field values can be kept. Any prediction made with a truncated simulation carries an error from the field values that were removed, and a simulation with scientific value needs a reliable estimate of the size of this error. Previous estimates were valid but extremely loose, and taking them at face value would require far more qubits than are actually needed. In this work, a method is developed for estimating the truncation error directly. The method is based on a property of the lattice Hamiltonian known as Hilbert space fragmentation. States with large electric fields have a large energy cost, and this energy gap makes it difficult for the dynamics to reach them. Perturbation theory in this gap is used to compute the leading contribution to the error from the truncation. It is shown that the error falls off as a factorial of the truncation, so that each additional field value kept reduces the error by a rapidly growing factor. These results indicate that accurate quantum simulations of gauge theories can be performed with far smaller truncations, and therefore far fewer qubits, than earlier estimates suggested.► BibTeX data@article{Ciavarella2026truncation, doi = {10.22331/q-2026-09-24-2216}, url = {https://doi.org/10.22331/q-2026-09-24-2216}, title = {Truncation uncertainties for accurate quantum simulations of lattice gauge theories}, author = {Ciavarella, Anthony N. and Hariprakash, Siddharth and Halimeh, Jad C. and Bauer, Christian W.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2216}, month = sep, year = {2026} }► References [1] Richard P. Feynman. ``Simulating physics with computers''. Int. J. Theor. Phys. 21, 467–488 (1982). https://doi.org/10.1007/BF02650179 [2] Travis S. Humble et al. ``Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research''. In Snowmass 2021. (2022). arXiv:2203.07091. arXiv:2203.07091 [3] Christian W. Bauer et al. ``Quantum Simulation for High-Energy Physics''. PRX Quantum 4, 027001 (2023). arXiv:2204.03381. https://doi.org/10.1103/PRXQuantum.4.027001 arXiv:2204.03381 [4] Alberto Di Meglio et al. ``Quantum Computing for High-Energy Physics: State of the Art and Challenges''. PRX Quantum 5, 037001 (2024). arXiv:2307.03236. https://doi.org/10.1103/PRXQuantum.5.037001 arXiv:2307.03236 [5] Douglas Beck et al. ``Quantum Information Science and Technology for Nuclear Physics. Input into U.S. Long-Range Planning, 2023'' (2023). arXiv:2303.00113. arXiv:2303.00113 [6] Christian W. Bauer, Marat Freytsis, and Benjamin Nachman. ``Simulating Collider Physics on Quantum Computers Using Effective Field Theories''. Phys. Rev. Lett. 127, 212001 (2021). arXiv:2102.05044. https://doi.org/10.1103/PhysRevLett.127.212001 arXiv:2102.05044 [7] Christian W. Bauer. ``Efficient use of quantum computers for collider physics'' (2025). arXiv:2503.16602. arXiv:2503.16602 [8] Thomas D. Cohen, Henry Lamm, Scott Lawrence, and Yukari Yamauchi. ``Quantum algorithms for transport coefficients in gauge theories''. Phys. Rev. D 104, 094514 (2021). arXiv:2104.02024. https://doi.org/10.1103/PhysRevD.104.094514 arXiv:2104.02024 [9] Francesco Turro, Anthony Ciavarella, and Xiaojun Yao. ``Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory''. Phys. Rev. D 109, 114511 (2024). arXiv:2402.04221. https://doi.org/10.1103/PhysRevD.109.114511 arXiv:2402.04221 [10] M. Luscher. ``Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 1.
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The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-09-24 14:07:13: Could not fetch cited-by data for 10.22331/q-2026-09-24-2216 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut–Susskind limit. In the electric basis, Hilbert space fragmentation has recently been shown to limit the excitation of large electric fields. Here, we leverage this to develop a formalism for estimating the size of truncation errors in the electric basis. Generically, the truncation error falls off as a factorial of the field truncation. Examples of this formalism are applied to the Schwinger model and a pure U(1) lattice gauge theory. For reasonable choices of parameters, we improve on previous error estimates by a factor of $10^{306}$.Popular summaryQuantum computers are expected to simulate the real time dynamics of the theories that describe the strong nuclear force, a task that classical computers cannot perform at scale. To run such a simulation, the gauge fields that carry the force must be stored in a finite number of qubits. However, a gauge field can in principle hold an unbounded amount of electric flux, so only a finite range of field values can be kept. Any prediction made with a truncated simulation carries an error from the field values that were removed, and a simulation with scientific value needs a reliable estimate of the size of this error. Previous estimates were valid but extremely loose, and taking them at face value would require far more qubits than are actually needed. In this work, a method is developed for estimating the truncation error directly. The method is based on a property of the lattice Hamiltonian known as Hilbert space fragmentation. States with large electric fields have a large energy cost, and this energy gap makes it difficult for the dynamics to reach them. Perturbation theory in this gap is used to compute the leading contribution to the error from the truncation. It is shown that the error falls off as a factorial of the truncation, so that each additional field value kept reduces the error by a rapidly growing factor. These results indicate that accurate quantum simulations of gauge theories can be performed with far smaller truncations, and therefore far fewer qubits, than earlier estimates suggested.► BibTeX data@article{Ciavarella2026truncation, doi = {10.22331/q-2026-09-24-2216}, url = {https://doi.org/10.22331/q-2026-09-24-2216}, title = {Truncation uncertainties for accurate quantum simulations of lattice gauge theories}, author = {Ciavarella, Anthony N. and Hariprakash, Siddharth and Halimeh, Jad C. and Bauer, Christian W.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2216}, month = sep, year = {2026} }► References [1] Richard P. Feynman. ``Simulating physics with computers''. Int. J. Theor. Phys. 21, 467–488 (1982). https://doi.org/10.1007/BF02650179 [2] Travis S. 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[2] Angus Kan, Jessica Lemieux, Olga Okrut, and Burak Şahinoğlu, "Optimized quantum algorithms for simulating the Schwinger effect", Physical Review D 113 11, 114503 (2026). [3] Yizhuo Tian, N. S. Srivatsa, Kaidi Xu, Jesse J. Osborne, Umberto Borla, and Jad C. Halimeh, "Role of Plaquette Term in Genuine $2+1$D String Dynamics on Quantum Simulators", arXiv:2508.05736, (2025). [4] Masanori Hanada, Shunji Matsuura, Emanuele Mendicelli, and Enrico Rinaldi, "Exponential improvement in quantum simulations of bosons", arXiv:2505.02553, (2025). [5] Xiaojun Yao, "Quantum error correction codes for truncated SU(2) lattice gauge theories", Physical Review D 113 11, 114512 (2026). [6] Kaidi Xu, Umberto Borla, Kevin Hemery, Rohan Joshi, Henrik Dreyer, Enrico Rinaldi, and Jad C. Halimeh, "Observation of glueball excitations and string breaking in a $2+1$D $\mathbb{Z}_2$ lattice gauge theory on a trapped-ion quantum computer", arXiv:2604.07435, (2026). [7] Rohan Joshi, Yizhuo Tian, Kevin Hemery, N. S. Srivatsa, Jesse J. Osborne, Henrik Dreyer, Enrico Rinaldi, and Jad C. Halimeh, "Observation of genuine $2+1$D string dynamics in a U$(1)$ lattice gauge theory with a tunable plaquette term on a trapped-ion quantum computer", arXiv:2604.07436, (2026). [8] Gabriel Rouxinol, Tom Magorsch, Jesse J. Osborne, Nora Brambilla, and Jad C. Halimeh, "Schwinger Model with a Dynamical Axion", arXiv:2603.12194, (2026). [9] Klaus Liegener, Dominik Mattern, Alexander Korobov, Lisa Krüger, Manuel Geiger, Malay Singh, Longxiang Huang, Christian Schneider, Federico Roy, and Stefan Filipp, "Enhancing Variational Quantum Eigensolvers for SU(2) Lattice Gauge Theory via Systematic State Preparation", arXiv:2603.03799, (2026). [10] Peter Majcen, Jesse J. Osborne, Philipp Hauke, Bing Yang, Simone Montangero, and Jad C. Halimeh, "Towards $2+1$D quantum electrodynamics on a cold-atom quantum simulator", arXiv:2602.04948, (2026). [11] David Rogerson, João Barata, Robert M. Konik, Raju Venugopalan, and Ananda Roy, "Simulating Lattice Gauge Theories with Virtual Rishons", arXiv:2603.05151, (2026). [12] Neel S. Modi, Anthony N. Ciavarella, Jad C. Halimeh, and Christian W. Bauer, "Large Nc Truncations for SU(Nc) Lattice Yang-Mills Theory with Fermions", arXiv:2602.02344, (2026). [13] Jinghong Yang, Christopher F. Kane, and Shabnam Jabeen, "Tightening energy-based boson truncation bound using Monte Carlo-assisted methods", Physical Review D 114 3, 034517 (2026). [14] Vincent Chen, Berndt Müller, and Xiaojun Yao, "Minimally Truncated SU(3) Lattice Gauge Theory and String Tension", arXiv:2601.10065, (2026). [15] Zoë Webb-Mack and Natalie Klco, "Deforming the Trail: Baseline Quantum Circuitry for $\text{SU(2)}_k$ Lattice Gauge Theory", arXiv:2605.15076, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-09-24 14:07:15). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-09-24 14:07:13: Could not fetch cited-by data for 10.22331/q-2026-09-24-2216 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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