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arXiv:2605.04025

Fast, accurate, high-resolution simulation of large-scale Fermi-Hubbard models on a digital quantum processor

Gavin S. Hartnett, Khadijeh Sona Najafi, Aleksei Khindanov, Haoran Liao, Michael Schutzman, Michael R. Hush, Michael J. Biercuk, Yuval Baum

quant-phSubmitted May 5, 2026• Announced May 6, 2026• 0 citations• Revised Jul 15, 2026 (v2)
v1 · May 5, 2026v2 · Jul 15, 2026
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Abstract

We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art tensor-network methods. We encode this problem using up to 120 qubits through an efficient mapping that reduces circuit complexity, and we improve accuracy through error suppression to simulate dynamical evolution using up to 90 Trotter steps. From a vacancy defect introduced in the middle of an $L=31$-site (62-qubit) Néel initial state, we directly observe spin-charge separation to $t=9$ in natural units and quantitatively extract velocities $v_c$, $v_s$, which match classical simulations across model parameters, and analytics in appropriate regimes. We then extend experiments to $L=60$ fermions (120 qubits) and evolution times to $t=6$ using 30 Trotter steps. Quantum-processor outputs agree quantitatively with approximate classical simulations performed using a time-dependent variational principle (TDVP) solver and we observe that increasing the TDVP bond dimension through $χ= 4096$ expands the range of evolution times within which agreement has RMSE $\sim 1\%$ before the approaches diverge. Owing to the large scale of the simulation and the use of overhead-free error-suppression techniques, for simulated evolution times at the limit of quantum/classical agreement ($t\gtrsim 5$ in natural hopping units), the wall-clock runtime of the quantum processor is nearly three orders of magnitude faster than TDVP simulations with $χ= 4096$ and implemented using the ITensor and TeNPy packages. These results establish contemporary digital quantum processors as a versatile, quantitatively accurate, and competitive platform for the study of fermionic many-body dynamics in regimes where leading classical methods can become prohibitively expensive.

Comments
49 pages, 4 figures in main text + 22 figures in Supplementary Material

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We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art tensor-network methods. We encode this problem using up to 120 qubits through an efficient mapping that reduces circuit complexity, and we improve accuracy through error suppression to simulate dynamical evolution using up to 90 Trotter steps. From a vacancy defect introduced in the middle of an L=31L=31L=31-site (62-qubit) Néel initial state, we directly observe spin-charge separation to t=9t=9t=9 in natural units and quantitatively extract velocities vcv_cvc​, vsv_svs​, which match classical simulations across model parameters, and analytics in appropriate regimes. We then extend experiments to L=60L=60L=60 fermions (120 qubits) and evolution times to t=6t=6t=6 using 30 Trotter steps. Quantum-processor outputs agree quantitatively with approximate classical simulations performed using a time-dependent variational principle (TDVP) solver and we observe that increasing the TDVP bond dimension through χ=4096χ= 4096χ=4096 expands the range of evolution times within which agreement has RMSE ∼1%\sim 1\%∼1% before the approaches diverge. Owing to the large scale of the simulation and the use of overhead-free error-suppression techniques, for simulated evolution times at the limit of quantum/classical agreement (t≳5t\gtrsim 5t≳5 in natural hopping units), the wall-clock runtime of the quantum processor is nearly three orders of magnitude faster than TDVP simulations with χ=4096χ= 4096χ=4096 and implemented using the ITensor and TeNPy packages. These results establish contemporary digital quantum processors as a versatile, quantitatively accurate, and competitive platform for the study of fermionic many-body dynamics in regimes where leading classical methods can become prohibitively expensive.
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Establishing quantum advantage requires comparison against the best achievable classical simulation. The Q-CTRL team recently simulated quench dynamics of the one-dimensional Fermi-Hubbard model on an IBM processor, completing a L=60L=60L=60 evolution to time t=6t=6t=6 in under three minutes and claiming a 3000×3000\times3000× speedup over classical Time-Dependent Variational Principle (TDVP) simulation at bond dimension χ=4096χ=4096χ=4096. Their classical benchmark required over 160 hours on a CPU cluster, failed to converge in the high-entanglement regime t∈[5.2,6]t\in[5.2,6]t∈[5.2,6], and left the most challenging window of the experiment unverified. Here, we push the boundaries of classical simulation by exploiting the full U(1)×SU(2)\mathrm{U}(1)\times\mathrm{SU}(2)U(1)×SU(2) symmetry of the Fermi-Hubbard Hamiltonian combined with GPU-accelerated tensor contractions. Reaching bond dimensions up to χ≈62,000χ\approx62{,}000χ≈62,000 on four NVIDIA H200 GPUs -- among the largest ever achieved in TDVP simulations and fifteen times larger than Q-CTRL's classical baseline -- we achieve fully converged results across the entire simulation window, including rigorous certification of the previously unresolved high-entanglement regime t∈[5.2,6]t\in[5.2,6]t∈[5.2,6]. We further advance the classical frontier to t=7t=7t=7, which lies beyond the quantum hardware experiment and any previously verified classical evolution of the full wavefunction. At the bond dimension comparable to Q-CTRL's best classical run, our GPU implementation completes in ∼ ⁣100\sim\!100∼100 minutes, directly reducing the claimed 3000×3000\times3000× quantum advantage to ∼ ⁣36×\sim\!36\times∼36×. These results substantially narrow the quantum-classical performance gap and establish a new standard for tensor-network benchmarking of large-scale quantum simulations.
Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.
We present a scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.
The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Finally, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.