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arXiv:2606.04771

Pushing the Classical Frontier of 1D Fermi-Hubbard Quench Dynamics Beyond Current Quantum Simulations

Roman Rausch, Sukhbinder Singh, Saeed S. Jahromi, Augustine Kshetrimayum, Roman Orus

quant-phcond-mat.str-elSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
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Abstract

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 $L=60$ evolution to time $t=6$ in under three minutes and claiming a $3000\times$ speedup over classical Time-Dependent Variational Principle (TDVP) simulation at bond dimension $χ=4096$. Their classical benchmark required over 160 hours on a CPU cluster, failed to converge in the high-entanglement regime $t\in[5.2,6]$, and left the most challenging window of the experiment unverified. Here, we push the boundaries of classical simulation by exploiting the full $\mathrm{U}(1)\times\mathrm{SU}(2)$ symmetry of the Fermi-Hubbard Hamiltonian combined with GPU-accelerated tensor contractions. Reaching bond dimensions up to $χ\approx62{,}000$ 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 $t\in[5.2,6]$. We further advance the classical frontier to $t=7$, 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 $\sim\!100$ minutes, directly reducing the claimed $3000\times$ quantum advantage to $\sim\!36\times$. These results substantially narrow the quantum-classical performance gap and establish a new standard for tensor-network benchmarking of large-scale quantum simulations.

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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.
We study the Néel quench dynamics of a 1D Fermi-Hubbard model which has recently been simulated on quantum hardware. We demonstrate that the set of 7260 observable trajectories measured in the quantum experiment can be obtained more quickly and accurately through classical tensor network simulation using modest computation. Our result relies on transverse tensor network contraction, where a bond dimension of 32 is already sufficient to reproduce the quantum experiment. We further extend the converged observable trajectories to longer times than in the hardware simulation and in other recent classical simulations.
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.
Recent demonstrations of D-Wave's annealing-based quantum simulators have established new benchmarks for quantum computational advantage [arXiv:2403.00910]. However, the precise location of the classical-quantum computational frontier remains an open question, as classical simulation strategies continue to evolve. Here, we demonstrate that time-dependent variational Monte Carlo (t-VMC) with a physically motivated Jastrow-Feenberg wave function can efficiently simulate the quantum annealing of spin glasses up to system sizes previously thought to be intractable. Our approach achieves accuracy comparable to that of quantum processing units while requiring only polynomially scaling computational resources, in stark contrast to entangled-limited tensor network methods that scale exponentially. For systems up to 128 spins on a three-dimensional diamond lattice, we maintain correlation errors below 7%, which match or exceed the precision of existing quantum hardware. Rigorous assessments of residual energies and time-dependent variational principle errors establish clear performance benchmarks for classical simulations. These findings substantially shift the quantum advantage frontier and underscore that classical variational techniques, which are not fundamentally constrained by entanglement growth, remain competitive at larger system sizes than previously anticipated.
Classical simulation of quantum systems is indispensable for validating quantum algorithms, benchmarking near-term quantum hardware, and understanding quantum advantage boundaries. As quantum systems scale beyond 50 qubits -- entering the regime where exact statevector simulation requires 2^n complex amplitudes (16 petabytes for n=50) -- approximate and structure-exploiting classical simulation methods become essential. This paper proposes the Classical Quantum Simulation Benchmark (CQSB) framework, a systematic evaluation of six simulation techniques -- statevector simulation, tensor network contraction (MPS and MERA), Clifford circuit simulation, stabiliser state methods, Monte Carlo wavefunction simulation, and approximate tensor network methods -- across 48 quantum circuit benchmarks spanning 8 to 127 qubits. CQSB introduces the Simulation Efficiency Index (SEI) combining accuracy, runtime, and memory usage, and identifies the optimal simulation regime for each technique. Key results: MPS tensor networks achieve exact simulation to 127 qubits for circuits with bond dimension χ <= 512; Clifford simulation scales to 10,000 qubits in O(n2) time; approximate tensor network contraction produces fidelity > 0.95 for 72-qubit random circuits within 4.8 hours on a 256-GPU cluster. The framework provides simulation regime selection guidance and an open benchmark suite for the quantum computing community.
We classically simulate the IBM doped Clifford random circuit sampling experiment, comprising 707070 qubits, 707070 entangling layers, and 468468468 inserted TTT gates, as reported in the first version of arXiv:2607.25941. A deterministic temporal-boundary tensor network contraction approach is specifically designed to tackle such open-boundary one-dimensional brickwork circuits with operator-Schmidt-rank-222 entangling gates. For an nnn-qubit circuit of depth ddd, the resulting unsliced path evaluates an exact amplitude with contraction width ⌈d/2⌉\lceil d/2\rceil⌈d/2⌉; Ratcatcher calculations certify that no smaller width is possible for the tested instances. Because one-qubit gates are absorbed without changing the network topology, the width and dense scheduled contraction cost are independent of their values and of the number and placement of TTT gates. For this initial instance, its largest intermediate tensor contains 2352^{35}235 complex64 entries (256 times smaller than IBM's estimation), corresponding to a tensor payload of 256256256 GiB, and is distributed across eight GPUs within a node. Using 32 nodes, with eight NVIDIA H100 GPUs per node, we completed all 2051 amplitude batches corresponding to IBM's published output bitstrings in 37.3 minutes. The resulting probabilities yield a log-XEB estimate of 0.350340.350340.35034 with a 95% interval of [0.29763,0.40305][0.29763,0.40305][0.29763,0.40305]. Under the Porter--Thomas and scrambled-noise assumptions, this is numerically compatible with IBM's fidelity lower bound; separately, fidelity-weighted resource accounting projects a 583-contraction workload with a 10.6-minute makespan on the same 32 nodes. More broadly, the approach provides a practical diagnostic for experimental outputs and a quantitative tool for designing future doped Clifford sampling experiments.
Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to 6×6{6\times 6}6×6 using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.