We benchmark two error-mitigation strategies for digital quantum simulation of a long-range interacting fermionic model on IBM Heron r2 superconducting processors. The testbed is a minimal exactly solvable system—two spinless electrons on a 6-site ring with repulsive
1/r chord-distance Coulomb interactions—whose ground state exhibits a smooth Wigner-dimer localization crossover quantified by the antipodal occupation probability
P3(U) . Circuit parameters of a particle-number-conserving variational ansatz are optimized classically; the quantum processors execute only final energy and configuration measurements. We compare (i) zero-noise extrapolation (ZNE) applied to the full Hamiltonian with (ii) a hybrid estimator in which the off-diagonal kinetic energy is measured with ZNE while the diagonal interaction energy is reconstructed from particle-number post-selected bitstrings. Across eight interaction strengths
U/t∈[5,75] , five measurement sessions on two devices (ibm_fez, ibm_marrakesh), and three circuit depths, the hybrid estimator achieves, in the interacting regime
U/t⩾15 , relative ground-state energy errors of 4.3–14% that decrease systematically with
U —an order of magnitude better than full-Hamiltonian ZNE (29–85%)—and reproduces the localization crossover in
P3(U) . At
U/t=5 , where
E0≈0.08t renders the relative error ill-conditioned, the absolute hybrid error is
0.62t , in line with the rest of the scan. A depth scan at fixed
U/t=45 shows that the shallowest circuit wins despite a 1.8% ansatz expressivity penalty, quantifying the expressivity–noise trade-off. Shot-noise uncertainties, recovered exactly from per-noise-factor data, are below one percentage point in relative energy error for the hybrid estimator (versus 7–14 percentage points for ZNE at equal shot budget) and an order of magnitude smaller than the measured inter-session calibration spread. The exact variational bound
Eexp⩾Etheory is satisfied in all 27 full-Hamiltonian hardware energy measurements. All data were acquired with under nine minutes of QPU time on the free IBM Quantum Open Plan.
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 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.
Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.
Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2 . Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble-Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition4 . Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5-7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.
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
vc,
vs, 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
∼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≳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.
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with
10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the
λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.