In variational Monte Carlo (VMC) calculations of $N$-site quantum systems with arbitrary all-to-all two-body interactions, evaluating the local energy generally costs $O(N^3)$. We introduce a new framework that reduces this cost to $O(N)$ for tensor network states, capable of scalable and accurate computation of real-time dynamics and ground states. As a result, we obtain accurate simulations of the adiabatic real-time protocol of a $10\times10$ dipolar XY model realized in a Rydberg simulator [C. Chen et al., Nature 616, 691 (2023)], which was previously beyond the reach of classical simulation. Going beyond quantum experiments, we also directly perform ground state VMC to compare with the adiabatic state preparation. Our work demonstrates tensor network VMC as a powerful classical simulator for long-range quantum platforms such as Rydberg and ion-trap simulators, which are currently in urgent need of scalable classical benchmarking tools. As a separate technical contribution, we resolve the pathology of evolving from product states within of tensor network VMC.
Programmable quantum annealers can realize real-time dynamics of frustrated transverse-field Ising models on large, nontrivial graphs. Recent work by King et al. argued that the classical simulation of such experiments would require exponential computational resources for classical methods such as tensor networks and neural quantum states. Here, we numerically simulate the D-Wave spin-glass annealing protocol with time-dependent variational Monte Carlo (t-VMC) using a correlator state tailored to spin-glass dynamics. For the two-dimensional cylinder, three-dimensional dimer, diamond, and biclique instances considered, at annealing times of 7 and 20 ns, we show that systematically increasing the variational ansatz size enables t-VMC to approximate the final two-spin correlation errors of the quantum processing unit (QPU). We also perform an accurate large-scale simulation of a challenging biclique instance for which no other variational method is known to work, and we find close agreement with the quantum annealer. Through ablation studies, we identify poor Markov-chain mixing, high-variance local-energy estimators, and stochastic Runge-Kutta error estimates as the principal numerical failure modes. We address these numerical issues by using parallel tempering, blurred sampling and an importance-weighted differential equation solver, thereby clarifying the numerical requirements for stable, large-scale t-VMC simulations. Our results extend the frontier of classical simulation while providing a realistic assessment of the computational costs of simulating quantum dynamics at this scale.
Accurate real-time simulation of correlated quantum systems remains challenging for both classical methods and near-term quantum hardware. We introduce operator-projected variational quantum real-time evolution (OVQRTE), which updates a parameterized circuit by enforcing the Ehrenfest equations for a selected set of observables. OVQRTE requires only expectation-value measurements, while the choice of operator set enables a systematic trade-off between accuracy and measurement cost, substantially reducing quantum-resource requirements relative to existing variational real-time-evolution algorithms. After implementing OVQRTE dynamics of Heisenberg model on a simulator, we benchmark the algorithm for the Anderson impurity models on the IQM Emerald superconducting processor using up to 24 qubits. We further use OVQRTE to sample computational-basis states for quantum-selected configuration interaction (QSCI), enabling the calculation of the ground-state energy and density of states within a self-consistent ghost-Gutzwiller Ansatz (gGut) embedding loop. Our results establish OVQRTE as a promising approach for investigating correlated condensed-matter systems on near-term quantum hardware.
Aeishah Ameera Anuar, P. Sriluckshmy, Riccardo Rossi et al.· 0 citations
Polaron ground states and finite-temperature dynamics remain challenging to simulate because existing methods struggle to combine nonperturbative accuracy, systematic improvability, and scalability from models to materials-specific Hamiltonians. We introduce a translationally invariant variational coupled-cluster (CC) theory for polarons, termed delocalized CC (dCC), with closed-form energies at cost as low as $\mathcal{O}(N^3)$ and no phonon-number cutoff. dCC accurately describes the ground states of the one- and two-dimensional Holstein and Su--Schrieffer--Heeger (optical and bond) models and the Fr{\"o}hlich model, in close agreement with density matrix renormalization group (DMRG) and diagrammatic Monte Carlo benchmarks. A projected tangent-space response formalism built on the same ansatz yields electron-addition spectral functions and optical conductivities at zero and finite temperature. The resulting spectra agree well with DMRG, Lanczos, and neural-network quantum-state benchmarks while retaining a physically interpretable excitation hierarchy, and extend to two-dimensional lattices at finite temperature beyond the practical reach of these methods. The same framework applies directly to \textit{ab initio} electron--phonon matrix elements, yielding LiF electron- and hole-polaron binding energies that match state-of-the-art many-body calculations. These results establish dCC as a unified variational framework for polaron ground states and dynamics, from model systems to real materials.
Hamlin Wu, Moritz K A Baumgarten, Tong Jiang et al.· 0 citations
We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian--ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an $R_y$ product-state ansatz for the diagonal model to shallow $R_y$--CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.
Vojtěch Novák, Ivan Zelinka, Swagatam Das et al.· 1 citation
Additional levels in a qudit can serve as more than extra computational capacity and can represent physically relevant correlations when the algorithmic design reflects the underlying physics of the problem. We demonstrate this principle for quantum chemistry simulation using a qutrit-native spatial-orbital encoding, where $|0\rangle$, $|1\rangle$, and $|2\rangle$ denote orbital occupation states. We establish a qutrit simulation framework that combines number-conserving pair-transfer and broken-pair generators with a projected-Hamiltonian energy estimator constructed from qutrit populations and coherences. Benchmarks for H$_2$, LiH, and H$_2$O show that the encoding reproduces the relevant potential-energy curves, while retaining a compact quantum resource structure. Direct comparison with the pair-only restriction confirms that the third level reduces errors by tens of mHa in LiH and by more than 100 mHa in H$_2$O. Despite a partial spin-coupling truncation in the compact H$_2$O encoding, the resulting energy curve deviates from FCI by only a few mHa over the tested range. Compared with a conventional qubit-based UCCSD approach, the qutrit scheme requires half as many quantum units and reduces the scaling of the parameterized ansatz generator count from $O(M^4)$ to $O(M^2)$, where $M$ is the number of spatial orbitals. This work elucidates how a physically motivated qutrit encoding can reduce quantum-resource requirements while retaining controlled electronic-structure accuracy, thereby providing a concrete starting point for broader qudit-native quantum algorithm design.
Two-dimensional quantum gas microscopy provides an unparalleled tool to study quantum many-body systems using ultracold atoms. For the SU(2) Fermi Hubbard model (FHM), access to spin-resolved projective measurements has been vital for quantifying correlation functions and mapping out the phase diagram. Recent progress in quantum gas microscopy for experiments with ultracold alkaline-earth atoms, which are well described by the SU(N) FHM and are predicted to host exotic ground-state phases, calls for the development of theory-free numerical techniques to extract physical information from their projective measurements. To that end, we evaluate the multiscale structural complexity of snapshots of an SU(3) FHM in the square lattice at $1/3$-filling. We employ mean-field theory to generate spin-resolved density distributions and compute their structural complexity using rectangular coarse-graining windows. We demonstrate that these complexities are linked to relevant physical observables such as the entanglement entropy, and are extremely sensitive for locating phase boundaries. The results presented here validate the structural complexity as an efficient and reliable tool for analyzing the outputs of SU(N) quantum gas microscopes, offering a theory-free property, immediately accessible to experiments.
