arXiv subjects

Juan Carrasquilla

Publications and source records attributed to Juan Carrasquilla.

At least 19 recordsLinked to original sources

arXiv2026

Multipole splats for optimized and inverted effective potentials

In modern density functional theory, effective Hamiltonians are constructed to reproduce densities and forces of electrons at equilibrium. However, their nonlocal potentials leave systematic errors in spectral properties and real-time dynamics. Access to local optimized or inverted effective potentials would remove this limitation, but the numerical fragility in finite orbital bases has long prevented their wide adoption. Here, we introduce multipole splats, a class of trial potentials that carry the correct asymptotic decay required to support the unoccupied spectrum. By connecting the computation of effective potentials to variational and supervised variants of Hamiltonian learning, we recast both problems as stable nonlinear optimization formulated directly in standard orbital basis sets and applicable to any hybrid functional approximation. The resulting solver allows us to resolve spatial profiles of exchange-correlation potential errors during molecular dissociation and accurately reconstruct key excited states without empirical asymptotic corrections. We also show the deviation from the ionization potential theorem for different exchange-correlation approximations on a dataset of molecular systems. Multipole splats extract insights from established approximations and provide capacity for robust dataset generation for downstream processing and learning.

physics.chem-ph↗

arXiv2026

Adiabatic transport of neural network quantum states

Variational methods have offered controllable and powerful tools for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has enabled the accurate representation of a broad class of complex wavefunctions for many Hamiltonians of interest. We introduce a first-principles method for building neural network representations of many-body excited states by adiabatically continuing eigenstates of simple Hamiltonians into the strongly correlated regime. With controlled access to the full many-body gap, we obtain accurate estimates of critical exponents. Successive eigenstate estimates can be run entirely in parallel, enabling precise targeting of excited-state properties without reference to the rest of the spectrum, opening the door to large-scale numerical investigations of universal properties of entire phases of matter.

quant-ph↗

arXiv2026

Distributions of Noisy Expectation Values over Sets of Measurement Operators

Expectation values of measurement operators, interpreted as measurement probabilities, arise frequently throughout quantum algorithms. When quantum states are randomly distributed, their expectation values are also randomly distributed. In this work, with the goal of understanding non-unitary dynamics, we generalize previous derivations for distributions of expectation values [Campos et al., Phys. Lett. A 377, 1854 (2013)] to the case of sets of measurement operators and random mixed quantum states within variable sized environments. Using combinatorics approaches, we derive expressions for their moments. We proceed to construct empirical distributions of simulated Haar random brickwork quantum circuits with local depolarizing noise, and compare their form to a proposed effective global-depolarizing-like model with variable effective noise scales and environment dimensions. The fitted effective distributions reproduce peak behaviour across circuit depths, noise scales, and system sizes, while deviations in the distribution tails arise from local noise effects. The fit effective model parameters are also shown to vary smoothly and consistently with circuit depth and noise scale. Finally, sets of non-symmetric measurement operators are shown to exhibit distinct multi-modal distributions relative to uni-modal distributions for symmetric measurement operators, opening up questions about their simulability.

quant-ph↗

arXiv2026

Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems

The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum technology. Here we introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme that preserves Trotter accuracy and aims at maintaining computational efficiency. The framework is exact for quadratic Hamiltonians -- remaining restricted to a fixed low-weight sector determined by the physical observable -- admits variational initial states, and can be extended to interacting regimes via systematically controlled truncations. We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches, comparing against tensor network methods (MPS and fPEPS) and recent experimental data. The method achieves high accuracy on timescales comparable to state-of-the-art variational techniques and experiments, demonstrating that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.

cond-mat.quant-gas↗

arXiv2026

Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States

Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning.

quant-ph↗

arXiv2026

Neural network quantum states in the grand canonical ensemble

Variational Monte Carlo calculations have recently reached state-of-the-art accuracy in the approximation of ground state properties of quantum many-body systems. Making use of flexible neural quantum states and automatic differentiation has bypassed traditional computational obstacles such as reliance on basis sets. In this paper, we propose a neural quantum state architecture capable of representing symmetric bosonic wavefunctions in Fock space, enabling the study of systems with variable particle number. By supplementing our variational state with Monte Carlo sampling and geometric optimization, we demonstrate competitive variational energies across an array of one- and two-dimensional systems, converging to the physical boson number under a set chemical potential. Our approach enables accurate estimates of one-body reduced density matrices, opening access to observables such as condensate fractions and radial density profiles from first principles. Our method opens the door to numerical predictions of key measurable quantities in practical grand canonical systems.

quant-ph↗

arXiv2026

CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers

Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50 problems covering condensed matter theory (CMT) at the level of an expert researcher. Topics span analytical and computational approaches in quantum many-body, and classical statistical mechanics. The dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine problems they would want a research assistant to solve, including Hartree-Fock, exact diagonalization, quantum/variational Monte Carlo, density matrix renormalization group (DMRG), quantum/classical statistical mechanics, and model building. We evaluate LLMs by programmatically checking solutions against expert-supplied ground truth. We developed machine-grading, including symbolic handling of non-commuting operators via normal ordering. They generalize across tasks too. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. The best model, GPT5, solves 30\% of the problems; average across 17 models (GPT, Gemini, Claude, DeepSeek, Llama) is 11.4\pm2.1\%. Moreover, 18 problems are solved by none of the 17 models, and 26 by at most one. These unsolved problems span Quantum Monte Carlo, Variational Monte Carlo, and DMRG. Answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe this benchmark will guide development toward capable AI research assistants and tutors.

cs.LG↗

arXiv2026

Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling

Carrier transport in quantum networks is governed by a variety of factors, including network dimensionality and connectivity, on-site energies, couplings between sites and whether they are short- or long-range, leakage processes, and environmental effects. In this work, we identify classes of quasi-one-dimensional chains with energy profiles that optimize carrier transport under such influences. Specifically, we optimize on-site energies using Optax's optimistic gradient descent and AdaMax algorithms, enabled by the JAX automatic differentiation framework. Focusing on nonequilibrium steady-state transport, we study the system's behavior under combined unitary and nonunitary (dephasing and dissipative) effects using the Lindblad quantum master equation. After validating our optimization scheme on short chains, we extend the study to larger systems where we identify systematic patterns in energy profiles. Our analysis reveals that different types of energy landscapes enhance transport, depending on whether inter-site tunneling couplings in the chain are short- or long-range, the existence of environmental interactions, and the temperature of the environment. Our classification and insights of optimal energy landscapes offer guidance for designing efficient transport systems for electronic, photovoltaic and quantum communication applications.

quant-ph↗

arXiv2026

Entanglement and optimization within autoregressive neural quantum states

Neural quantum states (NQSs) are powerful variational ansätze capable of representing highly entangled quantum many-body wavefunctions. While the average entanglement properties of ensembles of restricted Boltzmann machines are well understood, the entanglement structure of autoregressive NQSs such as recurrent neural networks and transformers remains largely unexplored. We perform large-scale simulations of ensembles of random autoregressive wavefunctions for chains of up to $256$ spins and uncover signatures of transitions in their average entanglement scaling, entanglement spectra, and correlation functions. We show that the standard softmax normalization of the wavefunction suppresses entanglement and fluctuations, and introduce a square modulus normalization function that restores them. Finally, we connect the insights gained from our entanglement and activation function analysis to initialization strategies for finding the ground states of strongly correlated Hamiltonians via variational Monte Carlo.

quant-ph↗

arXiv2026

Connectivity determines the capability of sparse neural network quantum states

The Lottery Ticket Hypothesis (LTH) posits that within overparametrized neural networks, there exist sparse subnetworks that are capable of matching the performance of the original model when trained in isolation from the original initialization. We extend this hypothesis to the unsupervised task of approximating the ground state of quantum many-body Hamiltonians, a problem equivalent to finding a neural-network compression of the lowest-lying eigenvector of an exponentially large matrix. Focusing on two representative quantum Hamiltonians, the transverse field Ising model (TFIM) and the toric code (TC), we demonstrate that sparse neural networks can reach accuracies comparable to their dense counterparts, even when pruned by more than an order of magnitude in parameter count. Crucially, and unlike the original LTH, we find that performance depends only on the structure of the sparse subnetwork, not on the specific initialization, when trained in isolation. Moreover, we identify universal scaling behavior that persists across network sizes and physical models, where the boundaries of scaling regions are determined by the underlying Hamiltonian. At the onset of high-error scaling, we observe signatures of a sparsity-induced quantum phase transition that is first-order in shallow networks. Finally, we demonstrate that pruning enhances interpretability by linking the structure of sparse subnetworks to the underlying physics of the Hamiltonian.

quant-ph↗

arXiv2025

Fermionic neural Gibbs states

We introduce fermionic neural Gibbs states (fNGS), a variational framework for modeling finite-temperature properties of strongly interacting fermions. fNGS starts from a reference mean-field thermofield-double state and uses neural-network transformations together with imaginary-time evolution to systematically build strong correlations. Applied to the doped Fermi-Hubbard model, a minimal lattice model capturing essential features of strong electronic correlations, fNGS accurately reproduces thermal energies over a broad range of temperatures, interaction strengths, even at large dopings, for system sizes beyond the reach of exact methods. These results demonstrate a scalable route to studying finite-temperature properties of strongly correlated fermionic systems beyond one dimension with neural-network representations of quantum states.

quant-ph↗

arXiv2025

Circuit compression for 2D quantum dynamics

The study of out-of-equilibrium quantum many-body dynamics remains one of the most exciting research frontiers of physics, standing at the crossroads of our understanding of complex quantum phenomena and the realization of quantum advantage. Quantum algorithms for the dynamics of quantum systems typically require deep quantum circuits whose accuracy is compromised by noise and imperfections in near-term hardware. Thus, reducing the depth of such quantum circuits to shallower ones while retaining high accuracy is critical for quantum simulation. Variational quantum compilation methods offer a promising path forward, yet a core difficulty persists: ensuring that a variational ansatz $V$ faithfully approximates a target unitary $U$. Here we leverage Pauli propagation techniques to develop a strategy for compressing circuits that implement the dynamics of large two-dimensional (2D) quantum systems and beyond. As a concrete demonstration, we compress the dynamics of systems up to $30 \times 30$ qubits and achieve accuracies that surpass standard Trotterization methods by orders of magnitude at identical circuit depths. To experimentally validate our approach, we execute the compiled ansatz on Quantinuum's H1 quantum processor and observe that it tracks the system's dynamics with significantly higher fidelity than Trotterized circuits without optimization. Our circuit compression scheme brings us one step closer to a practical quantum advantage by allowing longer simulation times at reduced quantum resources and unlocks the exploration of large families of hardware-friendly ansätze.

quant-ph↗

arXiv2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

quant-ph↗

arXiv2025

Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the square lattice

Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign structure. While many state-of-the-art variational energies have been reached with these methods for finite-size systems, little work has been done to use these results to extract information about the target state in the thermodynamic limit. In this work, we employ recurrent neural networks (RNNs) as a variational ansätze, and leverage their recurrent nature to simulate the ground states of progressively larger systems through iterative retraining. This transfer learning technique allows us to simulate spin-$\frac{1}{2}$ systems on lattices with more than 1,000 spins without beginning optimization from scratch for each system size, thus reducing the demands for computational resources. In this study, we focus on the square-lattice antiferromagnetic Heisenberg model, where it is possible to carefully benchmark our results. We show that we are able to systematically improve the accuracy of the results from our simulations by increasing the training time, and obtain results for finite-sized lattices that are in good agreement with the literature values. Furthermore, we use these results to extract accurate estimates of the ground-state properties in the thermodynamic limit. This work demonstrates that RNN wavefunctions are able to extract accurate information about quantum many-body systems in the thermodynamic limit.

cond-mat.str-el↗

arXiv2025

Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the triangular lattice

Variational Monte Carlo simulations have been crucial for understanding quantum many-body systems, especially when the Hamiltonian is frustrated and the ground-state wavefunction has a non-trivial sign structure. In this paper, we use recurrent neural network (RNN) wavefunction ansätze to study the triangular-lattice antiferromagnetic Heisenberg model (TLAHM) for lattice sizes up to $30\times30$. In a recent study [M. S. Moss et al. arXiv:2502.17144], the authors demonstrated how RNN wavefunctions can be iteratively retrained in order to obtain variational results for multiple lattice sizes with a reasonable amount of compute. That study, which looked at the sign-free, square-lattice antiferromagnetic Heisenberg model, showed favorable scaling properties, allowing accurate finite-size extrapolations to the thermodynamic limit. In contrast, our present results illustrate in detail the relative difficulty in simulating the sign-problematic TLAHM. We find that the accuracy of our simulations can be significantly improved by transforming the Hamiltonian with a judicious choice of basis rotation. We also show that a similar benefit can be achieved by using variational neural annealing, an alternative optimization technique that minimizes a pseudo free energy. Ultimately, we are able to obtain estimates of the ground-state properties of the TLAHM in the thermodynamic limit that are in close agreement with values in the literature, showing that RNN wavefunctions provide a powerful toolbox for performing finite-size scaling studies for frustrated quantum many-body systems.

cond-mat.str-el↗

arXiv2025

The statistical mechanics and machine learning of the $α$-Rényi ensemble

We study the statistical physics of the classical Ising model in the so-called $α$-Rényi ensemble, a finite-temperature thermal state approximation that minimizes a modified free energy based on the $α$-Rényi entropy. We begin by characterizing its critical behavior in mean-field theory in different regimes of the Rényi index $α$. Next, we re-introduce correlations and consider the model in one and two dimensions, presenting analytical arguments for the former and devising a Monte Carlo approach to the study of the latter. Remarkably, we find that while mean-field predicts a continuous phase transition below a threshold index value of $α\sim 1.303$ and a first-order transition above it, the Monte Carlo results in two dimensions point to a continuous transition at all $α$. We conclude by performing a variational minimization of the $α$-Rényi free energy using a recurrent neural network (RNN) ansatz where we find that the RNN performs well in two dimensions when compared to the Monte Carlo simulations. Our work highlights the potential opportunities and limitations associated with the use of the $α$-Rényi ensemble formalism in probing the thermodynamic equilibrium properties of classical and quantum systems.

cond-mat.stat-mech↗

arXiv2025

Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D

We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of $SU(2)$ equivariant neural networks alongside an $SU(2)$ invariant, physics-inspired ansatz, we learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to $SU(N)$. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

hep-lat↗

arXiv2025

Biorthogonal Neural Network Approach to Two-Dimensional Non-Hermitian Systems

Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena, including non-Hermitian skin effects and exceptional points, that remain largely inaccessible to existing numerical techniques. In this work, we investigate the application of variational Monte Carlo and neural network wavefunction representations to examine their ground-state (the eigenstate with the smallest real part energy) properties. Due to the breakdown of the Rayleigh-Ritz variational principle in non-Hermitian settings, we develop a self-consistent symmetric optimization framework based on variance minimization with a dynamically updated energy estimate. Our approach respects the biorthogonal structure of left and right eigenstates, and is further strengthened by exploiting system symmetries and pseudo-Hermiticity. Tested on a two-dimensional non-Hermitian transverse field Ising model endowed with a complex longitudinal field, our method achieves high accuracy across both parity-time symmetric and broken phases. Moreover, we propose novel optimization routines that address the challenges posed by exceptional points and provide reliable convergence to the ground state in regimes where standard variational techniques fail. Lastly, we show, through extensive numerical evidence, that our method offers a scalable and flexible computational tool to investigate non-Hermitian quantum many-body systems, beyond the reach of conventional numerical techniques such as the density-matrix renormalization group algorithm.

quant-ph↗