arXiv subjects

Javier Robledo Moreno

Publications and source records attributed to Javier Robledo Moreno.

At least 19 recordsLinked to original sources

arXiv2026

Polynomial-time exact diagonalization via sparse guided eigenwalks

Computing quantum ground states is generically difficult, but additional structure can sometimes allow diagonalization to be recast as a more feasible problem. For example, when the desired ground state is sparse in a given basis, diagonalization can be facilitated via graph search. We make this reformulation precise by introducing the eigenwalk problem, which seeks the support of a sparse eigenvector of a Hermitian matrix by exploring the graph induced by its nonzero entries. However, it is not obvious whether the relevant support vertices must always be efficiently reachable by a search on the graph. To resolve this question, we prove that for every sparse eigenvector, there exists a (possibly different) sparse eigenvector with the same eigenvalue whose support is tightly localized in the graph, with diameter scaling only linearly in the sparsity and independently of the total number of vertices. As a consequence, if a $2^n$-dimensional, ${\rm poly}(n)$-sparse Hamiltonian has an $\mathcal{O}(1)$-sparse extremal eigenvector and one support element is known, then an exact eigenvector with the same eigenvalue can be computed classically in ${\rm poly}(n)$ time. The same conclusion follows when the $\mathcal{O}(1)$-sparse eigenvector is non-extremal, provided that it is sparser than every eigenvector with a different eigenvalue. These results hold with no assumptions on the degeneracy, locality, spectral width, or spectral gap of the Hamiltonian, and the underlying support-localization principle also extends to problems beyond exact diagonalization, such as sparse principal component analysis.

quant-ph↗

arXiv2026

ffsim: Faster simulation of fermionic quantum circuits

We present ffsim, an open-source software library for fast simulation of fermionic quantum circuits. ffsim exploits conservation of particle number and the z component of spin, symmetries present in a wide range of fermionic systems, to dramatically reduce memory usage and simulation time compared to general-purpose quantum circuit simulators. Compared to FQE, a library with similar functionality, ffsim differs in software design and is faster on a representative set of simulation benchmarks. Beyond state vector evolution by basic fermionic gates, ffsim offers a number of additional features including variational ansatzes, Hamiltonian time evolution via Trotter-Suzuki product formulas, efficient sampling of Slater determinants, seamless integration with Qiskit and PySCF, and comprehensive documentation. We demonstrate ffsim's capabilities on scientific applications involving quantum circuits of up to 64 qubits.

quant-ph↗

arXiv2026

Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes

We develop a workflow decomposing a molecule into fragments via quantum embedding and simulating them with a heterogeneous quantum-classical (HQC) method. We sample fragment electronic configurations on two 156-qubit quantum processors (ibm$\_$cleveland, ibm$\_$kobe), using up to 94 qubits, running 21,006 circuits for over 239 hours, collecting $3.0 \cdot 10^9$ measurement outcomes -- the most resource-intensive HQC computation for quantum chemistry to date. We compute fragment wavefunctions via optimized subspace diagonalization on supercomputers Fugaku, Miyabi-G, and ROQUO, achieving 72.5$\%$ parallel efficiency with scalable distributed linear algebra kernels. We simulate two protein-ligand complexes spanning dispersion- and electrostatics-dominated regimes (11,608, 12,635 atoms), demonstrate $>40\times$ increase in system size and up to $210\times$ improvement in accuracy over previous state-of-the-art, with HQC matching coupled-cluster (CCSD) accuracy in fragment energies. We present the first HQC protein-ligand binding prediction using a mixed-basis set and an automated end-to-end workflow enabling practical HQC calculations of large protein systems.

quant-ph↗

arXiv2026

Observation of Improved Accuracy over Classical Sparse Ground-State Solvers using a Quantum Computer

Demonstrating quantum advantage over classical algorithms for ground state energy problems is an outstanding open problem in quantum computation. We experimentally demonstrate that a quantum algorithm can outperform classical selected configuration interaction (SCI) methods, a key family of techniques used in computational chemistry and condensed matter physics. We construct a class of local Hamiltonian problems with sparse ground states, and show that SCI fails to find the ground state of a 49-qubit instance. We then show that sample-based Krylov quantum diagonalization, run on an IBM Heron R3 processor, succeeds at the same task. While the problem is solvable classically using iterative solvers designed to target our Hamiltonian construction, this work resolves the question of whether a sample-based quantum diagonalization algorithm can outperform standard SCI heuristics.

quant-ph↗

arXiv2026

Shallow-circuit Supervised Learning on a Quantum Processor

Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.

quant-ph↗

arXiv2025

Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization

Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase estimation, is out of reach of current quantum processors due to its high circuit-depths. Subspace-based quantum diagonalization methods offer a viable alternative for pre- and early-fault-tolerant quantum computers. Here, we introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces: a classical diagonalization based on quantum samples, and subspaces constructed with quantum Krylov states. We prove that our algorithm converges in polynomial time under the working assumptions of Krylov quantum diagonalization and sparseness of the ground state. We then demonstrate the scalability of our approach by performing the largest ground-state quantum simulation of impurity models using a Heron quantum processors and the Frontier supercomputer. We consider both the single-impurity Anderson model with 41 bath sites, and a system with 4 impurities and 7 bath sites per impurity. Our results are in excellent agreement with Density Matrix Renormalization Group calculations.

quant-ph↗

arXiv2025

Quantum-centric simulation of hydrogen abstraction by sample-based quantum diagonalization and entanglement forging

The simulation of electronic systems is an anticipated application for quantum-centric computers, i.e. heterogeneous architectures where classical and quantum processing units operate in concert. An important application is the computation of radical chain reactions, including those responsible for the photodegradation of composite materials used in aerospace engineering. Here, we compute the activation energy and reaction energy for hydrogen abstraction from 2,2-diphenyldipropane, used as a minimal model for a step in a radical chain reaction. Calculations are performed using a superconducting quantum processor of the IBM Heron family and classical computing resources. To this end, we combine a qubit-reduction technique called entanglement forging (EF) with sample-based quantum diagonalization (SQD), a method that projects the Schr\"{o}dinger equation into a subspace of configurations sampled from a quantum device. In conventional quantum simulations, a qubit represents a spin-orbital. In contrast, EF maps a qubit to a spatial orbital, reducing the required number of qubits by half. We provide a complete derivation and a detailed description of the combined EF and SQD approach, and we assess its accuracy across active spaces of varying sizes upto (39e,39o).

quant-ph↗

arXiv2024

Towards quantum-centric simulations of extended molecules: sample-based quantum diagonalization enhanced with density matrix embedding theory

Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly suited to these computational platforms: they combine high-level calculations on active regions of a molecule with low-level calculations on the surrounding environment, thereby avoiding expensive high-level full-molecule calculations and allowing to distribute computational cost across multiple and heterogeneous computing units. Here, we present the first density matrix embedding theory (DMET) simulations performed in combination with the sample-based quantum diagonalization (SQD) method. We employ the DMET-SQD formalism to compute the ground-state energy of a ring of 18 hydrogen atoms, and the relative energies of the chair, half-chair, twist-boat, and boat conformers of cyclohexane. The full-molecule 41- and 89-qubit simulations are decomposed into 27- and 32-qubit active-region simulations, that we carry out on the ibm_cleveland device, obtaining results in agreement with reference classical methods. Our DMET-SQD calculations mark a tangible progress in the size of active regions that can be accurately tackled by near-term quantum computers, and are an early demonstration of the potential for quantum-centric simulations to accurately treat the electronic structure of large molecules, with the ultimate goal of tackling systems such as peptides and proteins.

quant-ph↗

arXiv2024

Accurate quantum-centric simulations of supramolecular interactions

We present the first quantum-centric simulations of noncovalent interactions using a supramolecular approach. We simulate the potential energy surfaces (PES) of the water and methane dimers, featuring hydrophilic and hydrophobic interactions, respectively, with a sample-based quantum diagonalization (SQD) approach. Our simulations on quantum processors, using 27- and 36-qubit circuits, are in remarkable agreement with classical methods, deviating from complete active space configuration interaction (CASCI) and coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) within 1 kcal/mol in the equilibrium regions of the PES. Finally, we test the capacity limits of the quantum methods for capturing hydrophobic interactions with an experiment on 54 qubits. These results mark significant progress in the application of quantum computing to chemical problems, paving the way for more accurate modeling of noncovalent interactions in complex systems critical to the biological, chemical and pharmaceutical sciences.

quant-ph↗

arXiv2024

Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization

The simulation of molecular electronic structure is an important application of quantum devices. Recently, it has been shown that quantum devices can be effectively combined with classical supercomputing centers in the context of the sample-based quantum diagonalization (SQD) algorithm. This allowed the largest electronic structure quantum simulation to date (77 qubits) and opened near-term devices to practical use cases in chemistry toward the hundred-qubit mark. However, the description of many important physical and chemical properties of those systems, such as photo-absorption/-emission, requires a treatment that goes beyond the ground state alone. In this work, we extend the SQD algorithm to determine low-lying molecular excited states. The extended-SQD method improves over the original SQD method in accuracy, at the cost of an additional computational step. It also improves over quantum subspace expansion based on single and double electronic excitations, a widespread approach to excited states on pre-fault-tolerant quantum devices, in both accuracy and efficiency. We employ the extended SQD method to compute the first singlet (S$_1$) and triplet (T$_1$) excited states of the nitrogen molecule with a correlation-consistent basis set, and the ground- and excited-state properties of the [2Fe-2S] cluster.

quant-ph↗

arXiv2024

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2024

Neural-network quantum states for many-body physics

Variational quantum calculations have borrowed many tools and algorithms from the machine learning community in the recent years. Leveraging great expressive power and efficient gradient-based optimization, researchers have shown that trial states inspired by deep learning problems can accurately model many-body correlated phenomena in spin, fermionic and qubit systems. In this review, we derive the central equations of different flavors variational Monte Carlo (VMC) approaches, including ground state search, time evolution and overlap optimization, and discuss data-driven tasks like quantum state tomography. An emphasis is put on the geometry of the variational manifold as well as bottlenecks in practical implementations. An overview of recent results of first-principles ground-state and real-time calculations is provided.

cond-mat.dis-nn↗

arXiv2024

Extracting Off-Diagonal Order from Diagonal Basis Measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments.

cond-mat.str-el↗

arXiv2023

Mott Transition and Volume Law Entanglement with Neural Quantum States

The interplay between delocalisation and repulsive interactions can cause electronic systems to undergo a Mott transition between a metal and an insulator. Here we use neural network hidden fermion determinantal states (HFDS) to uncover this transition in the disordered, fully-connected Hubbard model. Whilst dynamical mean-field theory (DMFT) provides exact solutions to physical observables of the model in the thermodynamic limit, our method allows us to directly access the wave function for finite system sizes well beyond the reach of exact diagonalisation. We demonstrate how HFDS are able to obtain more accurate results in the metallic regime and in the vicinity of the transition than calculations based on a Matrix Product State (MPS) ansatz, for which the volume law of entanglement exhibited by the system is prohibitive. We use the HFDS method to calculate the energy and double occupancy, the quasi-particle weight and the energy gap and, importantly, the amplitudes of the wave function which provide a novel insight into this model. Our work paves the way for the study of strongly correlated electron systems with neural quantum states.

cond-mat.str-el↗

arXiv2023

Enhancing the Expressivity of Variational Neural, and Hardware-Efficient Quantum States Through Orbital Rotations

Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant under the reparametrization of the Hamiltonian by single-particle basis transformations. As a consequence, the representability of the ground-state wave function by the variational ansatz strongly dependents on the choice of the single-particle basis. In this manuscript we study the joint optimization of the single-particle basis, together with the variational state in the VMC (with neural quantum states) and VQE (with hardware-efficient circuits) approaches. We show that the joint optimization of the single-particle basis with the variational state parameters yields significant improvements in the expressive power and optimization landscape in a variety of chemistry and condensed matter systems. We also realize the first active-space calculation using neural quantum states, where the single-particle basis transformations are applied to all of the orbitals in the basis set.

quant-ph↗

arXiv2022

Fermionic Wave Functions from Neural-Network Constrained Hidden States

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden" additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint which is optimized, together with the single-particle orbitals, using a neural network parametrization. This construction draws inspiration from the success of hidden particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proven to be universal. We apply this construction to the ground state properties of the Hubbard model on the square lattice, achieving levels of accuracy which are competitive with state-of-the-art variational methods.

cond-mat.str-el↗

arXiv2021

Machine learning band gaps from the electron density

A remarkable consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of an injective map between the electronic density and any observable of the many electron problem in an external potential. In this work, we study the problem of predicting a particular observable, the band gap of semiconductors and band insulators, from the knowledge of the local electronic density. Using state-of-the-art machine learning techniques, we predict the experimental band gaps from computationally inexpensive density functional theory calculations. We propose a modified Behler-Parrinello (BP) architecture that greatly improves the model capacity while maintaining the symmetry properties of the BP architecture. Using this scheme, we obtain band gaps at a level of accuracy comparable to those obtained with state of the art and computationally intensive hybrid functionals, thus significantly reducing the computational cost of the task.

cond-mat.dis-nn↗

arXiv2020

Deep learning the Hohenberg-Kohn maps of Density Functional Theory

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions, in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.

cond-mat.dis-nn↗