arXiv subjects

Filippo Vicentini

Publications and source records attributed to Filippo Vicentini.

At least 19 recordsLinked to original sources

arXiv2026

Ground-state phases of $S = 1/2$ Heisenberg models on the body-centered cubic lattice

Simulating low-temperature properties of three-dimensional frustrated quantum magnets is challenging due to the sign problem and the system sizes required to mitigate substantial finite-size effects. However, there are many experimental examples of three-dimensional crystals that could host exotic low-temperature states of matter, such as quantum spin liquids. We calculate the ground-state phase diagrams of frustrated quantum spin models on the body-centered cubic lattice using neural quantum states. First, we study the antiferromagnetic $J_1-J_2$ model where we find a direct first-order phase transition between N\'eel and collinear long-range-ordered phases at $(J_2/J_1)_c = 0.705$, consistent with previous studies. Then, in a tetragonally-distorted variant, proposed as a minimal model of NaCa$_2$Cu$_2$(VO$_4$)$_3$, we find no evidence of a quantum paramagnetic ground state, with a first-order phase transition between N\'eel and chain phases at $(J_{2ab}/J_1)_c = 1.0375$. Therefore, the ground state of the tetragonally-distorted model does not reproduce the low-temperature magnetic properties of NaCa$_2$Cu$_2$(VO$_4$)$_3$, and the inclusion of other effects is necessary to rationalize experimental observations.

cond-mat.str-el↗

arXiv2025

Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra

We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it. The resulting quantum samples define an effective subspace of the Hilbert space, onto which the Hamiltonian is projected to enable efficient classical simulation of long-time dynamics. This subspace-based approach achieves high-resolution spectral reconstruction using shallow circuits and few samples. Benchmarks on molecular systems show excellent agreement with exact diagonalization and demonstrate access to dynamical timescales beyond the reach of purely classical methods, highlighting its suitability for near-term and early fault-tolerant quantum hardware.

quant-ph↗

arXiv2025

Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model

Accurate simulations of the Hubbard model are crucial to understanding strongly correlated phenomena, where small energy differences between competing orders demand high numerical precision. In this work, Neural Quantum States are used to probe the strongly coupled and underdoped regime of the square-lattice Hubbard model. We systematically compare the Hidden Fermion Determinant State and the Jastrow-Backflow ansatz, parametrized by a Vision Transformer, finding that in practice, their accuracy is similar. We also test different symmetrization strategies, finding that output averaging yields the lowest energies, though it becomes costly for larger system sizes. On cylindrical systems, we consistently observe filled stripes. On the torus, our calculations display features consistent with a doped Mott insulator, including antiferromagnetic correlations and suppressed density fluctuations. Our results demonstrate both the promise and current challenges of neural quantum states for correlated fermions.

cond-mat.str-el↗

arXiv2025

When Less is More: Approximating the Quantum Geometric Tensor with Block Structures

The natural gradient is central in neural quantum states optimizations but it is limited by the cost of computing and inverting the quantum geometric tensor, the quantum analogue of the Fisher information matrix. We introduce a block-diagonal quantum geometric tensor that partitions the metric by network layers, analogous to block-structured Fisher methods such as K-FAC. This layer-wise approximation preserves essential curvature while removing noisy cross-layer correlations, improving conditioning and scalability. Experiments on Heisenberg and frustrated $J_1$-$J_2$ models show faster convergence, lower energy, and improved stability.

quant-ph↗

arXiv2025

Variational subspace methods and application to improving variational Monte Carlo dynamics

We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend notions such as distance and energy to subspaces, as well as Monte Carlo estimators, recovering the excited states estimation method proposed by Pfau et al. As a practical application, we then introduce Bridge, a method that improves the performance of variational dynamics by extracting linear combinations of variational time-evolved states. We find that Bridge is both computationally inexpensive and capable of significantly mitigating the errors that arise from discretizing the dynamics, and can thus be systematically used as a post-processing tool for variational dynamics.

quant-ph↗

arXiv2025

Looking elsewhere: improving variational Monte Carlo gradients by importance sampling

Neural-network quantum states (NQS) offer a powerful and expressive ansatz for representing quantum many-body wave functions. However, their training via Variational Monte Carlo (VMC) methods remains challenging. It is well known that some scenarios - such as sharply peaked wave functions emerging in quantum chemistry - lead to high-variance gradient estimators hindering the effectiveness of variational optimizations. In this work we investigate a systematic strategy to tackle those sampling issues by means of adaptively tuned importance sampling. Our approach is explicitly designed to (i) target the gradient estimator instead of the loss function, (ii) not introduce additional hyperparameters and (iii) be computationally inexpensive. We benchmarked our approach across the ground-state search of a wide variety of hamiltonians, including frustrated spin systems and ab-initio quantum chemistry. We also show systematic improvements on the infidelity minimization in the context of neural projected quantum dynamics. Overall, our approach can reduce the computational cost of vanilla VMC considerably, up to a factor of 100x when targeting highly peaked quantum chemistry wavefunctions.

quant-ph↗

arXiv2025

Quantum computing and artificial intelligence: status and perspectives

This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.

quant-ph↗

arXiv2025

Design principles of deep translationally-symmetric neural quantum states for frustrated magnets

Deep neural network quantum states have emerged as a leading method for studying the ground states of quantum magnets. Successful architectures exploit translational symmetry, but the root of their effectiveness and differences between architectures remain unclear. Here, we apply the ConvNext architecture, designed to incorporate elements of transformers into convolutional networks, to quantum many-body ground states. We find that it is remarkably similar to the factored vision transformer, which has been employed successfully for several frustrated spin systems, allowing us to relate this architecture to more conventional convolutional networks. Through a series of numerical experiments we design the ConvNext to achieve greatest performance at lowest computational cost, then apply this network to the Shastry-Sutherland and J1-J2 models, obtaining variational energies comparable to the state of the art, providing a blueprint for network design choices of translationally-symmetric architectures to tackle challenging ground-state problems in frustrated magnetism.

cond-mat.str-el↗

arXiv2024

Time-dependent Neural Galerkin Method for Quantum Dynamics

We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time window by minimizing a loss function that enforces the Schr\"odinger's equation. The variational state is parametrized with a Galerkin-inspired ansatz based on a time-dependent linear combination of time-independent Neural Quantum States. This structure is particularly well-suited for exploring long-time dynamics and enables bounding the error with the exact evolution via the global loss function. We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D, uncovering signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, our method is competitive compared to state-of-the-art time-dependent variational approaches, while unlocking previously inaccessible dynamical regimes of strongly interacting quantum systems.

quant-ph↗

arXiv2024

Neural Projected Quantum Dynamics: a systematic study

We investigate the challenge of classical simulation of unitary quantum dynamics with variational Monte Carlo approaches, addressing the instabilities and high computational demands of existing methods. By systematically analyzing the convergence of stochastic infidelity optimizations, examining the variance properties of key stochastic estimators, and evaluating the error scaling of multiple dynamical discretization schemes, we provide a thorough formalization and significant improvements to the projected time-dependent Variational Monte Carlo (p-tVMC) method. We benchmark our approach on a two-dimensional Ising quench, achieving state-of-the-art performance. This work establishes p-tVMC as a powerful framework for simulating the dynamics of large-scale two-dimensional quantum systems, surpassing alternative VMC strategies on the investigated benchmark problems.

quant-ph↗

arXiv2024

Efficiency of neural quantum states in light of the quantum geometric tensor

Neural quantum state (NQS) ans\"atze have shown promise in variational Monte Carlo algorithms by their theoretical capability of representing any quantum state. However, the reason behind the practical improvement in their performance with an increase in the number of parameters is not fully understood. In this work, we systematically study the efficiency of a shallow neural network to represent the ground states in different phases of the spin-1 bilinear-biquadratic chain, as the number of parameters increases. We train our ansatz by a supervised learning procedure, minimizing the infidelity w.r.t. the exact ground state. We observe that the accuracy of our ansatz improves with the network width in most cases, and eventually saturates. We demonstrate that this can be explained by looking at the spectrum of the quantum geometric tensor (QGT), particularly its rank. By introducing an appropriate indicator, we establish that the QGT rank provides a useful diagnostic for the practical representation power of an NQS ansatz.

quant-ph↗

arXiv2023

Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias or exponential sample complexity when the wave function contains some (possibly approximate) zeros, an important case for fermionic systems and quantum information protocols; (ii) show that a different scheme based on the solution of an optimization problem at each time step is free from such problems; (iii) improve the sample complexity of this latter approach by several orders of magnitude with respect to previous proofs of concept. Finally, we apply our advancements to study the high-entanglement phase in a protocol of non-Clifford unitary dynamics with local random measurements in 2D, first benchmarking on small spin lattices and then extending to large systems.

quant-ph↗

arXiv2023

Variational Embeddings for Many Body Quantum Systems

We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire system, and is naturally suited for scenarios where an accurate description is only needed in a smaller subspace. We show how to include quantum devices as high-accuracy solvers on these correlated degrees of freedom, while handling the remaining contributions with a classical device. We demonstrate the effectiveness of the protocol on spin chains and small molecules and provide insights into its accuracy and computational cost.

quant-ph↗

arXiv2023

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel methods. Our scheme is an approximate realization of the power method, where supervised learning is used to learn the next step of the power iteration. We show that the ground state properties of arbitrary gapped quantum hamiltonians can be reached with polynomial resources under the assumption that the supervised learning is efficient. Using kernel ridge regression, we provide numerical evidence that the learning assumption is verified by applying our scheme to find the ground states of several prototypical interacting many-body quantum systems, both in one and two dimensions, showing the flexibility of our approach.

quant-ph↗

arXiv2023

Variational dynamics of open quantum systems in phase space

We present a method to simulate the dynamics of large driven-dissipative many-body open quantum systems using a variational encoding of the Wigner or Husimi-Q quasi-probability distributions. The method relies on Monte-Carlo sampling to maintain a polynomial computational complexity while allowing for several quantities to be estimated efficiently. As a first application, we present a proof of principle investigation into the physics of the driven-dissipative Bose-Hubbard model with weak nonlinearity, providing evidence for the high efficiency of the phase space variational approach.

quant-ph↗

arXiv2023

Empirical Sample Complexity of Neural Network Mixed State Reconstruction

Quantum state reconstruction using Neural Quantum States has been proposed as a viable tool to reduce quantum shot complexity in practical applications, and its advantage over competing techniques has been shown in numerical experiments focusing mainly on the noiseless case. In this work, we numerically investigate the performance of different quantum state reconstruction techniques for mixed states: the finite-temperature Ising model. We show how to systematically reduce the quantum resource requirement of the algorithms by applying variance reduction techniques. Then, we compare the two leading neural quantum state encodings of the state, namely, the Neural Density Operator and the positive operator-valued measurement representation, and illustrate their different performance as the mixedness of the target state varies. We find that certain encodings are more efficient in different regimes of mixedness and point out the need for designing more efficient encodings in terms of both classical and quantum resources.

quant-ph↗

arXiv2023

From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.

quant-ph↗

arXiv2023

Variational dynamics as a ground-state problem on a quantum computer

We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits. We prepare the Feynman-Kitaev Hamiltonian acting on the composed system as a qubit operator and find an approximate ground state using the Variational Quantum Eigensolver. We apply the algorithm to the study of the dynamics of a transverse field Ising chain with an increasing number of spins and time steps, proving a favorable scaling in terms of the number of two qubit gates. Through numerical experiments, we investigate its robustness against noise, showing that the method can be use to evaluate dynamical properties of quantum systems and detect the presence of dynamical quantum phase transitions by measuring Loschmidt echoes.

quant-ph↗