arXiv subjects

Giuseppe Carleo

Publications and source records attributed to Giuseppe Carleo.

At least 55 records · Page 3Linked to original sources

arXiv2024

Predicting Topological Entanglement Entropy in a Rydberg analog simulator

Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also numerically. This work proposes a variational approach based on a time-dependent correlated Ansatz, focusing on the dynamical preparation of a quantum-spin-liquid state on a Rydberg-atom simulator. Within this framework, we are able to faithfully represent the state of the system throughout the entire dynamical preparation protocol. The flexibility of our approach does not only allow one to match the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology. This is unlike previous numerical studies which were constrained to simplified versions of the problem through the modification of both the Hamiltonian and the lattice. Our approach further gives access to global quantities such as the topological entanglement entropy ($γ$), providing insight into the topological properties of the system. This is achieved by the introduction of the time-dependent variational Monte Carlo (t-VMC) technique to the dynamics of topologically ordered phases. Upon employing a Jastrow variational Ansatz with a scalable number of parameters, we are able to efficiently extend our simulations to system sizes matching state-of-the-art experiments and beyond. Our results corroborate experimental observations, confirming the presence of topological order during the dynamical state-preparation protocol, and additionally deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits (global) topological order and local properties resembling those of a resonating-valence-bond (RVB) state, it lacks the latter's characteristic topological entanglement entropy signature $γ= \ln(2)$, irrespective of the degree of adiabaticity of the protocol.

quant-ph↗

arXiv2024

Sparse Autoregressive Neural Networks for Classical Spin Systems

Efficient sampling and approximation of Boltzmann distributions involving large sets of binary variables, or spins, are pivotal in diverse scientific fields even beyond physics. Recent advances in generative neural networks have significantly impacted this domain. However, these neural networks are often treated as black boxes, with architectures primarily influenced by data-driven problems in computational science. Addressing this gap, we introduce a novel autoregressive neural network architecture named TwoBo, specifically designed for sparse two-body interacting spin systems. We directly incorporate the Boltzmann distribution into its architecture and parameters, resulting in enhanced convergence speed, superior free energy accuracy, and reduced trainable parameters. We perform numerical experiments on disordered, frustrated systems with more than 1000 spins on grids and random graphs, and demonstrate its advantages compared to previous autoregressive and recurrent architectures. Our findings validate a physically informed approach and suggest potential extensions to multivalued variables and many-body interaction systems, paving the way for broader applications in scientific research.

cond-mat.stat-mech↗

arXiv2024

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↗

arXiv2024

Real-time quantum dynamics of thermal states with neural thermofields

Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal density matrices, 1D systems, and/or zero-temperature states. In this work, we propose a method to study the real-time dynamics of thermal states in two dimensions, based on thermofield dynamics, variational Monte Carlo, and neural-network quantum states. To this aim, we introduce two novel tools: (i) a procedure to accurately simulate the cooling down of arbitrary quantum variational states from infinite temperature, and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO) Ansatz that allows for direct sampling from the density matrix using thermofield basis rotations. We apply our technique to the transverse-field Ising model subject to an additional longitudinal field and demonstrate that the time-dependent observables, including correlation operators, can be accurately reproduced for a 4x4 spin lattice. We provide predictions of the real-time dynamics on a 6x6 lattice that lies outside the reach of exact simulations.

quant-ph↗

arXiv2024

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↗

arXiv2024

Comment on "Can Neural Quantum States Learn Volume-Law Ground States?"

Passetti et al. [Physical Review Letters 131, 036502 (2023)] recently assessed the potential of neural quantum states (NQS) in learning ground-state wave functions with volume-law entanglement scaling. They focused on NQS using feedforward neural networks, specifically applied to the complex SYK Hamiltonian for fermions. Their numerical results hint at an exponential increase in the required variational parameters as the system size grows, apparently tied to the entanglement growth within the SYK ground state. This challenges the general utility of NQS for highly entangled wavefunctions, contrasting with established analytical and numerical findings. Based on our experiments, we show that suitably chosen NQS can learn ground states with volume-law entanglement both for spin and fermionic problems. We argue that the setup utilized in the aforementioned letter reveals the inefficiency of non-fermionic NQS to learn fermionic states, rather than a general connection between entanglement content and learnability hardness.

quant-ph↗

arXiv2024

Hybrid Ground-State Quantum Algorithms based on Neural Schrödinger Forging

Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis states, or bitstrings, when performing the Schmidt decomposition of the whole system. To overcome this challenge, we propose a new method for entanglement forging employing generative neural networks to identify the most pertinent bitstrings, eliminating the need for the exponential sum. Through empirical demonstrations on systems of increasing complexity, we show that the proposed algorithm achieves comparable or superior performance compared to the existing standard implementation of entanglement forging. Moreover, by controlling the amount of required resources, this scheme can be applied to larger, as well as non permutation invariant systems, where the latter constraint is associated with the Heisenberg forging procedure. We substantiate our findings through numerical simulations conducted on spins models exhibiting one-dimensional ring, two-dimensional triangular lattice topologies, and nuclear shell model configurations.

quant-ph↗

arXiv2024

Overhead-constrained circuit knitting for variational quantum dynamics

Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their practical application remains hindered by limited scale and pervasive noise. In this work, we propose an approach that addresses these challenges by employing circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. The evolution of the system is governed by the projected variational quantum dynamics (PVQD) algorithm, supplemented with constraints on the parameters of the variational quantum circuit, ensuring that the sampling overhead imposed by the circuit knitting scheme remains controllable. We test our method on quantum spin systems with multiple weakly entangled blocks each consisting of strongly correlated spins, where we are able to accurately simulate the dynamics while keeping the sampling overhead manageable. Further, we show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.

quant-ph↗

arXiv2024

Simulating adiabatic quantum computation with a variational approach

The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a variational approach to substantially alleviate this problem in many situations of interest. Our approach is based on the time-dependent Variational Monte Carlo method, in conjunction with a correlated and time-dependent Jastrow ansatz. We demonstrate that accurate results can be obtained in a variety of problems, ranging from the description of defect generation through a dynamical phase transition in 1D to the complex dynamics of frustrated spin-glass problems both on fully-connected and Chimera graphs.

quant-ph↗

arXiv2023

Message-Passing Neural Quantum States for the Homogeneous Electron Gas

We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. Symmetry constraints, such as continuous translation symmetries, can be readily embedded in the model. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions at different densities and system sizes. With orders of magnitude fewer parameters than state-of-the-art neural-network wave functions, we demonstrate better or comparable ground-state energies. Reducing the parameter complexity allows scaling to $N=128$ electrons, previously inaccessible to neural-network wave functions in continuous space, enabling future work on finite-size extrapolations to the thermodynamic limit. We also show the Ansatz's capability of quantitatively representing different phases of matter.

quant-ph↗

arXiv2023

A rapidly mixing Markov chain from any gapped quantum many-body system

We consider the computational task of sampling a bit string $x$ from a distribution $π(x)=|\langle x|ψ\rangle|^2$, where $ψ$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the inverse spectral gap of $H$ and the mixing time of an associated continuous-time Markov Chain with steady state $π$. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes $\langle y|ψ\rangle/\langle x|ψ\rangle$ are efficiently computable, the spectral gap of $H$ is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain.

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

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 Quantum Time Evolution without the Quantum Geometric Tensor

The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational quantum time evolution is a promising candidate for these tasks, as the required circuit model can be tailored to trade off available device capabilities and approximation accuracy. However, even if the circuits can be reliably executed, variational quantum time evolution algorithms quickly become infeasible for relevant system sizes due to the calculation of the Quantum Geometric Tensor (QGT). In this work, we propose a solution to this scaling problem by leveraging a dual formulation that circumvents the explicit evaluation of the QGT. We demonstrate our algorithm for the time evolution of the Heisenberg Hamiltonian and show that it accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms. As an application of quantum imaginary-time evolution, we calculate a thermodynamic observable, the energy per site, of the Heisenberg model.

quant-ph↗

arXiv2023

Adaptive projected variational quantum dynamics

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number of variational parameters. Instead of fixing a variational ansatz at the beginning of the simulation, the circuit is grown systematically during the time evolution. Moreover, the adaptive step does not require auxiliary qubits and the gate search can be performed in parallel on different quantum devices. We apply the new algorithm, named Adaptive pVQD, to the simulation of driven spin models and fermionic systems, where it shows an advantage when compared to both Trotterized circuits and non-adaptive variational methods. Finally, we use the shallower circuits prepared using the Adaptive pVQD algorithm to obtain more accurate measurements of physical properties of quantum systems on hardware.

quant-ph↗

arXiv2023

Neural-network quantum states for ultra-cold Fermi gases

Ultra-cold Fermi gases display diverse quantum mechanical properties, including the transition from a fermionic superfluid BCS state to a bosonic superfluid BEC state, which can be probed experimentally with high precision. However, the theoretical description of these properties is challenging due to the onset of strong pairing correlations and the non-perturbative nature of the interaction among the constituent particles. This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture to efficiently encode pairing, and other quantum mechanical correlations. Our approach offers substantial improvements over comparable ansätze constructed within the Slater-Jastrow framework and outperforms state-of-the-art diffusion Monte Carlo methods, as indicated by our lower ground-state energies. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions. Moreover, we demonstrate that transfer learning stabilizes and accelerates the training of the neural-network wave function, enabling the exploration of the BCS-BEC crossover region near unitarity. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.

cond-mat.quant-gas↗

arXiv2023

Stochastic Approximation of Variational Quantum Imaginary Time Evolution

The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an exponentially large wave function, quantum computers are emerging as a promising platform for this task. However, variational approaches, suitable for near-term quantum computers, struggle with a prohibitive number of measurements and impractical runtimes for relevant system sizes. Here, we suggest a stochastic approach to variational quantum imaginary-time evolution, which allows a significant reduction in runtimes. Our approach allows trading off invested resources and accuracy, which makes it also suitable for ground state preparation, where simulating the exact dynamics is not required. We demonstrate the efficiency of our algorithm in simulations and show a hardware experiment performing the imaginary-time evolution of the transverse field Ising model on 27 qubits.

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↗