arXiv subjects

Elisa Ercolessi

Publications and source records attributed to Elisa Ercolessi.

At least 19 recordsLinked to original sources

arXiv2026

Benchmarking dynamical-structure-factor protocols in programmable neutral-atom geometries

The dynamical structure factor is a central observable in condensed-matter physics, providing direct insight into the excitation spectrum and dynamical response of quantum materials. While it is traditionally accessed in real materials through inelastic neutron scattering, recent works have shown that analogous information can be extracted in quantum simulators using suitable dynamical protocols. So far, these approaches have been demonstrated mainly in paradigmatic integrable one-dimensional models. In this work, we use numerical emulations of a neutral-atom quantum processing unit to assess the feasibility of measuring the dynamical structure factor in a broader class of Ising-like spin systems. Beyond the standard one-dimensional transverse-field Ising chain, we benchmark the protocol in chains with dimerized interactions and in the two-dimensional transverse-field Ising model, where spectral properties are difficult to access with classical numerical methods at large scales. We further analyze the robustness of the protocol under realistic experimental conditions, including finite simulation times, pulse modulation, positional disorder, and laser noise. Our results show that neutral-atom quantum simulators can provide a practical route to probing dynamical response functions in regimes where classical simulations become increasingly demanding, paving the way toward experimental implementation.

quant-ph↗

arXiv2026

Practical Use Cases of Neutral Atoms Quantum Computers

Quantum computing has quickly emerged as a revolutionary paradigm that holds the potential for greatly enhanced computational capability and algorithmic efficiency, in a wide range of areas. Among the various hardware platforms, neutral atom quantum processors based on Rydberg interactions are gaining increasing interest because of their scalability, qubit-connection flexibility, and intrinsic appropriateness for solving combinatorial optimization challenges. This paper provides an overview of the present capabilities, standards, and applications of neutral atom quantum computers. We first discuss recent hardware advancements and register mapping optimization techniques that enhance circuit fidelity and performance. We next review their uses as quantum simulators, in both classical and quantum hard problems, such as MIS and QUBO problems, quantum many-body models and molecules in chemistry and pharmacology. Applications for enhancing machine learning are also covered.

quant-ph↗

arXiv2025

Analog QAOA with Bayesian Optimisation on a neutral atom QPU

This study explores the implementation of the Quantum Approximate Optimisation Algorithm (QAOA) in its analog form using a neutral atom quantum processing unit to solve the Maximum Independent Set problem. The analog QAOA leverages the natural encoding of problem Hamiltonians by Rydberg atom interactions, while employing Bayesian Optimisation to navigate the quantum-classical parameter space effectively under the constraints of hardware noise and resource limitations. We evaluate the approach through a combination of simulations and experimental runs on Pasqal's first commercial quantum processing unit, Orion Alpha, demonstrating effective parameter optimisation and noise mitigation strategies, such as selective bitstring discarding and detection error corrections. Results show that a limited number of measurements still allows for a quick convergence to a solution, making it a viable solution for resource-efficient scenarios.

quant-ph↗

arXiv2025

Quantum Natural Gradient optimizer on noisy platforms: QAOA as a case study

We investigate the performance of the Quantum Natural Gradient (QNG) optimizer in the presence of noise. Specifically, we evaluate the efficacy of QNG within the Quantum Approximate Optimization Algorithm (QAOA) for finding the ground state of the Transverse Field Ising Model (TFIM). Its performance is benchmarked against the Vanilla Gradient Descent optimizer across two prominent quantum computing platforms: Rydberg atoms and superconducting circuits. Our analysis includes simulations under both idealized noise-free conditions and realistic noisy environments based on calibration data from actual devices. Results demonstrate that QNG consistently outperforms Vanilla Gradient Descent, exhibiting faster convergence on average and greater robustness against random initializations of parameters. This robustness is attributed to the distance regularization in parameter space inherent to QNG. Additionally, QNG achieves a higher convergence rate to the solution, effectively avoiding certain local minima. These findings highlight QNG as a promising tool for optimizing variational quantum algorithms in noisy intermediate-scale quantum (NISQ) devices.

quant-ph↗

arXiv2025

A digital Rydberg simulation of dynamical quantum phase transitions in the Schwinger model

We present the simulation of the quench dynamics of the Z3 Schwinger model, that describes an approximation of one-dimensional Quantum Electrodynamics, on a digital noisy Rydberg atom platform, aiming at the observation of multiple dynamical quantum phase transitions. In order to reach long-time dynamics, we exploit an enconding dictated by the symmetries, combined with a circuit compression procedure. We focus on a quench that evolves the Dirac vacuum by means of a Hamiltonian depending on a negative mass parameter. This leads to resonant Rabi oscillations between the Dirac vacuum and mesonic states. The population concentration exhibits oscillations with negligible fluctuations of detuned states also with the inclusion of combined noise sources, from which we can clearly detect multiple dynamical phase transitions.

quant-ph↗

arXiv2025

Electromagnetism: an intrinsic approach to Hadamard's method of descent

We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge star operator, we implement descent conditions on differential forms that reduce Maxwell's equations in four-dimensional spacetime to electromagnetic theories in lower dimensions. We also consider multiple descent along pairwise commuting vector fields of invariance, yielding a finer decomposition of Maxwell's equations. Our results provide a unified and geometrically transparent interpretation of dimensional reduction, with potential applications to field theories in lower-dimensional spacetimes.

math-ph↗

arXiv2025

Approximate inverse measurement channel for shallow shadows

Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the randomization step is performed via unitary circuits of variable depth $t$, defining the so-called shallow shadows. For sufficiently large $t$, this approach allows one to get around the use of non-local unitaries to probe global properties such as the fidelity with respect to a target state or the purity. Still, shallow shadows involve the inversion of a many-body map, the measurement channel, which requires non-trivial computations in the post-processing step, thus limiting its applicability when the number of qubits $N$ is large. In this work, we put forward a simple approximate post-processing scheme where the infinite-depth inverse channel is applied to the finite-depth classical shadows and study its performance for fidelity and purity estimation. The scheme allows for different circuit connectivity, as we illustrate for geometrically local circuits in one and two spatial dimensions and geometrically non-local circuits made of two-qubit gates. For the fidelity, we find that the resulting estimator coincides with a known linear cross-entropy, achieving an arbitrary small approximation error $δ$ at depth $t=O(\log (N/δ))$ (independent of the circuit connectivity). For the purity, we show that the estimator becomes accurate at a depth $O(N)$. In addition, at those depths, the variances of both the fidelity and purity estimators display the same scaling with $N$ as in the case of global random unitaries. We establish these bounds by analytic arguments and extensive numerical computations in several cases of interest. Our work extends the applicability of shallow shadows to large system sizes and general circuit connectivity.

quant-ph↗

arXiv2025

Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model

Quantum computing gives direct access to the study of real-time dynamics of quantum many-body systems. In principle, it is possible to directly calculate non-equal-time correlation functions, from which one can detect interesting phenomena, such as the presence of quantum scars or dynamical quantum phase transitions. In practice, these calculations are strongly affected by noise, due to the complexity of the required quantum circuits. As a testbed for the evaluation of real-time evolution of observables and correlations, the dynamics of the Zn Schwinger model in a one dimensional lattice is considered. To control the computational cost, we adopt a quantum-classical strategy that reduces the dimensionality of the system by restricting the dynamics to the Dirac vacuum sector and optimizes the embedding into a qubit model by minimizing the number of three-qubit gates. We derive a digital circuit implementation of the time-evolution of particle-density correlation operators and their correlation, comparing results from exact evolution, bare noisy simulations and simulations with different error mitigation techniques. For the evolution of the particle-density operators we also perform runs on a physical IBM quantum device.

quant-ph↗

arXiv2024

3-phases Confusion Learning

The use of Neural Networks in quantum many-body theory has seen a formidable rise in recent years. Among the many possible applications, one surely is to make use of their pattern recognition power when dealing with the study of equilibrium phase diagram. Within this context, Learning by Confusion has emerged as an interesting, unbiased scheme. The idea behind it briefly consists in iteratively label numerical results in a random way and then train and test a Neural Network; while for a generic random labeling the Network displays low accuracy, the latter shall display a peak when data are divided into a correct, yet unknown way. Here, we propose a generalization of this confusion scheme for systems with more than two phases, for which it was originally proposed. Our construction simply relies on the use of a slightly different Neural Network: from a binary classificator we move to a ternary one, more suitable to detect systems exhibiting three phases. After introducing this construction, we test is onto the free and the interacting Kitaev chain and on the one-dimensional Extended Hubbard model, always finding results compatible with previous works. Our work opens the way to wider use of Learning by Confusion, showing once more the usefulness of Machine Learning to address quantum many-body problems.

cond-mat.str-el↗

arXiv2024

Women for Quantum -- Manifesto of Values

Data show that the presence of women in quantum science is affected by a number of detriments and their percentage decreases even further for higher positions. Beyond data, from our shared personal experiences as female tenured quantum physics professors, we believe that the current model of scientific leadership, funding, and authority fails to represent many of us. It is time for a real change that calls for a different kind of force and for the participation of everyone. Women for quantum calls for a joint effort and aims with this initiative to contribute to such a transformation.

physics.soc-ph↗

arXiv2024

Quantum Circuit for Imputation of Missing Data

The imputation of missing data is a common procedure in data analysis that consists in predicting missing values of incomplete data points. In this work we analyse a variational quantum circuit for the imputation of missing data. We construct variational quantum circuits with gates complexity $O(N)$ and $O(N^2)$ that return the last missing bit of a binary string for a specific distribution. We train and test the performance of the algorithms on a series of datasets finding good convergence of the results. Finally, we test the circuit for generalization to unseen data. For simple systems, we are able to describe the circuit analytically, making possible to skip the tedious and unresolved problem of training the circuit with repetitive measurements. We find beforehand the optimal values of the parameters and we make use of them to construct an optimal circuit suited to the generation of truly random data.

quant-ph↗

arXiv2024

Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models

We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model, implying that the different sectors of the gauge theory can show quite different phase diagrams. In order to investigate this and see if confined phases might emerge, we perform a numerical analysis for $N = 2, 3, 4$, using exact diagonalization and DMRG.

hep-lat↗

arXiv2023

Quantum Fisher Information and multipartite entanglement in spin-1 chains

In this paper, we study the ground state Quantum Fisher Information (QFI) in one-dimensional spin-1 models, as witness to Multipartite Entanglement. The models addressed are the Bilinear-Biquadratic model, the most general isotropic SU(2)-invariant spin-1 chain, and the XXZ spin-1 chain, both with nearest-neighbor interactions and open boundary conditions. We show that the scaling of the QFI of strictly non-local observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. Analysing its behavior at the critical phases we are also able to recover the scaling dimensions of the order parameters both for local and string observables. The numerical results have been obtained by exploiting the Density Matrix Renormalization Group algorithm and Tensor Network techniques.

quant-ph↗

arXiv2023

Hybrid classical-quantum branch-and-bound algorithm for solving integer linear problems

Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. All the results are actual runs on the quantum annealer D-Wave Advantage.

quant-ph↗

arXiv2023

Bayesian Optimization for QAOA

The Quantum Approximate Optimization Algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of a quantum circuit. In this work we present a Bayesian optimization procedure to fulfil this optimization task, and we investigate its performance in comparison with other global optimizers. We show that our approach allows for a significant reduction in the number of calls to the quantum circuit, which is typically the most expensive part of the QAOA. We demonstrate that our method works well also in the regime of slow circuit repetition rates, and that few measurements of the quantum ansatz would already suffice to achieve a good estimate of the energy. In addition, we study the performance of our method in the presence of noise at gate level, and we find that for low circuit depths it is robust against noise. Our results suggest that the method proposed here is a promising framework to leverage the hybrid nature of QAOA on the noisy intermediate-scale quantum devices.

quant-ph↗

arXiv2023

Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model with a high degree of accuracy. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

cond-mat.supr-con↗

arXiv2023

Entanglement Classification via Witness Operators generated by Support Vector Machine

Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few special cases of higher dimensional systems. In this work, we use a machine learning algorithm, the support vector machine with polynomial kernel, to classify separable and entangled states. We apply it to two-qubit and three-qubit systems, and we show that, after training, the support vector machine is able to recognize if a random state is entangled with an accuracy up to 92% for the two-qubit system and up to 98% for the three-qubit system. We also describe why and in what regime the support vector machine algorithm is able to implement the evaluation of an entanglement witness operator applied to many copies of the state, and we describe how we can translate this procedure into a quantum circuit.

quant-ph↗

arXiv2022

Dimensional reduction of the Dirac equation in arbitrary spatial dimensions

We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which consists in conceiving low-dimensional theories as a specialization of high-dimensional ones that are uniform along the additional space coordinate. We show that the Dirac equation reduces to either a single Dirac equation or two decoupled Dirac equations, depending on whether the higher-dimensional manifold has even or odd spatial dimensions, respectively. Furthermore, we construct and discuss an explicit hierarchy of representations in which this procedure becomes manifest and can easily be iterated.

quant-ph↗