arXiv subjects

Giuseppe E. Santoro

Publications and source records attributed to Giuseppe E. Santoro.

At least 19 recordsLinked to original sources

arXiv2026

Parity Mapping for Quantum Optimization on Frustrated Ising Rings

The frustrated Ising ring is one of the simplest models exhibiting exponential closing spectral gaps, making it a paradigmatic and challenging benchmark for quantum annealing (QA). Ground-state preparation for this model has therefore been studied extensively in both continuous-time QA and digitized protocols such as the Quantum Approximate Optimization Algorithm (QAOA). Here, we use the frustrated Ising ring to investigate how the parity mapping affects the performance of both QA and QAOA. For QA, finite-size calculations show that the parity mapping increases the minimum spectral gap under the energy normalization used in this work, thereby enabling faster continuous-time ground state preparation protocols. An ideal implementation of Parity-QA, with a single global constraint, shows no evidence of exponential gap closing over the accessible system sizes, whereas a hardware-motivated decomposition into local constraints restores the exponential decrease, albeit with a smaller fitted exponent than conventional QA. For the digitized protocol, we find that the number of Parity-QAOA layers required to prepare the exact ground state remains constant over the simulated sizes, improving upon the quadratic scaling required by conventional QAOA. To investigate the role of constraints in Parity-QAOA, we further consider a modified Ising ring instance in which the constraint term is essential for preparing the target ground state. We then compare the corresponding resource requirements with those of conventional QAOA.

quant-ph↗

arXiv2026

Digital techniques for the frustrated Ising ring: the role of counter-diabatic terms

We investigate the role of local counter-diabatic (CD) terms in enhancing the performance of discrete-time digital protocols for a frustrated Ising ring, a system with an exponentially small spectral gap that acts as a bottleneck for conventional quantum annealing. The techniques investigated range from a digitised version of a fixed-schedule protocol, including lowest-order analytical CD terms, all the way to a full-fledged Quantum Approximate Optimisation Algorithm (QAOA), including variational CD terms (DC-QAOA). By analyzing the resulting residual energy, we show that DC-QAOA combined with Chopped RAndom Basis (CRAB) quantum control techniques for optimizing the circuit parameters, can outperform all the other strategies. By monitoring the ground-state population during the dynamics we learn that DC-QAOA finds effective shortcuts towards the target state through intermediate excited states, a process that is unexpectedly enhanced by the inclusion of local CD unitaries. Our results highlight the importance of flexible variational control of CD dynamics and demonstrate that digital optimization can explore operator dynamics that remain inaccessible to standard analytical CD constructions.

quant-ph↗

arXiv2025

Phononic frictional losses of a particle crossing a crystal: linear-response theory

We address weak-coupling frictional sliding with phononic dissipation by means of analytic many-body techniques. Our model consists of a particle (the "slider") moving through a two- or three-dimensional crystal and interacting weakly with its atoms, and therefore exciting phonons. By means of linear-response theory we obtain explicit expressions for the friction force slowing down the slider as a function of its speed, and compare them to the friction obtained by simulations, demonstrating a remarkable accord.

cond-mat.mes-hall↗

arXiv2025

Dynamics of edge modes in monitored Su-Schrieffer-Heeger Models

We investigate the effect of dissipation on the dynamics of edge modes in the monitored Su-Schrieffer-Heeger (SSH) model. Our study considers both a linear observable and a nonlinear entanglement measure, namely the two-point correlation function and the Disconnected Entanglement Entropy (DEE), as diagnostic tools. While dissipation inevitably alters the entanglement properties observed in the closed system, statistical analysis of quantum trajectories reveals that by protecting the chain's edges from dissipation, it is possible to recover characteristic features analogous to those found in the unitary limit. This highlights the fundamental role of spatial dissipation patterns in shaping the dynamics of edge modes in monitored systems.

quant-ph↗

arXiv2025

From Exponential to Quadratic: Optimal Control for a Frustrated Ising Ring Model

Exponentially small spectral gaps are known to be the crucial bottleneck for traditional Quantum Annealing (QA) based on interpolating between two Hamiltonians, a simple driving term and the complex problem to be solved, with a linear schedule in time. One of the simplest models showing exponentially small spectral gaps was introduced by Roberts et al., PRA 101, 042317 (2020): a ferromagnetic Ising ring with a single frustrating antiferromagnetic bond. A previous study of this model (Côté et al., QST 8, 045033 (2023)) proposed a continuous-time diabatic QA, where optimized non-adiabatic annealing schedules provided good solutions, avoiding exponentially large annealing times. In our work, we move to a digital framework of Variational Quantum Algorithms, and present two main results: 1) we show that the model is digitally controllable with a scaling of resources that grows quadratically with the system size, achieving the exact solution using the Quantum Approximate Optimization Algorithm (QAOA); 2) We combine a technique of quantum control -- the Chopped RAndom Basis (CRAB) method -- and digitized quantum annealing (dQA) to construct smooth digital schedules yielding optimal solutions with very high accuracy.

quant-ph↗

arXiv2025

Striped twisted state in the orientational epitaxy on quasicrystals

The optimal "twisted" geometry of a crystalline layer on a crystal is long known, but that on a quasicrystal is still unknown and open. We predict analytically that the layer equilibrium configuration will generally exhibit a nonzero misfit angle. The theory perfectly agrees with numerical optimization of a colloid monolayer on a quasiperiodic decagonal optical lattice. Strikingly different from crystal-on-crystal epitaxy, the structure of the novel emerging twisted state exhibits an unexpected stripe pattern. Its high anisotropy should reflect on the tribomechanical properties of this unconventional interface.

cond-mat.mes-hall↗

arXiv2024

The quantum Ising chain for beginners

We present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. In particular, we analyse the form of the ground state and excitations of the model, relating them to the symmetry-breaking physics, and illustrate aspects connected to calculating dynamical quantities, thermal averages, correlation functions and entanglement entropy. A few problems provide simple applications of the techniques.

quant-ph↗

arXiv2024

Parent Hamiltonian Reconstruction via Inverse Quantum Annealing

Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|ψ\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a numerical method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the states $|ψ(λ(t))\rangle$, starting from a simple state $|ψ_0\rangle$ with a known $\hat{\mathcal{H}}_0$, generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. The method, implemented through a projection onto a set of local operators, only requires the knowledge of local expectation values, and, for long annealing times, leads to an approximate parent Hamiltonian whose degree of locality depends on the correlations built up by the states $|ψ(λ)\rangle$. We illustrate the method on two paradigmatic models: the Kitaev fermionic chain and a quantum Ising chain in longitudinal and transverse fields.

quant-ph↗

arXiv2023

Quantum Effects on the Synchronization Dynamics of the Kuramoto Model

The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external baths following the Caldeira-Leggett approach. Studying the mean-field model in the overdamped limit using Feynman-Vernon theory, we show how quantum mechanics modifies the phase diagram. Specifically, we demonstrate that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We examine the phase transition into the synchronized phase at various temperatures, revealing that classical results are recovered at high temperatures while a quantum phase transition occurs at zero temperature. Additionally, we derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters, and examine the differences between classical and quantum behavior.

quant-ph↗

arXiv2023

A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas

We show that a two-body Jastrow wave function is able to capture the ground-state properties of the $S=1$ antiferromagnetic Heisenberg chain with the single-ion anisotropy term, in both the topological and trivial phases. Here, the optimized Jastrow pseudo potential assumes a very simple form in Fourier space, i.e., $v_{q} \approx 1/q^2$, which is able to give rise to a finite string-order parameter in the topological regime. The results are analysed by using an exact mapping from the quantum expectation values over the variational state to the classical partition function of the one-dimensional Coulomb gas of particles with charge $q=\pm 1$. Here, two phases are present at low temperatures: the first one is a diluted gas of dipoles (bound states of particles with opposite charges), which are randomly oriented (describing the trivial phase); the other one is a dense liquid of dipoles, which are aligned thanks to the residual dipole-dipole interactions (describing the topological phase, with the finite string order being related to the dipole alignment). Our results provide an insightful interpretation of the ground-state nature of the spin-1 antiferromagnetic Heisenberg model.

cond-mat.str-el↗

arXiv2023

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

quant-ph↗

arXiv2022

Clean two-dimensional Floquet time-crystal

We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. Employing careful scaling analysis, we show the feasibility of a two-dimensional discrete time-crystal (DTC) pre-thermal phase. Despite an unbounded energy pumped into the system, in the high-frequency limit, a well-defined effective Hamiltonian controls a finite-temperature intermediate regime, wherein local time averages are described by thermal averages. As a consequence, the long-lived stability of the DTC relies on the existence of a long-range ordeblack phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.

cond-mat.stat-mech↗

arXiv2022

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.

quant-ph↗

arXiv2022

Kondo nanomechanical dissipation in the driven Anderson impurity model

The cyclic sudden switching of a magnetic impurity from Kondo to a non-Kondo state and back was recently shown to involve an important dissipation of the order of several $k_BT_K$ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by e.g., ultrasensitive Atomic Force Microscope (AFM) tools currently represents an unusual and interesting form of spectroscopy. Here we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and slow switching, respectively. By applying a recently established matrix-product-state based time-dependent variational algorithm to the magnetic field-induced Kondo switching in an Anderson model of the magnetic impurity, we find that dissipation requires switching within the Kondo time scale $\hbar(k_B T_K)^{-1}$ or faster. While such a fast switching seems problematic for current AFM setups, the challenge is open for future means to detect this dissipation by time-dependent magnetic fields, electrostatic impurity level shift, or hybridization switching.

cond-mat.str-el↗

arXiv2021

Quantum Approximate Optimization Algorithm applied to the binary perceptron

We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At variance with the usual QAOA applications to MaxCut, or to quantum spin-chains ground state preparation, the classical Hamiltonian is characterized by highly non-local multi-spin interactions. Yet, we provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem, and we prove numerically an enhanced performance of QAOA over traditional QA. We also investigate on the role of the QAOA optimization landscape geometry in this problem, showing that the detrimental effect of a gap-closing transition encountered in QA is also negatively affecting the performance of our implementation of QAOA.

quant-ph↗

arXiv2021

Quenching the Anderson impurity model at finite temperature: Entanglement and bath dynamics using matrix product states

We study the dynamics of the quenched Anderson model at finite temperature using matrix product states. Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearest-neighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes -- possible when simulating the full dynamics of impurity plus bath -- we find clear signatures of the Kondo effect in the quench dynamics.

cond-mat.str-el↗

arXiv2020

Efficient mapping for Anderson impurity problems with matrix product states

We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while keeping the short-range nature of the couplings. Our approach naturally extends to finite temperatures, with applications to dynamical mean field theory, non-equilibrium dynamics and quantum transport.

cond-mat.str-el↗

arXiv2020

Polynomial scaling of QAOA for ground-state preparation of the fully-connected p-spin ferromagnet

We show that the quantum approximate optimization algorithm (QAOA) can construct with polynomially scaling resources the ground state of the fully-connected p-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a Quantum Annealing (QA) approach, due to the exponentially small gaps encountered at first-order phase transition for ${\rm p} \ge 3$. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve a good performance of the algorithm when the number of variational parameters $2{\rm P}$ is much smaller than the system size ${\rm N}$, because of the large number of sub-optimal local minima. Instead, when ${\rm P}$ exceeds a critical value ${\rm P}^*_{\rm N} \propto {\rm N}$, the structure of the parameter space simplifies, as all minima become degenerate. This allows to achieve the ground state with perfect fidelity with a number of parameters scaling extensively with ${\rm N}$, and with resources scaling polynomially with ${\rm N}$.

quant-ph↗