arXiv subjects

Dario Poletti

Publications and source records attributed to Dario Poletti.

At least 19 recordsLinked to original sources

arXiv2026

Long-time Dynamics of Many-body Open Quantum Systems using Quantum Generating Functions

The interplay between coherent unitary evolution and environment-induced dissipation can give rise to a wide range of non-equilibrium dynamics in open quantum systems, ranging from interesting transport phenomena to dynamical phase transitions. However, accessing such long-time dynamics remains challenging for the existing methods developed for the simulation of many-body open quantum systems. We address this problem by developing a quantum generating function (QGF) formalism for open many-body systems for both ensemble-averaged dynamics governed by a Markovian quantum master equation and trajectory-resolved dynamics described by the quantum trajectory formalism, including quantum jumps, and quantum state diffusion. Our approach computes the dynamics of higher-order moments and fluctuation statistics without explicitly evolving the quantum state, thereby providing an efficient and scalable approach for investigating many-body open quantum systems. We demonstrate the versatility of the formalism by applying it to both the integrable open XXZ chain and the nonintegrable open next-nearest-neighbor XXZ spin chain, where it uncovers distinct initial state dependent long-time transport regimes. Our work establishes quantum generating functions as an efficient and scalable framework for investigating long-time dynamics in open quantum many-body systems.

cond-mat.stat-mech↗

arXiv2026

SMT-AD: a scalable quantum-inspired anomaly detection approach

Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD from Superposition of Multiresolution Tensors for Anomaly Detection. It is based upon the superposition of bond-dimension-1 matrix product operators to transform the input data with Fourier-assisted feature embedding, where the number of learnable parameters grows linearly with feature size, embedding resolutions, and the number of additional components in the matrix product operators structure. We demonstrate successful anomaly detection when applied to standard datasets, including credit card transactions, and find that, even with minimal configurations, it achieves competitive performance against established anomaly detection baselines. Furthermore, it provides a straightforward way to reduce the weight of the model and even improve the performance by highlighting the most relevant input features.

cs.LG↗

arXiv2026

Dependence of Lindbladian spectral statistics on the integrability of no-jump Hamiltonians and the recycling terms

Spectral statistics probe integrability versus chaos and have recently been extended to Markovian open quantum systems described by Lindbladians, whose quantum-trajectory unraveling decomposes the evolution into no-jump dynamics generated by an effective non-Hermitian Hamiltonian and recycling jumps. In this work, we perform spectrum-statistics diagnostics for Lindbladians and their effective non-Hermitian Hamiltonians. We show that recycling processes, symmetry constraints, and the Liouville-space structure crucially shape the spectral correlations. In particular, we identify a family of spectrally separable Lindbladians whose spectra exhibit robust Poisson statistics, despite the effective non-Hermitian Hamiltonian varying from Poisson to Ginibre statistics. Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians, deepening our understanding of spectral properties in open many-body systems.

quant-ph↗

arXiv2026

Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform

Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor networks naturally accommodate non-unitary maps. This flexibility lets us design quantum-inspired methods that start from a quantum algorithmic structure, yet go beyond unitarity to achieve speedups. Here we introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform (in contrast to the Fourier transform). We encode a length-$N$ signal on two paired $n$-qubit registers and decompose the overall map into a non-unitary exponential Damping Transform followed by a Quantum Fourier Transform, both compressed in a single matrix-product operator. This decomposition admits strong MPO compression to low bond dimension resulting in significant acceleration. We demonstrate simulations up to $N=2^{30}$ input data points, with up to $2^{60}$ output data points, and quantify how bond dimension controls runtime and accuracy, including precise and efficient pole identification.

quant-ph↗

arXiv2025

Concentrated Monte Carlo sampling for local observables in quantum spin chains

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the concentrated Monte Carlo sampling approach, which builds on the idea that in systems with only short range correlations, to obtain accurate expectation values for local observables, one would favor detailed information in the surroundings of this observable compared to far away from it. In this approach we consider all possible configurations in the surroundings of a local observable, and unique samples from the remaining of the setup drawn using Markov chain Monte Carlo. We have tested the performance of this approach for ground states of the spin-1/2 tilted Ising model in different phases, and also for thermal states in the a spin-1 bilinear-biquadratic model. Our results demonstrate that CMCS yields higher accuracy for local observables in short-range correlated states while requiring substantially fewer samples, showcasing in which regimes one can obtain acceleration for the evaluation of expectation values.

quant-ph↗

arXiv2025

Entanglement transition in unitary system-bath dynamics

The evolution of a system coupled to baths is commonly described by a master equation that, in the long-time limit, yields a steady-state density matrix. However, when the same evolution is unraveled into quantum trajectories, it is possible to observe a transition in the scaling of entanglement within the system as the system-bath coupling increases - a phenomenon that is invisible in the trajectory-averaged reduced density matrix of the system. Here, we go beyond the paradigm of trajectories from master equations and explore whether a qualitatively analogous entanglement-scaling transition emerges in a single unitary evolution of the combined system-bath setup, without monitoring the dynamics of the system. We investigate the scaling of entanglement in a unitary quantum setup composed of a two-dimensional lattice of free fermions, where each site is coupled to a fermionic bath. As the system-bath coupling increases, the logarithmic fermionic negativity reveals an entanglement transition from logarithmic-law to area-law scaling. This occurs while the system's steady-state properties are trivial, highlighting that the signatures of these different scalings are within the bath-bath correlations. Evidence of the transition is also found in the mutual information and the correlations of the full system-bath setup, suggesting that the entanglement transition is underpinned by a change in the spatial structure of quantum information.

quant-ph↗

arXiv2025

Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems

Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two aspects: the limitation in expressive power and the approximate extraction of information. Here we investigate the performance of superposition-of-product-states (SPS) ansatz, a variational framework structurally related to canonical polyadic tensor decomposition. The ansatz does not compress information as effectively as tensor networks, but it has the advantages (i) of allowing accurate extraction of information, (ii) of being structurally independent of the geometry of the system, (iii) of being readily parallelizable, and (iv) of allowing analytical shortcuts. We first study the typical properties of the SPS ansatz for spin-$1/2$ systems, including its entanglement entropy, and its trainability. We then use this ansatz for ground state search in tilted Ising models -- including one-dimensional and three-dimensional with short- and long-range interaction, and a random network -- demonstrating that SPS can attain high accuracy.

quant-ph↗

arXiv2025

Quantum dynamics in lattices in presence of bulk dephasing and a localized source

The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with nearest-neighbor and beyond, i.e., long-ranged (power-law) hopping, and (ii) a lattice that is interacting via short-range interactions modeled by a fermionic quartic Hamiltonian. We study the evolution of the local density profile $n_i(t)$ within the system and the growth of the total particle number $N(t)$ in it. For case (i), we provide analytical insights into the dynamics of the nearest-neighbor model using an adiabatic approximation, which relies on assuming faster relaxation of coherences of the single particle density matrix. For case (ii), we perform numerical computations using the time-evolving block decimation (TEBD) algorithm and analyze the density profile and the growth exponent in $N(t)$. Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems, such as local source and bulk dephasing. It brings out rich dynamics, including universal dynamical scaling and anomalous behavior across various time scales and is of relevance to various quantum simulation platforms.

quant-ph↗

arXiv2025

Ergodicity and hydrodynamics: from quantum to classical spin systems

We show that in classical spin systems the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium thermodynamic properties of the corresponding observable. We provide numerical results for one- and two-dimensional systems and present theoretical considerations that only rely on the notion of ergodicity. Our result extends to the classical framework the relaxation-overlap inequality, first introduced in Capizzi et al. Phys. Rev. X 15, 011059 (2025)] for quantum many-body systems satisfying the eigenstate thermalization hypothesis.

cond-mat.stat-mech↗

arXiv2025

Continuous-time parametrization of neural quantum states for quantum dynamics

Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time steps to approximate the wave function at each point in time. Given the differentiability of the wave function stemming from the Schr\"odinger equation, here we impose a time-continuous and differentiable parameterization of the neural network by expressing its parameters as linear combinations of temporal basis functions with trainable, time-independent coefficients. We test this ansatz, referred to as the smooth neural quantum state (\textit{s}-NQS) with a loss function defined over an extended time interval, under a sudden quench of a non-integrable many-body quantum spin chain. We demonstrate accurate time evolution using a restricted Boltzmann machine as the instantaneous neural network architecture. We show that the parameterization enables accurate simulations with fewer variational parameters, independent of time-step resolution. Furthermore, the smooth neural quantum state also allows us to initialize and evaluate the wave function at times not included in the training set, both within and beyond the training interval.

quant-ph↗

arXiv2025

Emergence of thermodynamic functioning regimes from finite coupling between a quantum thermal machine and a load

Autonomous quantum thermal machines are particularly suited to understand how correlations between thermal baths, a load, and a thermal machine affect the overall thermodynamic functioning of the setup. Here, we show that by tuning the operating temperatures and the magnitude of the coupling between machine and load, the thermal machine can operate in four modes: engine, accelerator, heater, or refrigerator. In particular, we show that as we increase the coupling strength, the engine mode is suppressed, and the refrigerator mode is no longer attainable, leaving the heater as the most pronounced functioning modality, followed by the accelerator. This regime switching can be amplified by quantum effects, such as the bosonic enhancement factor for a harmonic oscillator load, which modifies the effective machine-load coupling, making the thermodynamic functioning sensitive to the initial preparation of the load.

quant-ph↗

arXiv2024

Loop Quantum Photonic Chip for Coherent Multi-Time-Step Evolution

Quantum evolution is crucial for the understanding of complex quantum systems. However, current implementations of time evolution on quantum photonic platforms are limited by both low photon generation efficiency and high propagation loss, making photon detection difficult. Furthermore, the single-layer complexity of most implementations cannot support multi-step quantum simulations. In this work, we present a loop quantum photonic chip (Loop-QPC) designed to efficiently simulate quantum dynamics over multiple time steps in a single chip. Our approach employs a recirculating loop structure to reuse computational resources and eliminate the need for multiple quantum tomography steps or chip reconfigurations. A cycle-or-measure circuit at the input and output stages allows dynamic routing of photons between evolution and measurement, enabling efficient control over the simulation loop and minimizing loss. We experimentally demonstrate the dynamics of the spin-boson model on a low-loss Silicon Nitride integrated photonic chip. The Loop-QPC achieves a three-step unitary evolution closely matching the theoretical predictions. These results establish the Loop-QPC as a promising method for efficient and scalable quantum simulation, advancing the development of quantum simulation on programmable photonic circuits.

quant-ph↗

arXiv2024

Emergence of steady quantum transport in a superconducting processor

Non-equilibrium quantum transport is crucial to technological advances ranging from nanoelectronics to thermal management. In essence, it deals with the coherent transfer of energy and (quasi-)particles through quantum channels between thermodynamic baths. A complete understanding of quantum transport thus requires the ability to simulate and probe macroscopic and microscopic physics on equal footing. Using a superconducting quantum processor, we demonstrate the emergence of non-equilibrium steady quantum transport by emulating the baths with qubit ladders and realising steady particle currents between the baths. We experimentally show that the currents are independent of the microscopic details of bath initialisation, and their temporal fluctuations decrease rapidly with the size of the baths, emulating those predicted by thermodynamic baths. The above characteristics are experimental evidence of pure-state statistical mechanics and prethermalisation in non-equilibrium many-body quantum systems. Furthermore, by utilising precise controls and measurements with single-site resolution, we demonstrate the capability to tune steady currents by manipulating the macroscopic properties of the baths, including filling and spectral properties. Our investigation paves the way for a new generation of experimental exploration of non-equilibrium quantum transport in strongly correlated quantum matter.

quant-ph↗

arXiv2024

Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in time complexity, but has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation cost scales economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering applications, such as the sub-diffusion equation, the non-linear Burgers' equation and a coupled diffusive epidemic model. We assess quantum hardware performance under realistic noise conditions, further validating the practical utility of our algorithm.

quant-ph↗

arXiv2024

Paths towards time evolution with larger neural-network quantum states

In recent years, the neural-network quantum states method has been investigated to study the ground state and the time evolution of many-body quantum systems. Here we expand on the investigation and consider a quantum quench from the paramagnetic to the anti-ferromagnetic phase in the tilted Ising model. We use two types of neural networks, a restricted Boltzmann machine and a feed-forward neural network. We show that for both types of networks, the projected time-dependent variational Monte Carlo (p-tVMC) method performs better than the non-projected approach. We further demonstrate that one can use K-FAC or minSR in conjunction with p-tVMC to reduce the computational complexity of the stochastic reconfiguration approach, thus allowing the use of these techniques for neural networks with more parameters.

quant-ph↗

arXiv2024

Hydrodynamics and the eigenstate thermalization hypothesis

The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the off-diagonal part of ETH at small energy differences, and (ii) the smooth profile of the diagonal part of ETH as a function of the energy density. We establish this connection from the decay of the autocorrelation functions of local operators, which is constrained by the presence of local conserved quantities whose evolution is described by hydrodynamics. We corroborate our predictions with numerical simulations of two non-integrable spin-1 Ising models, one diffusive and one super-diffusive, which we perform using dynamical quantum typicality up to 18 spins.

quant-ph↗

arXiv2024

Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics

Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle problems in the classical domain. In this work, we focus on matrix product operators, a prominent numerical technique to study many-body quantum systems, especially in one dimension. It has been previously shown that such a tool can be used for classification, learning of deterministic sequence-to-sequence processes and of generic quantum processes. We further develop a matrix product operator algorithm to learn probabilistic sequence-to-sequence processes and apply this algorithm to probabilistic cellular automata. This new approach can accurately learn probabilistic cellular automata processes in different conditions, even when the process is a probabilistic mixture of different chaotic rules. In addition, we find that the ability to learn these dynamics is a function of the bit-wise difference between the rules and whether one is much more likely than the other.

cond-mat.stat-mech↗

arXiv2023

Randomised benchmarking for characterizing and forecasting correlated processes

The development of fault-tolerant quantum processors relies on the ability to control noise. A particularly insidious form of noise is temporally correlated or non-Markovian noise. By combining randomized benchmarking with supervised machine learning algorithms, we develop a method to learn the details of temporally correlated noise. In particular, we can learn the time-independent evolution operator of system plus bath and this leads to (i) the ability to characterize the degree of non-Markovianity of the dynamics and (ii) the ability to predict the dynamics of the system even beyond the times we have used to train our model. We exemplify this by implementing our method on a superconducting quantum processor. Our experimental results show a drastic change between the Markovian and non-Markovian regimes for the learning accuracies.

quant-ph↗