arXiv subjects

Dario De Santis

Publications and source records attributed to Dario De Santis.

14 recordsLinked to original sources

arXiv2026

Temporal information processing on a 4,500-qubit quantum annealer

Quantum machine learning could uncover statistical structure beyond the reach of classical models, but this requires quantum models large and expressive enough to be useful and cheap enough to read out. Most approaches optimize many quantum parameters and are thus limited by expensive training loops. Here we report a quantum machine-learning model implemented on a programmable superconducting quantum annealer that processes temporal data at large scale using up to 4,500 qubits-the largest quantum machine-learning experiment performed to date. Following the quantum reservoir computing paradigm, the untrained native many-body dynamics generated by reverse annealing is directly used to process temporal data. We prove that the interactions produced during annealing are indispensable-a non-interacting reservoir retains no memory of its input. We evaluate our model experimentally on standard memory benchmarks and demonstrate that it can successfully forecast chaotic time series. These results establish quantum annealers as a scalable platform for large-scale quantum machine learning.

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arXiv2026

A resource-efficient quantum-walker Quantum RAM

Efficient and coherent data retrieval and storage are essential for harnessing quantum algorithms' speedup. Such a fundamental task is addressed by a quantum Random Access Memory (qRAM). Despite their promising scaling properties, current qRAM proposals demand excessive resources and rely on operations beyond the capabilities of current hardware requirements, rendering their practical realization inefficient. We introduce a novel architecture that significantly reduces resource requirements while preserving optimal complexity scaling for quantum queries. Moreover, unlike previous proposals, our algorithm design leverages a simple, repeated operational block based exclusively on local unitary operations and short-range interactions between a limited number of quantum walkers traveling over a single binary tree. This novel approach not only simplifies experimental requirements by reducing the complexity of necessary operations but also enhances the architecture's scalability by ensuring a resource-efficient, modular design that maintains optimal quantum query performance.

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arXiv2025

Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping

We investigate tensor network simulations of the two-dimensional Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure minimizes the range of effective interactions in the mapped model. This enables a more compact matrix product state (MPS) representation compared to conventional snake mapping. Through systematic benchmarks, we show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension, with the advantage increasing for larger system sizes and in physically relevant interaction regimes. Our implementation reaches clusters up to $32\times32$ sites with open and periodic boundary conditions, delivering reliable ground-state energies and correlation functions in agreement with established results, but at significantly reduced computational cost. These findings establish space-filling curve mappings, particularly the Hilbert curve, as a powerful tool for extending tensor-network studies of strongly correlated two-dimensional quantum systems beyond the limits accessible with standard approaches.

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arXiv2025

Characterizing (non-)Markovianity through Fisher Information

A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as a natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, both for classical and quantum dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction.

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arXiv2024

Optimized QUBO formulation methods for quantum computing

Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for these QUBO reformulations in order to unlock the possibility to efficiently obtain optimal solutions for a class of optimization problems with NISQ devices. This is achieved by introducing novel tools that allow an efficient use of slack variables, even for problems with non-linear constraints, without the need to approximate the starting problem. We divide our new techniques in two independent parts, called the iterative quadratic polynomial and the master-satellite methods. Hence, we show how to apply our techniques in case of an NP-hard optimization problem inspired by a real-world financial scenario called Max-Profit Balance Settlement. We follow by submitting several instances of this problem to two D-wave quantum annealers, comparing the performances of our novel approach with the standard methods used in these scenarios. Moreover, this study allows to appreciate several performance differences between the D-wave Advantage and Advantage2 quantum annealers.

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arXiv2024

Quantum Fisher Information and its dynamical nature

The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich range of possible quantum Fisher information, only a handful are typically used and studied. This review aims at collecting a number of results scattered in the literature that can be useful to people who begin the study of Fisher information and to those who are already working on it to have a more organic understanding of the topic. Moreover, we complement the review with new results about the relation between Fisher information and physical evolutions. Extending the study done in [1], we prove that all the physically realisable dynamics can be defined solely in terms of their relation with respect to the Fisher information metric. Moreover, other properties as Markovianity, retrodiction or detailed balance can be expressed in the same formalism. These results show a fact that was partially overseen in the literature, namely the inherently dynamical nature of Fisher information.

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arXiv2024

Physicality of evolution and statistical contractivity are equivalent notions of maps

Statistical quantifiers are generically required to contract under physical evolutions, following the intuition that information should be lost under noisy transformations. This principle is very relevant in statistics, and it even allows to derive uniqueness results based on it: by imposing their contractivity under any physical maps, the Chentsov-Petz theorem singles out a unique family of metrics on the space of probability distributions (or density matrices) called the Fisher information metrics. This result might suggest that statistical quantifiers are a derived concept, as their very definition is based on physical maps. The aim of this work is to disprove this belief. Indeed, we present a result dual to the Chentsov-Petz theorem, proving that among all possible linear maps, the only ones that contract the Fisher information are exactly the physical ones. This result shows that, contrary to the common opinion, there is no fundamental hierarchy between physical maps and canonical statistical quantifiers, as either of them can be defined in terms of the other.

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arXiv2023

Pure non-Markovian evolutions

Non-Markovian dynamics are characterized by information backflows, where the evolving open quantum system retrieves part of the information previously lost in the environment. Hence, the very definition of non-Markovianity implies an initial time interval when the evolution is noisy, otherwise no backflow could take place. We identify two types of initial noise, where the first has the only effect of degrading the information content of the system, while the latter is essential for the appearance of non-Markovian phenomena. Therefore, all non-Markovian evolutions can be divided into two classes: noisy non-Markovian (NNM), showing both types of noise, and pure non-Markovian (PNM), implementing solely essential noise. We make this distinction through a timing analysis of fundamental non-Markovian features. First, we prove that all NNM dynamics can be simulated through a Markovian pre-processing of a PNM core. We quantify the gains in terms of information backflows and non-Markovianity measures provided by PNM evolutions. Similarly, we study how the entanglement breaking property behaves in this framework and we discuss a technique to activate correlation backflows. Finally, we show the applicability of our results through the study of several well-know dynamical models.

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arXiv2022

Ancillary Gaussian modes activate the potential to witness non-Markovianity

We study how the number of employed modes impacts the ability to witness non-Markovian evolutions via correlation backflows in continuous-variable quantum dynamics. We first prove the existence of non-Markovian Gaussian evolutions that do not show any revivals in the correlations between the mode evolving through the dynamics and a single ancillary mode. We then demonstrate how this scenario radically changes when two ancillary modes are considered. Indeed, we show that the same evolutions can show correlation backflows along a specific bipartition when three-mode states are employed, and where only one mode is subjected to the evolution. These results can be interpreted as a form of activation phenomenon in non-Markovianity detection and are proven for two types of correlations, entanglement and steering, and two classes of Gaussian evolutions, a classical noise model and the quantum Brownian motion model.

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arXiv2020

Verification of joint measurability using phase-space quasiprobability distributions

Measurement incompatibility is a distinguishing property of quantum physics and an essential resource for many quantum information processing tasks. We introduce an approach to verify the joint measurability of measurements based on phase-space quasiprobability distributions. Our results therefore establish a connection between two notions of non-classicality, namely the negativity of quasiprobability distributions and measurement incompatibility. We show how our approach can be applied to the study of incompatibility-breaking channels and derive incompatibility-breaking sufficient conditions for bosonic systems and Gaussian channels. In particular, these conditions provide useful tools for investigating the effects of errors and imperfections on the incompatibility of measurements in practice. To illustrate our method, we consider all classes of single-mode Gaussian channels. We show that pure lossy channels with 50% or more losses break the incompatibility of all measurements that can be represented by non-negative Wigner functions, which includes the set of Gaussian measurements.

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arXiv2020

Measuring non-Markovianity via incoherent mixing with Markovian dynamics

We introduce a measure of non-Markovianity based on the minimal amount of extra Markovian noise we have to add to the process via incoherent mixing, in order to make the resulting transformation Markovian too at all times. We show how to evaluate this measure by considering the set of depolarizing evolutions in arbitrary dimension and the set of dephasing evolutions for qubits.

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arXiv2019

A correlation measure detecting almost all non-Markovian evolutions

We investigate the ability of correlation measures to witness non-Markovian open quantum system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is non-bijective in finite time-intervals. Our proof is constructive and provides different initial states detecting the non-Markovian evolutions. These states are all separable and some are arbitrarily close to a product state.

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arXiv2019

Equivalence between non-Markovian dynamics and correlation backflows

The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear if for all non-Markovian dynamics it is possible to observe a non-monotonic evolution of this quantity, namely a backflow. We address this problem by considering correlations of finite-dimensional bipartite systems. For this purpose, we consider a class of correlation measures and prove that if the dynamics is non-Markovian there exists at least one element from this class that provides a correlation backflow. Moreover, we provide a set of initial probe states that accomplish this witnessing task. This result provides the first one-to-one relation between non-Markovian dynamics of finite-dimensional quantum systems and correlation backflows.

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arXiv2019

Witnessing non-Markovian dynamics through correlations

Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study the backflow in terms of the correlations the evolving system displays with another unperturbed system during the dynamics. In this work, we study the power of this approach to witness non-Markovian dynamics using different correlation measures. We identify simple dynamics where the failure of completely-positive divisibility is in one-to-one correspondence with a correlation backflow. We then focus on specific correlation measures, such as those based on entanglement and the mutual information, and identify their strengths and limitations. We conclude with a study of a recently introduced correlation measures based on state distinguishability and see how, for these measures, adding an extra auxiliary system enlarges the set of detectable non-Markovian dynamics.

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