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Dario Villani

Publications and source records attributed to Dario Villani.

10 recordsLinked to original sources
arXiv2026

Shallow-circuit Supervised Learning on a Quantum Processor

Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.

quant-ph↗
arXiv2025

Quantum Cognition Machine Learning for Forecasting Chromosomal Instability

The accurate prediction of chromosomal instability from the morphology of circulating tumor cells (CTCs) enables real-time detection of CTCs with high metastatic potential in the context of liquid biopsy diagnostics. However, it presents a significant challenge due to the high dimensionality and complexity of single-cell digital pathology data. Here, we introduce the application of Quantum Cognition Machine Learning (QCML), a quantum-inspired computational framework, to estimate morphology-predicted chromosomal instability in CTCs from patients with metastatic breast cancer. QCML leverages quantum mechanical principles to represent data as state vectors in a Hilbert space, enabling context-aware feature modeling, dimensionality reduction, and enhanced generalization without requiring curated feature selection. QCML outperforms conventional machine learning methods when tested on out of sample verification CTCs, achieving higher accuracy in identifying predicted large-scale state transitions (pLST) status from CTC-derived morphology features. These preliminary findings support the application of QCML as a novel machine learning tool with superior performance in high-dimensional, low-sample-size biomedical contexts. QCML enables the simulation of cognition-like learning for the identification of biologically meaningful prediction of chromosomal instability from CTC morphology, offering a novel tool for CTC classification in liquid biopsy.

q-bio.QM↗
arXiv2025

Quantum Geometry of Data

We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum geometry description endows the dataset with rich geometric and topological structure - including intrinsic dimension, quantum metric, and Berry curvature - derived directly from the data. QCML captures global properties of data, while avoiding the curse of dimensionality inherent in local methods. We illustrate this on a number of synthetic and real-world examples. Quantum geometric representation of QCML could advance our understanding of cognitive phenomena within the framework of quantum cognition.

cs.LG↗
arXiv2025

Supervised Similarity for Firm Linkages

We introduce a novel proxy for firm linkages, Characteristic Vector Linkages (CVLs). We use this concept to estimate firm linkages, first through Euclidean similarity, and then by applying Quantum Cognition Machine Learning (QCML) to similarity learning. We demonstrate that both methods can be used to construct profitable momentum spillover trading strategies, but QCML similarity outperforms the simpler Euclidean similarity.

q-fin.ST↗
arXiv2024

Robust estimation of the intrinsic dimension of data sets with quantum cognition machine learning

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically to the estimation of intrinsic dimension of data sets. The idea is to learn a representation of each data point as a quantum state, encoding both local properties of the point as well as its relation with the entire data. Inspired by ideas from quantum geometry, we then construct from the quantum states a point cloud equipped with a quantum metric. The metric exhibits a spectral gap whose location corresponds to the intrinsic dimension of the data. The proposed estimator is based on the detection of this spectral gap. When tested on synthetic manifold benchmarks, our estimates are shown to be robust with respect to the introduction of point-wise Gaussian noise. This is in contrast to current state-of-the-art estimators, which tend to attribute artificial ``shadow dimensions'' to noise artifacts, leading to overestimates. This is a significant advantage when dealing with real data sets, which are inevitably affected by unknown levels of noise. We show the applicability and robustness of our method on real data, by testing it on the ISOMAP face database, MNIST, and the Wisconsin Breast Cancer Dataset.

stat.ML↗
arXiv2000

Looking Forward to Pricing Options from Binomial Trees

We reconsider the valuation of barrier options by means of binomial trees from a "forward looking" prospective rather than the more conventional "backward induction" one used by standard approaches. This reformulation allows us to write closed-form expressions for the value of European and American put barrier-options on a non-dividend-paying stock.

physics.gen-ph↗
arXiv1997

The two-dimensional t-t'-U model as a minimal model for cuprate materials

The addition to the Hubbard Hamiltonian of a t' diagonal hopping term, which is considered to be material dependent for high-Tc cuprate superconductors, is generally suggested to obtain a model capable to describe the physics of high-Tc cuprate materials. In this line of thinking, the two-dimensional t-t'-U model has been studied by means of the Composite Operator Method, which allows to determine the dynamics in a fully self-consistent way by use of symmetry requirements, as the ones coming from the Pauli principle. At first, some local quantities have been calculated to be compared with quantum Monte Carlo data. Then, the structure of the energy bands, the shape of the Fermi surface and the position of the van Hove singularity have been computed as functions of the model parameters and studied by the light of the available experimental data. The results of our study show that there exists two sets of parameters that allows the model to describe the relevant features of 1-layer compounds NCCO and LSCO. On the other hand, for the 2-layer compound YBCO is not possible to find a reasonable set of parameters which could reproduce the position of the van Hove singularity as predicted by ARPES experiments. Hence, it results questionable the existence of an unique model that could properly describe the variety of cuprate superconductors, as the t-t'-U model was thought to be.

cond-mat.supr-con↗
arXiv1997

Incommensurate spin fluctuations in the two-dimensional t-t'-U model

Magnetic properties of the two-dimensional t-t'-U model are investigated by studying the static spin magnetic susceptibility as a function of momentum for various temperatures. The calculations are performed by means of the Composite Operator Method in the static approximation. By increasing the value of the t' parameter the magnetic scattering in the reciprocal space evolves to an isotropic structure. It is shown that the results are in qualitative agreement with the experimental situation observed in LSCO and YBCO compounds.

cond-mat.supr-con↗
arXiv1997

Local properties in the two-dimensional t-t'-U model

We have studied the t-t'-U model by means of the composite operator method. The effect of the bare diagonal hopping term t' that appears to be material dependent for high-Tc cuprate superconductors is analyzed in detail. In particular, some local quantities are computed and a comprehensive comparison with the data by numerical simulations on finite size lattices is presented. The result show a good agreement with those obtained by Monte Carlo methods.

cond-mat.str-el↗