arXiv subjects

Kharen Musaelian

Publications and source records attributed to Kharen Musaelian.

7 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↗

arXiv2025

Supervised Similarity for High-Yield Corporate Bonds with Quantum Cognition Machine Learning

We investigate the application of quantum cognition machine learning (QCML), a novel paradigm for both supervised and unsupervised learning tasks rooted in the mathematical formalism of quantum theory, to distance metric learning in corporate bond markets. Compared to equities, corporate bonds are relatively illiquid and both trade and quote data in these securities are relatively sparse. Thus, a measure of distance/similarity among corporate bonds is particularly useful for a variety of practical applications in the trading of illiquid bonds, including the identification of similar tradable alternatives, pricing securities with relatively few recent quotes or trades, and explaining the predictions and performance of ML models based on their training data. Previous research has explored supervised similarity learning based on classical tree-based models in this context; here, we explore the application of the QCML paradigm for supervised distance metric learning in the same context, showing that it outperforms classical tree-based models in high-yield (HY) markets, while giving comparable or better performance (depending on the evaluation metric) in investment grade (IG) markets.

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↗

arXiv2020

A scale-dependent notion of effective dimension

We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size $1/\sqrt{n}$ needed to cover the model space when endowed with the Fisher Information Matrix as metric, $n$ being the number of observations. The number of observations fixes a natural scale or resolution. The effective dimension is then measured via the spectrum of the Fisher Information Matrix regularized using this natural scale.

stat.ML↗