arXiv subjects

Vladimir Rastunkov

Publications and source records attributed to Vladimir Rastunkov.

6 recordsLinked to original sources

arXiv2025

Quantum Time Series Similarity Measures and Quantum Temporal Kernels

This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various similarity-based classification, clustering, and regression algorithms. An effective strategy for devising problem-specific kernels is leveraging existing generative models of the example space. In this study we assume that a quantum generative model, known as quantum hidden Markov model (QHMM), describes the underlying distributions of the examples. The sequence structure and probability are determined by transitions within model's density operator space. Consequently, the QHMM defines a mapping from the example space into the broader quantum space of density operators. Sequence similarity is evaluated using divergence measures such as trace and Bures distances between quantum states. We conducted extensive simulations to explore the relationship between the distribution of kernel-estimated similarity and the dimensionality of the QHMMs Hilbert space. As anticipated, a higher dimension of the Hilbert space corresponds to greater sequence distances and a more distinct separation of the examples. To empirically evaluate the performance of the kernels, we defined classification tasks based on a simplified generative model of directional price movement in the stock market. We implemented two widely-used kernel-based algorithms - support vector machines and k-nearest neighbors - using both classical and quantum kernels. Across all classification task scenarios, the quantum kernels consistently demonstrated superior performance compared to their classical counterparts.

quant-ph↗

arXiv2025

Implementation and Learning of Quantum Hidden Markov Models

In this article, we use the theory of quantum channels and open quantum systems to provide an efficient unitary characterization of a class of stochastic generators known as quantum hidden Markov models (QHMMs). By utilizing the unitary characterization, we demonstrate that any QHMM can be implemented as a quantum circuit with mid-circuit measurement. We prove that QHMMs are more compact and more expressive definitions of stochastic process languages compared to the equivalent classical hidden Markov models (HMMs). Starting with the formulation of QHMMs as quantum channels, we employ Stinespring's construction to represent these models as unitary quantum circuits with mid-circuit measurement. By utilizing the unitary parameterization of QHMMs, we define a formal QHMM learning model. The model formalizes the empirical distributions of target stochastic process languages, defines hypothesis space of quantum circuits, and introduces an empirical stochastic divergence measure - hypothesis fitness - as a success criterion for learning. We demonstrate that the learning model has a smooth search landscape due to the continuity of Stinespring's dilation. The smooth mapping between the hypothesis and fitness spaces enables the development of efficient heuristic and gradient descent learning algorithms. We propose two practical learning algorithms for QHMMs. The first algorithm is a hyperparameter-adaptive evolutionary search. The second algorithm learns the QHMM as a quantum ansatz circuit using a multi-parameter non-linear optimization technique.

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arXiv2023

Quantum Multiple Kernel Learning in Financial Classification Tasks

Financial services is a prospect industry where unlocked near-term quantum utility could yield profitable potential, and, in particular, quantum machine learning algorithms could potentially benefit businesses by improving the quality of predictive models. Quantum kernel methods have demonstrated success in financial, binary classification tasks, like fraud detection, and avoid issues found in variational quantum machine learning approaches. However, choosing a suitable quantum kernel for a classical dataset remains a challenge. We propose a hybrid, quantum multiple kernel learning (QMKL) methodology that can improve classification quality over a single kernel approach. We test the robustness of QMKL on several financially relevant datasets using both fidelity and projected quantum kernel approaches. We further demonstrate QMKL on quantum hardware using an error mitigation pipeline and show the benefits of QMKL in the large qubit regime.

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arXiv2023

Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction

Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.

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arXiv2022

Reservoir Computing via Quantum Recurrent Neural Networks

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.

cs.NE↗

arXiv2022

Boosting Method for Automated Feature Space Discovery in Supervised Quantum Machine Learning Models

Quantum Support Vector Machines (QSVM) have become an important tool in research and applications of quantum kernel methods. In this work we propose a boosting approach for building ensembles of QSVM models and assess performance improvement across multiple datasets. This approach is derived from the best ensemble building practices that worked well in traditional machine learning and thus should push the limits of quantum model performance even further. We find that in some cases, a single QSVM model with tuned hyperparameters is sufficient to simulate the data, while in others - an ensemble of QSVMs that are forced to do exploration of the feature space via proposed method is beneficial.

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