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arXiv:1803.05169 · Journal of Physics A Mathematical and Theoretical

Geometrical versus time-series representation of data in quantum control learning

M Ostaszewski, Jarosław Adam Miszczak, P Sadowski

Published Mar 23, 2020• 2 citations
arXivHTMLPDF

Abstract

Abstract Recently, machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations implementing the given quantum logical operation. In this context we analyse the flexibility of the data representation and compare the applicability of two machine learning approaches based on different representations of data. We demonstrate that the utilization of the geometrical structure of control pulses is sufficient for achieving high-fidelity of the implemented evolution. We also demonstrate that artificial neural networks, unlike geometrical methods, possess generalization abilities enabling them to generate control pulses for the systems with variable strength of the disturbance. The presented results suggest that in some quantum control scenarios, geometrical data representation and processing is competitive to more complex methods.

DOI
10.1088/1751-8121/ab8244

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Abstract Recently, machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations implementing the given quantum logical operation. In this context we analyse the flexibility of the data representation and compare the applicability of two machine learning approaches based on different representations of data. We demonstrate that the utilization of the geometrical structure of control pulses is sufficient for achieving high-fidelity of the implemented evolution. We also demonstrate that artificial neural networks, unlike geometrical methods, possess generalization abilities enabling them to generate control pulses for the systems with variable strength of the disturbance. The presented results suggest that in some quantum control scenarios, geometrical data representation and processing is competitive to more complex methods.
Objectives. Fast data analysis based on hidden patterns is one of the main issues for adaptive artificial intelligence systems development. This paper aims to propose and verify a method of such analysis based on the representation of data in the form of a quantum state, or, alternatively, in the form of a geometric object in a space allowing online machine learning. Methods. This paper uses Feynman formalism to represent quantum states and operations on them, the representation of quantum computing in the form of quantum circuits, geometric transformations, topological classification, as well as methods of classical and quantum machine learning. The Python programming language is used as a development tool. Optimization tools for machine learning are taken from the SciPy module. The datasets for analysis are taken from open sources. Data preprocessing was performed by the method of mapping features into numerical vectors, then the method of bringing the data to the desired dimension was applied. The data was then displayed in a quantum state. A proprietary quantum computing emulator is used (it is in the public domain). Results. The results of computational experiments revealed the ability of very simple quantum circuits to classify data without optimization. Comparative indicators of classification quality are obtained without the use of optimization, as well as with its use. Experiments were carried out with different datasets and for different values of the dimension of feature spaces. The efficiency of the models and methods of machine learning proposed in the work, as well as methods of combining them into network structures, is practically confirmed. Conclusions. The proposed method of machine learning and the model of quantum neural networks can be used to create adaptive artificial intelligence systems as part of an online learning module. Free online optimization learning process allows it to be applied in data streaming, that is, adapting to changes in the environment. The developed software does not require quantum computers and can be used in the development of artificial intelligence systems in Python as imported modules.
Abstract The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
Abstract Quantum Machine Learning was born during the past decade as the intersection of Quantum Computing and Machine Learning. Today, advances in quantum computer hardware and the design of simulation frameworks able to run quantum algorithms in classic computers make it possible to extend classic artificial intelligence models to a quantum environment. Despite these achievements, several questions regarding the whole quantum machine learning pipeline remain unanswered, for instance the problem of classical data representation on quantum hardware, or the methodologies for designing and evaluating quantum models for common learning tasks such as classification, function approximation, clustering, etc. These problems become even more difficult to solve in the case of Time Series processing, where the context of past historical data may influence the behavior of the decision-making model. In this piece of research, we address the problem of Time Series classification using quantum models, and propose an efficient and compact representation of time series in quantum data using amplitude embedding. The proposal is capable of representing a time series of length n in log2(n)log_2(n)log2​(n) l o g 2 ( n ) computational units, and experiments conducted on benchmark time series classification problems show that quantum models designed for classification can also outperform the accuracy of classic methods.
Quantum gate design is often represented as pulse optimization, although the physical object that implements a gate is the full controlled evolution generated by the pulse. Here we use physics-informed neural networks to represent single-qubit gate design at this evolution level: the control fields, the Bloch-state trajectories, and the total duration are learned together under the Bloch equation. This changes the optimized object from pulse amplitudes to a differentiable physical process whose structure can be inspected and refined. For rotation gates, the optimized evolutions recover the physical organization expected for bounded single-qubit control, with no prescribed pulse ansatz or duration scan. For a geometric gate, the representation identifies localized bottlenecks in maintaining the geometric condition and turns this diagnosis into feedback, reducing the residual path error while preserving high fidelity. Thus physics-informed learning is used not only to synthesize gates, but also to make optimized quantum controls physically readable, diagnosable, and locally refinable. This process-level view may be especially useful for adapting gates to hardware-specific, task-specific, and locally varying experimental constraints.
Quantum machine learning (QML) has gained significant interest by combining quantum computing and artificial intelligence, two topics that are expected to revolutionize the way of data processing. While gate-based quantum computing uses precisely defined unitary operations on qubits, currently available noisy intermediate-scale quantum (NISQ) devices are not ready for implementations of high-depth circuits. However, machine learning is one of the promising applications to be used on NISQ hardware via parameterized quantum circuits (PQCs). An alternative QML paradigm comes from a different direction: Quantum reservoir computing (QRC) relies on using physical systems as quantum artificial neural networks. Instead of using controlled gate operations, here the system dynamics are controlled by the underlying Hamiltonian, and the machine learning layer is performed at the output weights. Despite their distinct origin, both ML approaches are connected and can formally be mapped onto each other. We discuss this analogy by realizing a transverse-field Ising model on a gate-based quantum computing architecture establishing a fundamental connection on an abstract level between these two very different QML paradigms. This enables us to connect the known expressivity measure of PQC-QML with the quantification of expressiveness of physical dynamical systems.