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International Conference on Communication Systems & Networks (COMSNETS)

Generative Learning with Qopula Circuits

Amey Bhatuse, Ankit Khandelwal, M Girish Chandra

Published Jan 3, 2024• 0 citations
Publisher

Abstract

Multivariate distribution modeling is a crucial process employed to capture dependencies in experimental data in areas like physics, chemistry, finance, and climate science. Copula distributions are a special class of multivariate distributions that have uniform marginals and have been studied extensively to model non-trivial dependencies in high-dimensional data. In the last decade, various ways of applying machine learning techniques to model copulas have been proposed to improve the pre-existing parametric models. Recently, with the advent of uniting machine learning and quantum computing, quantum generative models have been used to generate various data objects like images, probability distributions, natural language data, etc, using hybrid models that have both classical and quantum components. In this paper, we build on the recent work on utilizing quantum circuits to generate copulas and aim to provide a near-holistic study of how different quantum generative models can be implemented and tuned to capture correlations in real-world finance data.

DOI
10.1109/comsnets59351.2024.10427073

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Multivariate distribution modeling is a crucial process employed to capture dependencies in experimental data in areas like physics, chemistry, finance, and climate science. Copula distributions are a special class of multivariate distributions that have uniform marginals and have been studied extensively to model non-trivial dependencies in high-dimensional data. In the last decade, various ways of applying machine learning techniques to model copulas have been proposed to improve the pre-existing parametric models. Recently, with the advent of uniting machine learning and quantum computing, quantum generative models have been used to generate various data objects like images, probability distributions, natural language data, etc, using hybrid models that have both classical and quantum components. In this paper, we build on the recent work on utilizing quantum circuits to generate copulas and aim to provide a near-holistic study of how different quantum generative models can be implemented and tuned to capture correlations in real-world finance data.
Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this paper, we show that any copula can be naturally mapped to a multipartite maximally entangled state. Thus, the task of learning joint probability distributions becomes the task of learning maximally entangled states. We prove that a variational ansatz we christen as a ``qopula'' based on this insight leads to an exponential advantage over classical methods of learning some joint distributions. As an application, we train a quantum generative adversarial network (QGAN) and a quantum circuit Born machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables in historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to eight qubits. Our experimental results show interesting findings such as the resilience against noise, outperformance against equivalent classical models and 20--1000 times less iterations required to converge as compared to equivalent classical models.
Quantum generative modeling is a growing area of interest for industry-relevant applications. This work systematically compares a broad range of techniques to guide quantum computing practitioners when deciding which models and methods to use in their applications. We compare fundamentally different architectural ansatzes of parametric quantum circuits: (1) A continuous architecture, which produces continuous-valued data samples, and (2) a discrete architecture, which samples on a discrete grid. We also compare the performance of different data transformations: the min-max and the probability integral transforms. We use two popular training methods: (1) quantum circuit Born machines (QCBM), and (2) quantum generative adversarial networks (QGAN). We study their performance and tradeoffs as the number of model parameters increases, with a baseline comparison of similarly trained classical neural networks. The study is performed on six low-dimensional synthetic and two real financial data sets. Our two key findings are that: (1) For all data sets, our quantum models require similar or fewer parameters than their classical counterparts. In the extreme case, the quantum models require two orders of magnitude less parameters. (2) We empirically find that a variant of the discrete architecture, which learns the copula of the probability distribution, outperforms all other methods.
In recent years, many generation-based machine learning algorithms such as generative adversarial networks, Boltzmann machine, auto-encoder, etc. are widely used in data generation and probability distribution simulation. On the other hand, the combined algorithms of quantum computation and classical machine learning algorithms are proposed in various styles. Especially, there exist many relevant researches about quantum generative models, which are regarded as the branch of quantum machine learning. Quantum generative models are hybrid quantum-classical algorithms, in which parameterized quantum circuits are introduced to obtain the cost function of the task as well as its gradient, and then classical optimization algorithms are used to find the optima. Compared with its classical counterpart, quantum generative models map the data stream to high-dimensional Hilbert space with parameterized quantum circuits. In the mapping space, data features are easier to learn, which can surpass classical generative models in some tasks. Besides, quantum generative models are potential to realize the quantum advantage in noisy intermediate-scale quantum devices.
Quantum machine learning (QML) is a cross-disciplinary subject made up of two of the most exciting research areas: quantum computing and classical machine learning (ML), with ML and artificial intelligence (AI) being projected as the first fields that will be impacted by the rise of quantum machines. Quantum computers are being used today in drug discovery, material & molecular modelling and finance. In this work, we explore emerging research areas in the application of hybrid classical quantum machine learning (QML) in finance. We focus on hybrid classical-quantum models that have gained significant interest in the financial world for various applications. We utilise a real-world cryptocurrency dataset to train a quantum generative adversarial networks (qGAN), and implement the real-life NVIDIA stock price data on quantum LSTM (QLSTM), comparing its performance with classical Long Short Term Memory (LSTM) model. Additionally, we investigate the application of quantum circuit Born machine (QCBM) using a toy dataset for applications in finance. For the qGAN, we define quantum circuits for generators and showcase the potential for future quantum advantage in finance through QML, possibly in combination with QLSTM and QCBM. Our findings suggest that, while training classical data is more efficient on LSTM, the test predictions of QLSTM is slightly superior to its classical counterpart making it a promising candidate for financial forecasting and analysis for timeseries type data.
The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine learning is solely based on classical resources, generative quantum machine learning can also employ quantum resources - such as parameterized quantum channels and quantum operators - to learn and sample from the probability model of interest. Applications of generative (quantum) models are multifaceted. The trained model can generate new samples that are compatible with the given data and extend the data set. Additionally, learning a model for the generation process of a data set may provide interesting information about the corresponding properties. With the help of quantum resources, the respective generative models have access to functions that are difficult to evaluate with a classical computer and may improve the performance or lead to new insights. Furthermore, generative quantum machine learning can be applied to efficient, approximate loading of classical data into a quantum state which may help to avoid - potentially exponentially - expensive, exact quantum data loading. The aim of this doctoral thesis is to develop new generative quantum machine learning algorithms, demonstrate their feasibility, and analyze their performance. Additionally, we outline their potential application to efficient, approximate quantum data loading. More specifically, we introduce a quantum generative adversarial network and a quantum Boltzmann machine implementation, both of which can be realized with parameterized quantum circuits. These algorithms are compatible with first-generation quantum hardware and, thus, enable us to study proof of concept implementations not only with numerical quantum simulations but also real quantum hardware available today.
Quantum machine learning (QML) is a cross-disciplinary subject made up of two of the most exciting research areas: quantum computing and classical machine learning (ML), with ML and artificial intelligence (AI) being projected as the first fields that will be impacted by the rise of quantum machines. Quantum computers are being used today in drug discovery, material & molecular modelling and finance. In this work, we discuss some upcoming active new research areas in application of quantum machine learning (QML) in finance. We discuss certain QML models that has become areas of active interest in the financial world for various applications. We use real world financial dataset and compare models such as qGAN (quantum generative adversarial networks) and QCBM (quantum circuit Born machine) among others, using simulated environments. For the qGAN, we define quantum circuits for discriminators and generators and show promises of future quantum advantage via QML in finance.