Generative quantum learning of joint probability distribution functions

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 pra...

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Published in:Physical review research Vol. 4; no. 4; p. 043092
Main Authors: Zhu, Elton Yechao, Johri, Sonika, Bacon, Dave, Esencan, Mert, Kim, Jungsang, Muir, Mark, Murgai, Nikhil, Nguyen, Jason, Pisenti, Neal, Schouela, Adam, Sosnova, Ksenia, Wright, Ken
Format: Journal Article
Language:English
Published: American Physical Society 01.11.2022
ISSN:2643-1564, 2643-1564
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Abstract 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.
AbstractList 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.
ArticleNumber 043092
Author Nguyen, Jason
Schouela, Adam
Wright, Ken
Zhu, Elton Yechao
Johri, Sonika
Bacon, Dave
Sosnova, Ksenia
Esencan, Mert
Kim, Jungsang
Muir, Mark
Pisenti, Neal
Murgai, Nikhil
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