Quantum stochastic modelling and tensor networks

Predicting a stochastic process' future lies at the heart of many scientific areas. A predictive model extracts information from a stochastic process' past and uses it to generate future statistics. There has been significant amount of effort expended towards finding optimal predictive mod...

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Main Author: Yang, Chengran
Other Authors: Gu Mile
Format: Thesis-Doctor of Philosophy
Language:English
Published: Nanyang Technological University 2020
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Online Access:https://hdl.handle.net/10356/144661
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spelling sg-ntu-dr.10356-1446612023-02-28T23:36:56Z Quantum stochastic modelling and tensor networks Yang, Chengran Gu Mile School of Physical and Mathematical Sciences gumile@ntu.edu.sg Science::Physics::Atomic physics::Quantum theory Science::Physics::Atomic physics::Statistical physics Predicting a stochastic process' future lies at the heart of many scientific areas. A predictive model extracts information from a stochastic process' past and uses it to generate future statistics. There has been significant amount of effort expended towards finding optimal predictive models that minimize the required amount of past information. By taking advantage of quantum resources, quantum models have been shown to reduce the memory requirements beyond classical limits. Meanwhile, tensor networks are an extremely useful mathematical tool for understanding quantum many-body systems. In this thesis, we explore the connection between tensor networks and quantum predictive models. A particular class of tensor networks, matrix product states (MPS), is utilized to further improve quantum models. First, we establish a connection between matrix product states (MPS) and the optimal classical predictive models. MPS methods offer a systematic method for constructing quantum predictive models and even an improved method for computing the amount of quantum memory. Second, we show that for some families of stochastic processes our method allows us to construct quantum models with unbounded memory advantages over the optimal classical models. Third, we propose a family of divergence measures to quantify the distance between two stochastic processes. This family of divergence measures overcomes certain weaknesses of the existing measures. Moreover, we propose an efficient means of computing the divergence measure using our MPS methods. Finally, we address the problem of constructing quantum predictive models solely from the output of an observed stochastic process. We use machine learning methods to propose a systematic algorithm for learning the quantum model. This provides an alternative method for constructing quantum models with fixed amounts of amount of memory. Doctor of Philosophy 2020-11-17T06:56:13Z 2020-11-17T06:56:13Z 2020 Thesis-Doctor of Philosophy Yang, C. (2020). Quantum stochastic modelling and tensor networks. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/144661 10.32657/10356/144661 en The National Research Foundation (NRF), Singapore, under its NRFF Fellow programme (Award No. NRF-NRFF2016-02) The Singapore Ministry of Education Tier 1 Grant No. MOE2017-T1-002-043 FQXi large grant: FQXi-RFP-1809 the role of quantum effects in simplifying adaptive agents, This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics::Atomic physics::Quantum theory
Science::Physics::Atomic physics::Statistical physics
spellingShingle Science::Physics::Atomic physics::Quantum theory
Science::Physics::Atomic physics::Statistical physics
Yang, Chengran
Quantum stochastic modelling and tensor networks
description Predicting a stochastic process' future lies at the heart of many scientific areas. A predictive model extracts information from a stochastic process' past and uses it to generate future statistics. There has been significant amount of effort expended towards finding optimal predictive models that minimize the required amount of past information. By taking advantage of quantum resources, quantum models have been shown to reduce the memory requirements beyond classical limits. Meanwhile, tensor networks are an extremely useful mathematical tool for understanding quantum many-body systems. In this thesis, we explore the connection between tensor networks and quantum predictive models. A particular class of tensor networks, matrix product states (MPS), is utilized to further improve quantum models. First, we establish a connection between matrix product states (MPS) and the optimal classical predictive models. MPS methods offer a systematic method for constructing quantum predictive models and even an improved method for computing the amount of quantum memory. Second, we show that for some families of stochastic processes our method allows us to construct quantum models with unbounded memory advantages over the optimal classical models. Third, we propose a family of divergence measures to quantify the distance between two stochastic processes. This family of divergence measures overcomes certain weaknesses of the existing measures. Moreover, we propose an efficient means of computing the divergence measure using our MPS methods. Finally, we address the problem of constructing quantum predictive models solely from the output of an observed stochastic process. We use machine learning methods to propose a systematic algorithm for learning the quantum model. This provides an alternative method for constructing quantum models with fixed amounts of amount of memory.
author2 Gu Mile
author_facet Gu Mile
Yang, Chengran
format Thesis-Doctor of Philosophy
author Yang, Chengran
author_sort Yang, Chengran
title Quantum stochastic modelling and tensor networks
title_short Quantum stochastic modelling and tensor networks
title_full Quantum stochastic modelling and tensor networks
title_fullStr Quantum stochastic modelling and tensor networks
title_full_unstemmed Quantum stochastic modelling and tensor networks
title_sort quantum stochastic modelling and tensor networks
publisher Nanyang Technological University
publishDate 2020
url https://hdl.handle.net/10356/144661
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