Modelling non-Markovian quantum systems using tensor networks
This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor n…
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- Full title :Modelling non-Markovian quantum systems using tensor networks / Aidan Strathearn.
Summary
This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.
Read More ↓Edition Statements
- Publication Date:2020
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:2020
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9783030549756, 3030549755
- oclc:on1192494271
- LC Classification:TK7874.885
- Dewey Decimal:530.12011
Table of Contents
Intro -- Supervisor's Foreword -- Abstract -- Acknowledgements -- Contents -- Abbreviations -- 1 Introduction -- References -- 2 Background -- 2.1 Theory of Open Quantum Systems -- 2.1.1 General Theory -- 2.1.2 Markovian Systems -- 2.1.3 Non-Markovian Systems -- 2.1.4 Summary -- 2.2 Tensor Networks -- 2.2.1 Notation -- 2.2.2 Matrix Products -- 2.2.3 Efficient Contraction of Matrix Products -- 2.2.4 Summary -- References -- 3 Method -- 3.1 Time Ordering as a Tensor Network -- 3.2 Discretised Influence Functional -- 3.3 Time-Evolving Matrix Product Operators -- 3.4 Finite Memory Approximation
3.5 Improved Finite Memory Approximation -- 3.6 Proof of Principle -- 3.7 Summary -- References -- 4 Results -- 4.1 Localisation -- 4.2 Environment Mediated Interactions -- 4.3 Driven-Dissipative Quantum Dot -- 4.4 Summary -- References -- 5 Conclusion -- References
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