Modelling Non-Markovian Quantum Systems Using Tensor Networks

A novel approach to modelling the dynamics of a quantum system that is strongly coupled to its environment is presented, using tensor networks. This method is highly efficient and has the potential to significantly impact future generations of physicists.

Format: Paperback / softback
Length: 103 pages
Publication date: 01 September 2021
Publisher: Springer Nature Switzerland AG

This thesis presents a groundbreaking approach to modelling the dynamics of a quantum system that is intricately connected to its immediate surroundings. This is a complex but pressing issue, particularly relevant for simulating decoherence in devices like quantum information processors and the transfer of quantum information between spatially distinct components of a quantum system. The central innovation of this work is the representation of general open quantum systems using tensor networks, a concept that has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed herein has demonstrated remarkable efficacy: In many scenarios, it may emerge as the most efficient method for computing open quantum dynamics. This research is replete with novel ideas and innovations, with the potential to profoundly impact the future generations of physicists.

Introduction:
The study of quantum systems has always been a subject of intense interest, as they possess unique properties that defy classical understanding. One of the most challenging aspects of modelling quantum systems is the strong coupling between the system and its environment, which can lead to complex and unpredictable behaviour. In this thesis, we present a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment.
Challenges:
Modelling the dynamics of a quantum system that is strongly coupled to its environment 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.
Tensor Network Methodology:
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 is because tensor networks allow for the efficient representation of complex systems in a compact and scalable manner. The methodology involves representing the quantum system as a network of tensors, where each tensor represents a physical quantity or a quantum state. The connections between tensors are defined by a set of rules, known as the tensor network contraction.
Efficacy of Tensor Network Methodology:
The efficacy of the tensor network methodology has been demonstrated in a wide range of scenarios. For example, it has been used to simulate the dynamics of a quantum system in the presence of noise, which is a major challenge in quantum computing. The methodology has also been used to simulate the decoherence of a quantum system, which is a key factor approach to quantum information processing.
Conclusion:
In conclusion, this thesis presents a groundbreaking approach to modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. The tensor network methodology developed here has proven to be extremely powerful, and has the potential to revolutionize the field of quantum computing and information processing. The work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.

Weight: 197g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030549770
Edition number: 1st ed. 2020