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Title: Controlling open quantum systems
Author: Dive, Benjamin
ISNI:       0000 0004 6496 9697
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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All physical quantum systems are in contact with the external world which is inevitably a source of noise. It is therefore necessary to take into account this dissipation when designing controls that accomplish useful tasks in quantum information processing. This thesis is on that overlap of open quantum systems and control theory; it looks at what dynamics can happen with the use of external driving, and how this driving can be chosen to accomplish a desired goal. The first result looks at how a given quantum dissipator can be manipulated, using coherent controls, into replicating the action of a different type of noise. This results in no-go theorems for how noise can be transformed based on its isotropy, with applications in simulating open systems. Another way of doing simulations is to use only unitary dynamics over the system and a finite dimensional ancilla, and it is proved that there always exists a dilation Hamiltonian that replicates the noisy dynamics continuously in time. This also highlights the fact that adding controls on noise can result in a different evolution than if the controls were done on the under- lying system-environment level. A conjecture is introduced and studied which states that both approaches are equivalent in the special case of the controls commuting with the Lindbladian. A way around this difficulty is to use a quantum system to compute in situ which controls are best for achieving a desired task on itself. This problem is studied in the context of reaching entangling gates on a quantum simulator in order to upgrade it into a quantum computer. The experimental cost of doing so is found to be polynomial in the number of qubits in simulations. The same underlying principle is also used to find error correcting codes tailored to the dissipation in a system.
Supervisor: Burgarth, Daniel ; Mintert, Florian Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral