Barros Henaut, Luciana; (2020) Non-classicality as a source of computational power. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The objects of study of this thesis are the origins of the quantum computational speed- up. For the past three decades research in quantum foundations pointed to a few dif- ferent properties of quantum systems that could be linked to computational power. We start our study investigating the power of correlations, as it is intrinsically found in the measurement-based model of quantum computation. An important recent contribu- tion to the field showed that measurements on three-qubit GHZ states lead to universal classical computation. In that scenario, a client initially limited to compute only sums modulo-2 can deterministically evaluate a non-linear (NAND) function when control- ling measurements on a GHZ state. We were interested in achieving deterministic computation of maximally non-linear functions using the same type of resource. Another interesting result related to the computation of a NAND function using GHZ states shows that it is possible to achieve the same task with unitary transfor- mations performed on a single qubit. Differently than in the protocol that uses GHZ states, in the single-qubit one, non-locality and traditional forms of contextuality can- not be linked to the computational advantage. In this thesis, we address the question of which type of non-classicality gives us the same computational power in the single- qubit scheme. We analyse carefully chosen variations of the protocol in terms of Bell’s and Tsirelson’s bounds and detect a connection between reversibility in transformations and the computational capability of the system.

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