Browsing by Author "Strydom, Conrad"

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    Quantum randomness
    (Stellenbosch : Stellenbosch University, 2023-03) Strydom, Conrad; Tame, M. S.; Bosman, G. W.; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: Randomness is a vital resource with many important applications in information theory. In particular, random numbers play a ubiquitous role in cryptography, simulation and coordination in computer networks. When ran- domness is generated using classical techniques, the unpredictability relies on incomplete knowledge which can introduce ordered features and compromise the application. This thesis explores the use of quantum techniques to generate true randomness and its application to quantum computing. The analogue of random numbers in quantum information are random unitary operators sampled from the uniform Haar ensemble, which are used in a number of quantum protocols. Unfortunately, these cannot be generated efficiently and so pseudorandom ensembles called unitary t-designs are frequently used as a substitute. In the first part of this thesis we investigate t-designs realised using a measurement-based approach on IBM quantum computers. In particular, we implement an exact single-qubit 3-design on IBM quantum computers by performing measurements on a 6-qubit graph state. We show that the ensemble of unitaries realised was a 1-design, but not a 2-design or a 3-design under the test conditions set, which we show to be a result of depolarising noise. We obtain improved results for the 2-design test by implementing an approximate 2-design, which uses a smaller 5-qubit graph state, but the test still does not pass for all states due to noise. To obtain a theoretical understanding of the effect of noise on t-designs, we investigate the effect of various noise channels on the quality of single-qubit t-designs. We show analytically that the 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4- and 5-design suggest that a 2t-design is significantly more sensitive to noise than a (2t − 1)-design and that, with the exception of amplitude damping, a (2t + 1)-design is as sensitive to noise as a 2t-design. Next, we test our approximate measurement-based 2-design on an important application in quantum com- puting, namely noise estimation. For this, we propose an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement- based gate. We demonstrate our protocol on IBM quantum computers by estimating the fidelity of a universal single-qubit gate set using graph states of up to 31 qubits. Estimated gate fidelities show good agreement with those calculated from process tomography, which shows that our approximate measurement-based 2-design is of sufficient quality for use in randomised benchmarking, despite not passing our test for all states. While IBM quantum computers provide a sophisticated platform for randomness generation, they are not specifically designed for this task. We therefore investigate randomness generation on custom-built hardware, by integrating an on-chip nanowire waveguide into an optical time-of-arrival based quantum random number generation setup. Despite loss, we achieve a random number generation rate of 14.4 Mbits/s. The generated bits did not require any post-processing to pass industry standard tests. Our experiment demonstrates an order of magnitude increase in generation rate and decrease in device size compared to previous studies.