- ItemQuantum 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.
- ItemPinhole interference in three-dimensional fuzzy space(Stellenbosch : Stellenbosch University, 2023-03) Trinchero, Dario; Scholtz, F. G.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: We investigate a quantum-to-classical transition which arises naturally within the fuzzy sphere formalism for three-dimensional non-commutative quantum mechanics. We focus on treating a two-pinhole interference configuration within this formalism, as it provides an illustrative toy model for which this transition is readily observed and quantified. Specifi- cally, we demonstrate a suppression of the quantum interference effects for objects passing through the pinholes with sufficiently-high energies or numbers of constituent particles. Our work extends a similar treatment of the double slit experiment, presented in , within the two-dimensional Moyal plane, only it addresses two key shortcomings that arise in that context. These are, firstly that the interference pattern in the Moyal plane lacks the expected reflection symmetry present in the pinhole setup, and secondly that the quantum-to-classical transition manifested in the Moyal plane occurs only at unrealistically high velocities and/or particle numbers. Both of these issues are solved in the fuzzy sphere framework.
- ItemDynamics of actin filaments in an actin-myosin motility assay(Stellenbosch : Stellenbosch University, 2023-03) Saffer, Olivia; Muller-Nedebock, Kristian K. ; Kriel, J. N.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: Actin filaments form important parts of biological cells. Actin filaments frequently interact with myosin motors. In particular, actin filaments and myosin motors are responsible for muscle contraction in animal cells: the myosin motors attach to the actin filaments and contract, causing the filaments in the muscle to slide over each other. One way to study muscle contraction is to use experiments known as actin-myosin motility assays. This is the system we strive to model and understand in this thesis. However, there is also a broader interest in these sort of systems, since the actin-myosin motility assay is an example of an active system. After setting up our model mathematically, we begin by investigating the dynamics of a single actin filament in a motility assay by using a Langevin equation. From there, we move to including the effects of other filaments. This is achieved using hydrodynamic considerations. In order to move to a fuller picture of the dynamics of multiple filaments in a dense system, we turn to the Martin-Siggia-Rose formalism and a systematic approximation scheme known as the Random Phase Approximation. Throughout our exploration of this system, we look to derive experimentally-measurable correlation functions. While we do this, we also identify intrinsic length and time scales.
- ItemDeveloping new experimental techniques to investigate the co-linear cluster tri-partitioning(Stellenbosch : Stellenbosch University, 2022-12) Korsten, Riaan Louw; Wyngaardt, Shaun M.; Malaza, Vusi D.; Pyatkov, Yu V.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: Computational simulations were developed to calculate data collection efficiency, as well as data accuracy for existing experimental setups used in the study of the exotic ternary decay of low excited heavy nuclei known as Co-linear Cluster Tri- partitioning (CCT) . The most populated CCT mode containing the so called “Ni-bump”. This bump is centered at the masses associated with the magic isotopes of Ni (which include ⁶⁸Ni and ⁷²Ni). The results from these simulations give new insight into the identification capability of heavy ions using current experimental equipment and hint at some possible solutions to increase data collection efficiency and data accuracy. As a charged particle interacts with the material of a semiconductor detector and deposits energy into it, it creates high conductivity plasma along the trajectory of the particle. This disrupts the internal electric field of the detector for some time which retards data collection. This effect is known as Plasma Delay (PD). Development of a new algorithm and subsequent computational implementation of this algorithm -Paraspline algorithm-, with the goal of more accurate time-of-flight (TOF) calculations, by correcting for the PD effect in semiconductor detectors. Testing of this algorithm show promising results, potentially improving the reliability of future experimental results.
- ItemSystematics of mean resonance spacing and average radiative width from random forest regression(Stellenbosch : Stellenbosch University, 2022-12) Bormans, Jeroen Peter; Wyngaardt, Shaun M.; Wiedeking, Mathis; Malatji, K.L.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: The interaction of a nucleus with γ-rays plays a key role in a theoretical understanding of competi- tion in and components of nuclear reactions. The photon strength function (PSF) gives the average response of a nucleus to an electromagnetic probe. In this thesis, a study is done of the nuclear level density (NLD) and PSF of 22 isotopes in the range (A = 46 − 90) arising from a (p,γ) reac- tion. The calculations for this analysis are done in TALYS. In addition, a machine-learning driven approach for determining experimentally obtained model parameters from the neutron/proton and mass number is given.