School of Physics - Theses

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Start date: 2020 × End date: 2022 × Type: Masters Coursework thesis ×

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    Simulating Noisy Quantum Algorithms and Low Depth Quantum State Preparation using Matrix Product States
    Nakhl, Azar Christian ( 2021)
    Since the proposal of Quantum Computation in the 1980s, many Quantum Algorithms have been proposed to solve problems in a wide variety of fields. However, due to the limitations of existing quantum devices, analysing the performance of these algorithms in a controlled manner must be performed classically. The leading technique to simulate quantum computers classically is based on the Matrix Product State (MPS) representation of quantum systems. We used this simulation method to benchmark the noise tolerance of a number of quantum algorithms including Grover’s Algorithm, finding that the algorithm’s ability to discern the marked state is exponentially suppressed under noise. We verified the existence of Noise-Induced Barren Plateaus (NIBPs) in the Quantum Approximate Optimisation Algorithm (QAOA) and found that the recursive QAOA (RQAOA) variation is resilient to NIBPs, a novel result. Also integral to the performance of quantum algorithms is the ability to efficiently prepare their initial states. We developed novel techniques to prepare low-depth circuits for slightly entangled quantum states using MPS. We found that we can reproduce Gaussian and W States with circuits of O(log(n)) depth, improving on current best known results which are of O(n).
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    Moments-Based Corrections to Variational Quantum Computation
    Jones, Michael Alexander ( 2020)
    Quantum Computing offers the potential to efficiently solve problems for which there are no known, efficient classical solutions such as factoring of semi-prime numbers and simulation of quantum- mechanical systems. This work considers a novel moments-based adaptation of the Variational Quantum Eigensolver (VQE), one of the leading candidates for demonstrating quantum supremacy. The method for improving the estimated ground state energy of a quantum system, obtained using the Variational Quantum Eigensolver, is presented and tested for Heisenberg model systems using IBM’s superconducting quantum devices. The method is based on the application of a Lanczos expansion technique based on the computation of Hamiltonian moments and is found to offer better accuracy than conventional VQE for most cases considered, allowing for a simpler trial state and offsetting the effects of noise.