School of Physics - Theses
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ItemMoments-Based Corrections to Variational Quantum Computation( 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.
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ItemMatrix product states in quantum information processing( 2015)We employ the newly developed Matrix Product State (MPS) formalism to simulate two problems in the context of quantum information processing. One is the Boson sampling problem, the other is the ground state energy density of an n-qubit Hamiltonian. We find that the MPS representation of the Boson sampling problem is inefficient due to large entan- glement as the number of photons increases. In the context of adiabatic quantum computing (AQC), MPS is used to find the first four moments of an n-qubit Hamiltonian to approximate the ground state energy density of the Hamiltonian. We show an advantage of using the first-four-moment method over the conventional adiabatic procedure. Future work around AQC using MPS is discussed.
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ItemDistributed Matrix Product State Simulations of Large-Scale Quantum Circuits( 2017)Before large-scale, robust quantum computers are developed, it is valuable to be able to classically simulate quantum algorithms to study their properties. To do so, we developed a numerical library for simulating quantum circuits via the matrix product state formalism on distributed memory architectures. By examining the multipartite entanglement present across Shor’s algorithm, we were able to effectively map a high-level circuit of Shor’s algorithm to the one-dimensional structure of a matrix product state, enabling us to perform a simulation of a specific 60 qubit instance in approximately 14 TB of memory: potentially the largest non-trivial quantum circuit simulation ever performed. We then applied matrix product state and matrix product density operator techniques to simulating one-dimensional circuits from Google’s quantum supremacy problem with errors and found it mostly resistant to our methods.
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ItemBackground estimation studies for hadronically decaying tau leptons at the ATLAS experiment( 2018)This project aims to develop a data-driven technique for the estimation of the dominant background contribution in the inclusive search for new physics signals where equally charged lepton pairs are featured in the final state and where an hadronically decaying tau lepton can be found in a pair. The studies presented in this thesis were performed with data collected by the ATLAS experiment. A data driven technique has been developed for the abundant background of jets originated from the hadronisation of quarks or gluons which are mis-identified as hadronically decaying tau leptons. Mis-identification weighting factors have been measured for the extrapolation of this background into the signal region of the analysis and have been validated using a selection independent with respect to the the signal region. Systematic uncertainties have also been estimated. The work presented in this thesis will be incorporated in a general extrapolation technique within the ATLAS experiment aiming to be used by all ATLAS searches featuring hadronic tau decays in the final state.