/library/oar/handle/123456789/132246 2025-11-04T21:51:01Z 2025-11-04T21:51:01Z /library/oar/handle/123456789/140597 2025-10-27T09:17:54Z 2025-01-01T00:00:00Z

Title: Variational quantum algorithms for thermal states preparation Abstract: The quantum simulation of thermal equilibrium states is a promising near-term application of quantum computation, with applicability in fields such as quantum chemistry. This dissertation investigates Gibbs state preparation of the free fermion Hamiltonian using a variational quantum algorithm (VQA). While the Grover-Rudolph algorithm can prepare an arbitrary distribution of 2n probabilities using 2n − 1 circuit parameters, it does not achieve quantum advantage, since it offers no exponential speed-up over classical methods. This work is motivated by the circuit optimisation problem: can the properties of the free fermion Hamiltonian be used to design a more efficient Ansatz for this problem with a reduced number of gate parameters? By investigating the properties of the Gibbs states for small numbers of qubits, results were found suggesting that the Gibbs states of the free fermion Hamiltonian can be generated with only n single-qubit gates, without requiring any entangling gates. This optimised single-qubit gate circuit was used as the Ansatz in a VQA for Gibbs state preparation, and the calculated and target probability distributions were compared for different system sizes and temperatures using the VQA cost function as well as various distance measures. The VQA results show that the single-qubit Ansatz is expressible enough for up to n = 5 qubits, reducing the circuit complexity for this problem. Description: B.Sc. (Hons)(Melit.)

2025-01-01T00:00:00Z /library/oar/handle/123456789/140596 2025-10-27T09:11:44Z 2025-01-01T00:00:00Z

Title: Dielectric and thermal properties of phantoms for electromagnetic based hyperthermic technologies Abstract: Hyperthermia, a therapeutic technique used in cancer treatment, relies on the precise heating of target tissues to enhance the effectiveness of radiotherapy or chemotherapy. To achieve this, electromagnetic (EM)-based hyperthermic technologies require accurate simulation of human tissue properties under hyperthermia conditions (40–48°C). However, existing tissue-mimicking phantoms face limitations, particularly at higher temperatures, hindering reliable testing of hyperthermia devices. This dissertation addresses this challenge by developing phantoms that replicate the dielectric and thermal properties of skin, fat, muscle, and tumour tissues at temperatures up to 50°C. This work improves the semi-solid phantom recipe proposed by Lazebnik et al. (2005) by replacing the gelling agent gelatine with agar-agar, thereby increasing the melting point while maintaining tissue-like behaviour. Additionally, the project will provide a thorough characterisation of the dielectric and thermal properties of these phantoms, ensuring they closely match the electromagnetic and thermal properties of real tissue across a range of frequencies and temperatures. The modified agar-based phantoms demonstrate successful replication of real tissue properties under hyperthermia conditions, exhibiting less than 20% deviation from literature values. This confirms their validity for precise laboratory evaluation of electromagnetic (EM)-based medical devices, particularly for hyperthermia treatment planning and device calibration. By developing these phantoms, this research aims to enable the accurate testing and optimisation of EM-based hyperthermic devices in the laboratory, reducing the need for extensive preclinical trials and accelerating the transition to clinical validation. This work has the potential to significantly improve the safety and efficacy of hyperthermic technologies, ultimately contributing to better outcomes in cancer treatment and other medical applications. Description: B.Sc. (Hons)(Melit.)

2025-01-01T00:00:00Z /library/oar/handle/123456789/140595 2025-10-27T09:04:01Z 2025-01-01T00:00:00Z

Title: Exploring late-time cosmic evolution through dynamical systems in non-minimally coupled scalar-tensor models Abstract: This dissertation explores late-time cosmic evolution through the lens of scalartensor theories using a dynamical systems approach. Although the Λ Cold Dark Matter (ΛCDM) model has been successful in accounting for the accelerated expansion of the Universe, it faces persistent theoretical challenges such as the cosmological constant problem and observational tensions like the Hubble constant (H0) discrepancy. Scalar fields central to early-universe inflation and now considered candidates for dark energy offer a promising extension to standard cosmology. We construct dynamical systems by introducing non-minimal scalar field couplings into the cosmological equations, focussing on exponential and power-law potentials. The resulting systems are analysed using critical points, stability theory, and phase portraits to reveal attractor solutions and asymptotic behaviours. Our study demonstrates that certain scalar-field models can replicate the late-time acceleration of the Universe while offering richer dynamics than the cosmological constant alone. Many of the models explored exhibit the key critical points found in ΛCDM and, in some cases, additional points that reflect a more nuanced evolution profile. These results underscore the utility of dynamical systems in probing beyond-ΛCDM scenarios and provide a pathway for future observational tests of scalar-tensor cosmologies. Description: B.Sc. (Hons)(Melit.)

2025-01-01T00:00:00Z /library/oar/handle/123456789/140592 2025-10-24T14:32:39Z 2025-01-01T00:00:00Z

Title: Optical spring limitations in phonon lasing Abstract: This report provides a comprehensive review of optomechanical systems and cavity physics, with a focus on the effects of the optical spring effect, particularly in multimode phonon lasing. In contrast with single-mode coupling in traditional optomechanical cavities, this research explores how the optical spring effect has a comparatively smaller impact in systems with multiple mechanical modes. This is especially relevant when these systems achieve a mode-locked state through techniques like Floquet dynamics. Experimental and theoretical investigations suggest that multimode phonon lasing can lead to significantly improved long-term frequency stability when compared to single-mode operation. This analysis delves into the conditions under which the frequency shifts induced by the optical spring effect remain smaller than the mechanical linewidths, specifically considering three modes in the multimode system, ensuring robust mode locking and stable operation. This work paves the way for future exploration into increasing the mode count for multimode systems to potentially achieve even stronger effects and enhance the functionalities of these systems. Description: B.Sc. (Hons)(Melit.)

2025-01-01T00:00:00Z