https://www.um.edu.mt/library/oar/handle/123456789/132246 Sun, 05 Apr 2026 08:28:37 GMT 2026-04-05T08:28:37Z https://www.um.edu.mt/library/oar/handle/123456789/144840 Title: Variational quantum algorithms for combinatorial optimisation : navigating the NISQ era Abstract: Optimisation algorithms aim to solve a wide range of problems, including those related to physical systems and everyday challenges. Examples include optimising the shape or material distribution of structures to maximise strength and minimise weight, designing optimal investment portfolios, balancing risks and returns, planning efficient routes, optimising container placement on ships, and improving the manufacturing plan in factories. Optimising manufacturing plans in factories is the primary focus of my research. The goal of each optimisation problem typically involves reducing the costs by adjusting the algorithm’s configuration. For instance, in route optimisation, costs typically involve time and fuel, but constraints such as time windows or availability at destinations must also be considered. Incorporating more parameters can lead to solutions that better reflect real-world scenarios. However, increasing the number of parameters adds complexity to the problem, and more resources are required to achieve an optimal solution. In many practical applications, finding the exact optimal solution is often unnecessary. In many cases, finding a solution optimising the current status within an acceptable time frame is sufficient. The challenge of optimising the manufacturing plan in factories, often referred to as the Job-Shop Scheduling Problem (JSSP), involves balancing several parameters. These include sale orders and their requested delivery dates, the expected arrival dates for raw materials derived from the bill of materials of the products listed in sale orders, and resource availability, both machines and human resources required in the production process. Additionally, the process is subject to several constraints, such as sequential dependencies—for example, producing one component before another—and process coordination, such as synchronising different production stages, where manufacturing must be completed before packaging can begin. Operators balance these parameters and constraints to minimise costs, such as reducing changes in the configuration of machines or reducing clean-up tasks between the manufacturing of different components and maximising resource utilisation while keeping up with promised delivery dates to customers. The JSSP is a combinatorial optimisation problem that is NP-hard, meaning it becomes computationally difficult to compute as the number of parameters increases using classical computing methods. However, there are still various classical approaches to the problem, which result primarily in heuristic solutions. These include Integer Linear Programming (ILP), Dispatching Rules, Genetic Algorithms, or Simulated Annealing. In this dissertation, I investigate the quantum computing algorithm Quantum Approximate Optimization Algorithm (QAOA) to address the JSSP problem. Quantum computing is still in its infancy. Its foundation lies in quantum mechanics, which involves mathematical concepts such as linear algebra, complex numbers, and probability amplitudes. Key properties of quantum mechanics like superposition, entanglement and quantum interference allow quantum computers to explore the solution space of a problem more effectively than classical computers. In this dissertation, I first examine the properties of quantum mechanics, which can help me investigate QAOA and study tools that I can use to program a quantum computer. Then, I explore the mathematical models used to represent the problem, in this case, the Job-Shop Scheduling Problem (JSSP). JSSP involves several interdependent parameters. I expressed these parameters in mathematical models containing these interactions, some containing three or more parameters interacting with each other. The result was mathematical formulations involving problems with multivariate objective functions, which were then solved with QAOA. Another objective of my dissertation was to explore the possibility of reducing resource requirements while still achieving sufficiently good results based on relevant figures of merit. In this dissertation, I investigate various configurations of QAOA, evaluating their success while factoring in the computational resources required for execution to achieve an optimal result. I propose a configuration of QAOA, which I call k-interaction Angle QAOA (ka-QAOA). I show that ka-QAOA performs comparably to other proposed QAOA configurations while reducing the computational resources required to achieve similarly good approximations. While the results are promising, as parameters in problems increase, testing the different configurations of QAOA becomes a daunting task. More robust, error-free quantum computers are needed to model and solve real-world optimisation problems like JSSP. In the interim, we can still experiment with problems having few parameters to find optimal quantum algorithms. Description: M.Sc.(Melit.) Wed, 01 Jan 2025 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/144840 2025-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/140597 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.) Wed, 01 Jan 2025 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/140597 2025-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/140596 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.) Wed, 01 Jan 2025 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/140596 2025-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/140595 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.) Wed, 01 Jan 2025 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/140595 2025-01-01T00:00:00Z