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Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum…
The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to…
Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum…
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
Solving Hamiltonian matrix is a central task in quantum many-body physics and quantum chemistry. Here we propose a novel quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the…
Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing…
Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…
Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We…
The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue,…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
While quantum computers are a very promising tool for the far future, in their current state of the art they remain limited both in size and quality. This has given rise to hybrid quantum-classical algorithms, where the quantum device…