Quantum computing promises to revolutionise many fields, including chemical simulations and machine learning. At the present moment those promises have not been realised, due to the large resource requirements of fault tolerant quantum computers, not excepting the scientific and engineering challenges to building a fault tolerant quantum computer. Instead, we currently have access to quantum devices that are both limited in qubit number, and have noisy qubits.
This thesis deals with the challenges that these devices present, by investigating applications in quantum simulation for molecules and solid state systems, quantum machine learning, and by presenting a detailed simulation of a real ion trap device. We firstly build on a previous algorithm for state discrimination using a quantum machine learning model, and we show how to adapt the algorithm to work on a noisy device. This algorithm outperforms the analytical best POVM if ran on a noisy device. We then discuss how to build a quantum perceptron – the building block of a quantum neural network.
We also present an algorithm for simulating the Dynamical Mean Field Theory (DMFT) using a quantum device, for two sites. We also discuss some of the difficul- ties found in scaling up that system, and present an algorithm for building the DMFT ansatz using the quantum device. We also discuss modifications to the algorithm that make it more ‘device-aware’.
Finally we present a pule-level simulation of the noise in an ion trap device, designed to match the specifications of a device at the National Physical Laboratory (NPL), which we can use to direct future experimental focus. Each of these sections is preceded by a review of the relevant literature.