Resumen de Algorithmic techniques for noisy intermediate scale quantum computers
The field of quantum computing is generating huge excitement within the scientific community and beyond. The promise of quantum computing is to solve different problems in number theory and physics more efficiently than classical computing architectures. In addition, further advantages may be possible in the regimes of combinatorial optimisation and machine learning. However, many key engineering challenges remain and the full power of quantum computing appears to be a distant prospect. Nevertheless, in recent years small scale, noisy quantum computing devices have become widely available. This has resulted in the so-called Noisy Intermediate Scale Quantum Computing era (NISQ). This regime refers to quantum computers with several hundreds of qubits, where noise is present in any computation as error correction methods require an overhead that is too costly to implement. In this thesis we present an overview of current techniques employed in attempt to obtain useful computation using these small, noisy quantum computers. The aim of this thesis is to provide the reader with a good understanding of both the underlying principles behind these techniques and their practical utility, with a particular focus on error mitigation, quantum simulation and variational quantum algorithms. To set the stage, we begin by introducing the fundamental concepts of quantum computing and establishing the notation that will be employed throughout this thesis. Next, we delve into the core principles that underpin near-term quantum computing. Finally, we unveil the novel research conducted in this thesis, offering a fresh perspective on the subject matter. Firstly, we explore the budding field of error mitigation. Error mitigation methods aim to reduce the effect of noise in quantum computational processes, rather than remove noise completely. They require far less overhead than error correction methods. In particular, we present a framework used to unify several popular error mitigation techniques and explore their unification using numerical simulations. In our numerical experiments we find that the unified error mitigation methods offer an advantage over those of which they are made up. We then explore the implementation of these error mitigation techniques in a prime use case for quantum computers, quantum simulation. In particular, we explore simulating a quantum quench on a real digital quantum computer using a trotterised evolution. We employ several error mitigation techniques and compare their performance. In addition, we present a method to translate the famous algebraic Bethe ansatz to the form of a quantum circuit, which can then be used to prepare eigenstates of integrable models. We explore this approach with numerical simulations and implementation on a real quantum device, further exhibiting the utility of error mitigation in today’s quantum computers. We turn our attention to variational quantum algorithms (VQAs) and quantum machine learning (QML). VQAs are hybrid quantum-classical algorithms. They use a small amount of parameterised instructions provided to a quantum computer. These parameters are optimised classically to minimise a cost function which defines the problem to be solved. VQAs have emerged as a prime candidate to exhibit near-term useful quantum advantage, but recent research has shown these methods are plagued with optimisation difficulties. First, we present a resource frugal optimiser that can be used in all VQAs and many QML approaches. We then show how a QML framework can be used to produce a good quantum sensor using a novel approach called inference based quantum sensing. This chapter serves to give a broad overview of the ubiquity of VQAs and QML approaches. Finally, we conclude with a brief discussion of the prospects of quantum advantage using the techniques introduced in this work, as well as a discussion of future research directions
