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Abstract:

Identifying the types of algorithms and applications that can be solved on today's quantum computers is one of the fundamental goals of modern quantum algorithms research. Underpinning this effort is the potential leap in human technology should it be shown that quantum computers can perform useful classically-intractable calculations in the absence of quantum error correction. In this thesis we study the new paradigm of variational quantum algorithms (VQAs), designed specifically to solve optimisation problems on near-term hardware. We develop several novel algorithms spanning a range of application areas and provide estimates of the physical resources required to match classical methods. Thereafter, we attempt to run these algorithms on current quantum computers, probing their capabilities in the process. In this endeavour, we also develop our own algorithmic solution to device noise in the form of a new approach to approximate quantum circuit recompilation. We begin with studying the feasibility of simulating the time evolution of quantum systems on current quantum computers, an important problem due to its classical hardness. We build an algorithm specifically focused on the electron-phonon Hamiltonian and subsequently realise the first demonstration of obtaining its dynamics on real quantum hardware. Subsequently, we test whether a similar result is possible for time-evolution based VQAs. For this we construct a near-term quantum computing approach to dynamical mean-field theory and find that whilst not possible currently, such an algorithm could be realistically evaluated on the next generation of quantum computers in the immediate future. We then show how quantum circuits can be used as machine learning models and apply them to self-supervised learning, one of the most demanding tasks in deep learning. Through our experiments we observe a numerical advantage for the learning of visual representations using small-scale quantum neural networks over equivalently structured classical networks, a first step on the ladder towards general quantum advantage. Through this, we also highlight the potential of near-term quantum computing in problems with only empirically established classical complexity

Abstract:

Many complex systems can spontaneously oscillate under nonperiodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical nonlinear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators.

Abstract:

Variational quantum algorithms (VQAs) are increasingly being applied in simulations of strongly bound (covalently bonded) systems using full molecular orbital basis representations. The application of quantum computers to the weakly bound intermolecular and noncovalently bonded regime, however, has remained largely unexplored. In this work, we develop a coarse-grained representation of the electronic response that is ideally suited for determining the ground state of weakly interacting molecules using a VQA. We require qubit numbers that grow linearly with the number of molecules and derive scaling behavior for the number of circuits and measurements required, which compare favorably to traditional variational quantum eigensolver methods. We demonstrate our method on IBM superconducting quantum processors and show its capability to resolve the dispersion energy as a function of separation for a pair of nonpolar molecules—thereby establishing a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, we conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but nevertheless chemically ubiquitous and biologically important regime. Finally, we perform experiments on simulated and real quantum computers for systems of three, four, and five oscillators as well as oscillators with anharmonic onsite binding potentials; the consequences of the latter are unexamined in large systems using classical computational methods but can be incorporated here with low computational overhead.

Abstract:

The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human annotation. However, the staggering computational complexity of these methods is such that for state-of-the-art performance, classical hardware requirements represent a significant bottleneck to further progress. Here we take the first steps to understanding whether quantum neural networks (QNNs) could meet the demand for more powerful architectures and test its effectiveness in proof-of-principle hybrid experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale QNN over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks.