Recompilation-enhanced simulation of electron–phonon dynamics on IBM quantum computers

Journal article

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

Authors: Jaderberg, B; Eisfeld, A; Jaksch, D; Mostame, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: New Journal of Physics
• Volume: 24
• Issue: 9
• Pages: 093017-093017
• Publication date: 2022-08-17
• DOI: 10.1088/1367-2630/ac8a69
• EISSN: 1367-2630
• ISSN: 1367-2630
• Language: English
• Keywords: Quantum; Noise (video); Physics; Quantum computer; Quantum simulator; Quantum dynamics; Phonon; Quantum mechanics; Statistical physics; Computer science; Artificial intelligence; Hamiltonian (control theory); IBM