Accreditation for Analogue Quantum Computing Systems

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The use of quantum systems as information carrying and processing units promises a new paradigm for computation that could offer significantly greater computational power than existing "classical" computing in crucial tasks, from chemistry, material science, biology to optimisation, machine learning and finance. This theoretical possibility, during the last decade, has started to emerge as a very realistic prospect, where governmental and industrial initiatives have contributed to the development of quantum computing systems that have started offering computational quantum advantage.One of the most important practical and theoretical question is how to verify or benchmark the performance of a quantum computing system, especially where it cannot be simulated with classical computers in reasonable time. The practical relevance of this question is evident: has a quantum computer achieved quantum advantage ? Is the computation correct or do imperfections compromise the performance advantage, and thus , should a client pay a quantum computing provider?Many verification and benchmarking methods have been developed, each with their strengths and short-comings (Eisert et al Nature Reviews Physics 2020). To name a few: a universal method for verifying any digital quantum computation efficiently has been developed and realised (e.g. Bartz, Fitzsimons, Kashefi, Walther Nature Physics 2013), but requires a digital, fault-tolerant system, and requires additional overhead. If one is satisfied with a performance benchmarking that relies on several assumptions on the errors , randomised benchmarking works. Improving the efficiency of reconstructing the output quantum state is still exponentially expensive but has applications (e.g. "efficient" tomography and direct fidelity estimation). While recently some methods have also been adapted for noisy intermediate scale quantum devices (Leichtle et al PRX Quantum 2021, Ferracin, Kapourniotis, Datta NJP 2019). Quantum computing devices can broadly be grouped into two categories. Digital quantum computers (DQC), similar to classical computers the possible operations are discrete, for example it consist from a set of a finite (universal) gate set. Analogue quantum computers (AQC) that use quantum systems that evolve continuously in time (under some tuneable interaction). In AQC one includes quantum simulators, quantum annealers (such as D-Wave) and adiabatic quantum computers . The latter category currently scales better in terms of qubits but is harder to apply quantum error correction techniques. Thus, at least in the near-term, it is very likely that AQC may provide more examples of useful quantum advantage. Interestingly, while extensive work has been done in verifying and benchmarking DQC, little has been done for AQC, since the techniques do not generally apply, opening up an exciting gap in the research. In this project we will address verification and benchmarking for analogue quantum computing, building on the existing methods for DQC. We will first focus on extending early results on the analogue version of randomised benchmarking, generalising the mathematical tools (twirling, approximate 2-designs, etc), providing the theoretical basis and modifying the method to be practically implementable. We will then concentrate on other methods of verification and explore which ones can be modified for each of the different analogue quantum computing systems of interest such as quantum simulators, quantum annealing, adiabatic quantum computers.