Hybrid Quantum-Classical Computation

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Hybrid quantum-classical computing combines the power of quantum and classical processors to compute faster. This is of particular relevance in the current Noisy Intermediate-Scale Quantum (NISQ) computing era, when quantum processors are still very limited. Moreover, hybrid computing bears the strongest potential for reaching a practical quantum advantage, as it will take a long time before fault-tolerant quantum computers completely replace classical machines, if ever. For these reasons, hybrid quantum-classical architectures have taken center stage in the recent heuristic exploration of the potential of quantum computers. A rigorous framework is, however, painfully lacking to date. The goal of project HQCC is to put this important field onto solid theoretical footing. We aim to address the fundamental questions about the power of hybrid computation:- What problems are more amenable to the hybrid quantum-classical approach? - With what algorithms can we solve them?- What data structures and encodings perform better under this approach? - Can we classify how hard these problems are in this context, namely can we define hybrid quantum-classical computational complexity classes? To address these questions, project HQCC is structured into three complementary parts: one dealing with complexity-theoretic aspects (such as the regimes in which quantum advantage is possible), one concerned with algorithms for hybrid computation (for example, variational quantum algorithms and the most efficient ways to encode data into them), and one dealing with learning and training processes. These three components will be developed in dialogue with each other to extract a comprehensive understanding of hybrid quantum-classical computation.