Modest-sized quantum computers now exist in the real world and the next generation of these devices may be too big to simulate on a classical computer. A quantum computer which is too big to classically simulate has an inherent computational advantage of sorts. How can we harness this advantage, sufficiently protect it from noise, and use it to solve computational problems of interest? Can we achieve these goals without incurring large overheads such as those required for fault-tolerant quantum computation? These are the central questions in an emerging field of approximate quantum computing which touches upon areas including quantum advantage, quantum simulation, hardware-efficient algorithms, heuristic quantum algorithms, error mitigation, and more.
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