Quantum computers promise to efficiently solve not only problems believed tobe intractable for classical computers, but also problems for which verifyingthe solution is also considered intractable. This raises the question of howone can check whether quantum computers are indeed producing correct results.This task, known as quantum verification, has been highlighted as a significantchallenge on the road to scalable quantum computing technology. We review themost significant approaches to quantum verification and compare them in termsof structure, complexity and required resources. We also comment on the use ofcryptographic techniques which, for many of the presented protocols, has provenextremely useful in performing verification. Finally, we discuss issues relatedto fault tolerance, experimental implementations and the outlook for futureprotocols.
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