Verification of quantum computation: An overview of existing approaches
This is an incremental overview addressing the verification problem for quantum computing researchers and developers.
The paper reviews existing approaches to verifying quantum computations, comparing their structure, complexity, and resource requirements, and discusses the use of cryptographic techniques and future challenges.
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether quantum computers are indeed producing correct results. This task, known as quantum verification, has been highlighted as a significant challenge on the road to scalable quantum computing technology. We review the most significant approaches to quantum verification and compare them in terms of structure, complexity and required resources. We also comment on the use of cryptographic techniques which, for many of the presented protocols, has proven extremely useful in performing verification. Finally, we discuss issues related to fault tolerance, experimental implementations and the outlook for future protocols.