Verification of quantum computation: An overview of existing approaches

TL;DR

This paper reviews various methods for verifying quantum computations, highlighting their structures, complexities, and resource requirements, and discusses cryptographic techniques, fault tolerance, and experimental challenges in quantum verification.

Contribution

It provides a comprehensive overview and comparison of existing quantum verification approaches, emphasizing their advantages, limitations, and future prospects.

Findings

Cryptographic techniques enhance verification protocols

Resource requirements vary across methods

Fault tolerance remains a key challenge

Abstract

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.