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arXiv:1309.0005 · Nature Physics

Experimental verification of quantum computation

Stefanie Barz, Joseph F. Fitzsimons, Elham Kashefi, Philip John Walther

Published Sep 29, 2013• 148 citations
arXivHTMLPDF
DOI
10.1038/nphys2763

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•Sep 6, 2026•0 citations
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.
With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation within the framework of interactive proofs has been fruitful for addressing this problem. Specifically, an untrusted agent (prover) alleging to perform quantum computations can have his claims verified by another agent (verifier) who only has access to classical computation and a small quantum device for preparing or measuring single qubits. However, when this quantum device is prone to errors, verification becomes challenging and often existing protocols address this by adding extra assumptions, such as requiring the noise in the device to be uncorrelated with the noise on the prover's devices. In this paper, we present a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions. This protocol is based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input. We also perform a simulation of the protocol, for a one-qubit computation, and find the error thresholds when using the qubit repetition code as well as the Steane code.
Quantum computing is rapidly advancing, demanding robust verification techniques to ensure the correctness and reliability of quantum algorithms. Current verification methods often suffer from limitations in scalability and computational complexity, hindering the exploration of larger and more complex quantum systems. This paper introduces a novel quantum verification algorithm, based on adaptive topology, leveraging quantum entanglement to achieve more precise and efficient validation of geometric quantum states. The core mechanism utilizes a dynamically adjusted topology to represent and verify the state of a quantum system, effectively streamlining the verification process. We demonstrate the algorithm's effectiveness through theoretical analysis and preliminary experimental results, showcasing its potential to significantly enhance the accuracy and speed of quantum verification. The research addresses the limitations of traditional verification approaches and proposes a new paradigm for quantum system validation.