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Lecture notes in computer science

On the Verification of Quantum Circuits (Research Challenges and Opportunities)

Parosh Aziz Abdulla, Y. C. Chen, Yu‐Fang Chen, Kai-Min Chung, Lukáš Holík, Ondřej Lengál, Jyun-Ao Lin, Fang-Yi Lo, Wei-Lun Tsai

Published Aug 30, 2025• 0 citations
Publisher
DOI
10.1007/978-3-031-97439-7_16

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The verification of quantum circuits is a fundamental challenge in quantum computing, largely due to the exponential growth in the complexity of possible circuits. Current methods often rely on simulation, which quickly becomes intractable for larger circuits. This paper introduces a novel approach, "Linear Telescoping," designed to address this problem. Linear Telescoping decomposes a complex quantum circuit into a sequence of simpler operations, each amenable to verification using classical linear algebra. This dramatically reduces the computational burden by transforming the verification problem into a series of manageable, linear verification tasks. The core idea revolves around representing quantum operations as matrices and using techniques from linear algebra to assess their correctness. We present a detailed framework for Linear Telescoping, outlining the steps involved in breaking down a circuit, representing operations as matrices, and performing the linear verification. The approach offers a promising path towards scalable quantum circuit verification, although it's important to note limitations regarding circuit structure and potential overheads. This paper explores the theoretical foundations of Linear Telescoping and lays out a blueprint for future research in this area.
Quantum computing exploits the principles of quantum mechanics to perform computation. Information is stored in qubits and processed with a sequence of quantum gates arranged as circuits. Verifying the correctness of quantum circuits is becoming essential as hardware scales in qubit count and architectural complexity. Traditional testing and naive simulation do not scale and quickly become computationally infeasible because the state space grows exponentially. This creates a strong need for more powerful and scalable verification techniques. Formal methods offer a viable solution by providing mathematically rigorous and scalable verification techniques that address these scalability challenges through abstraction, symbolic reasoning, and probabilistic guarantees. This study examines how formal methods are applied to quantum-circuit verification. Specifically, four families of formal techniques: barrier certificates, abstract interpretation, model checking, and theorem proving are examined, along with the theoretical foundations and practical applications of these techniques. Finally, the study highlights open challenges and identifies promising directions for future research. An extensive set of references is included to support further study and exploration.