Formal Specification of Quantum Algorithms via Tensor Networks

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum algorithms offer the potential for exponential speedups over classical algorithms for specific computational tasks. However, the inherent complexity and probabilistic nature of quantum mechanics pose significant challenges in verifying and understanding these algorithms. Traditional approaches, relying on simulations and theoretical arguments, often struggle to provide definitive proof of correctness and to guide the optimization of quantum circuits. This paper proposes a novel approach to formally specifying quantum algorithms by representing them using tensor networks. Tensor networks provide a powerful mathematical framework for describing multi-dimensional quantum states and operations, allowing for a precise and rigorous description of the algorithm's evolution. We demonstrate how tensor network techniques can be used to capture the unitary transformations that constitute a quantum algorithm, providing a foundation for automated verification and optimization strategies. The key contribution of this work is the application of tensor networks to the formal specification of quantum algorithms, addressing a critical gap in the field and paving the way for more robust and reliable quantum computation. The formal specification allows for the definition of the algorithm's state space and the evolution operator, enabling the application of mathematical techniques to analyze and improve the algorithm's performance.

DOI: 10.5281/zenodo.22192527

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