Paper 2025/1915

A Framework for Efficient Quantum Implementations of Linear Layers

Abstract

Quantum depth plays a critical role in determining the performance of quantum implementations, yet quantum programming tools often fail to produce depth-optimal compilations of linear layers. In this work, we present a systematic and automated framework that reorders quantum gate sequences of linear layers to obtain depth-efficient quantum implementations. Our method consistently produces circuits with lower depth compared to prior implementations. We apply the framework to a range of cryptographic operations, including the AES MixColumn, internal layers of the AES S-box, binary field squaring, and modular reduction in binary field multiplication. In all these cases, our method achieves meaningful reductions in quantum depth—for example, lowering the depth of the AES MixColumn and S-box circuits. This work explores optimal quantum circuit designs for quantum programming tools, improves the accuracy of quantum resource estimation for cryptanalysis, and supports more realistic evaluations of post-quantum security.