Algorithm for solving quantum linear systems of equations with coherent superposition and extended applications.

The article focuses on the development of two quantum algorithms designed to solve quantum linear systems of equations with coherent superposition, which are significant for cryptographic applications. These algorithms differ in their approach to managing the data registers: one maintains entanglement with the data register while the other uses an auxiliary register to store solutions, allowing for disentanglement. The authors apply these algorithms as subroutines in various quantum cryptanalysis methods, including parallel Simon's algorithm and Grover Meets Simon algorithm, demonstrating their effectiveness in attacking lightweight symmetric ciphers. The paper also discusses the implications of these algorithms for quantum computing, particularly in the context of ion-trap quantum computers, and provides a rigorous analysis of their success probabilities and resource requirements. [Extracted from the article]