LuGo: an Enhanced Quantum Phase Estimation Implementation

Abstract: Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing redundant circuit duplication, as well as parallelization techniques to achieve faster circuit generation and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements while maintaining high accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to solve a $2^6\times 2^6$ system matrix by a factor of $50.68$ and over $31\times$ reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.