LuGo: an Enhanced Quantum Phase Estimation Implementation

TL;DR

The paper tackles the practical bottlenecks of Quantum Phase Estimation by introducing LuGo, a parallelized framework that generates QPE circuits with greatly reduced duplication and circuit depth. By independently constructing each controlled-unitary e^{iH2^j} via matrix exponentials, LuGo achieves substantial reductions in circuit generation time and gate counts while preserving fidelity, enabling larger quantum linear system demonstrations (HHL) and complex simulations (e.g., Hele-Shaw flow) on powerful simulators. Key results show ~50x faster QPE circuit generation and >30x reductions in gates and depth for moderately large systems, with scalable performance on Frontier and preserved accuracy. These advances move QPE-based applications closer to practical, real-world quantum computing tasks, though further improvements in unitary decomposition and memory management are identified as future work.

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 circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit 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 without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves 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. We demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Figures (12)

• Figure 1: Standard QPE circuit generation process.
• Figure 2: QPE circuit to estimate phase of input $u$. The QPE algorithm will estimate the state of $\ket{u}$ and generate eigenvalues $\lambda$ of matrix $u$
• Figure 3: Quantum circuit for the HHL algorithm. The circuit includes the QPE part, eigenvalue reciprocal part, the conditional rotation part, and the inverse QPE part. Measurement of the ancilla qubit determines the success of the algorithm.
• Figure 4: Proposed LuGo designing process. We highlight the operation that obtained acceleration over standard QPE.321
• Figure 5: Time to generate HHL circuits using standard QPE and LuGo with single thread version. LuGo demonstrates advantages on circuit generation of QPE and inverse QPE, Other components of QPE circuits, and circuit storage in most of the scenarios.