Extending UNIQuE: Quantum Simulation Speedup for the HHL Algorithm

2026-04-27

AI Summary

This work addresses the exponential growth in computational complexity associated with traditional state-vector methods when simulating the HHL quantum algorithm, which scales with both system size and the maximum eigenvalue. To overcome this limitation, the authors develop an efficient classical simulator based on the UNIQuE framework, extending it for the first time to the HHL algorithm. By leveraging the structural properties of UNIQuE, the proposed approach optimizes the classical simulation of quantum circuits, reducing the complexity to depend solely on the number of qubits required to represent the system—thereby eliminating dependence on the maximum eigenvalue. Experimental results on small-scale linear systems demonstrate that the method significantly outperforms the Intel Quantum Simulator in runtime, confirming its effectiveness and superiority.

Abstract

In an extension of the Unconventional Noiseless Intermediate Quantum Emulator, this work introduces a classical emulation of the quantum Harrow-Hassidim-Lloyd algorithm for sampling from the solution space of linear systems. The emulated HHL algorithm scales exponentially with the number of qubits required to represent the linear system, which is an advantage over the state vector simulation of the HHL algorithm, which scales exponentially as a function of both the size of the linear system and the magnitude of its largest (scaled) eigenvalue. We benchmark our emulator by comparing it with the Intel Quantum Simulator and demonstrate a runtime advantage for small linear systems.

Problem

• quantum simulation
• HHL algorithm
• linear systems
• classical emulation
• computational scaling

Innovation

• quantum simulation
• HHL algorithm
• classical emulation
• UNIQuE
• linear systems