Solving linear systems on quantum hardware with hybrid HHL++

Experimental validation of Hybrid HHL++, showing strong agreement between quantum and exact solutions for portfolio optimization. For the quantum executions we utilized Quantinuum’s trapped-ion device H1, its emulator and noiseless simulation. This plot shows that even on today’s noisy quantum computers, our hybrid approach can produce solutions that are very close to the exact solution.

This paper tackles a very practical question: how can we make quantum computers useful today, even though they are still noisy and limited? One of the most important tasks in science, finance, and engineering is solving systems of equations. Quantum algorithms like HHL promise major speedups for these problems, but in practice they are still too complex for current hardware.

To address this, we introduce Hybrid HHL++, which combines quantum and classical computing. It carefully splits the work: the quantum part handles what it does best, while classical steps simplify and guide the process, bringing us closer to real-world quantum applications. It is shown that this approach improves solution quality for portfolio optimization while using fewer resources, highlighting a practical path forward for quantum computing.This marked the largest execution of a HHL circuit by that time.