The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for solving linear systems of equations and theoretically promises exponential speed-up over its classical counterparts. However, its practical implementation can demand substantial circuit depth, increasing noise on near-term quantum devices. The hybrid HHL algorithm tackles this challenge by leveraging quantum phase estimation to extract eigenvalue information, thereby reducing the number of multicontrolled unitary operators required. In this work, we further refine the hybrid HHL approach, reducing not only the number of multi-controlled unitary operators but also the overall resource usage. As a result, our method is expected to reduce noise stemming from deeper circuits and enhance the practical viability of the HHL algorithm for near-term quantum devices.

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