Improved circuit implementation of the HHL algorithm and its simulations on QISKIT.

Area of Science:

• Quantum computing
• Quantum algorithms
• Linear systems

Background:

• The Harrow-Hassidim-Lloyd (HHL) algorithm offers a quantum approach to solving linear systems.
• Previous hybrid HHL algorithms reduced errors but did not optimize quantum resource usage in key stages.
• Existing implementations often lack detailed circuit process illustrations.

Purpose of the Study:

• To propose an improved circuit implementation of the HHL algorithm.
• To reduce quantum resource requirements in the HHL algorithm.
• To enhance error avoidance in quantum computations for linear systems.

Main Methods:

• Developing an improved circuit based on hybrid HHL and generic HHL circuit concepts.
• Verifying the improved circuit's feasibility using IBM's qiskit.
• Illustrating the improved circuit's performance on a [Formula: see text] linear system.

Main Results:

• The improved HHL circuit implementation effectively reduces quantum resources.
• The enhancement does not compromise the fidelity of the obtained results.
• The proposed method demonstrates superior error avoidance compared to existing HHL implementations.

Conclusions:

• The improved HHL circuit implementation offers a more efficient and robust solution for linear systems.
• This work advances practical applications of quantum algorithms by optimizing resource utilization.
• The findings pave the way for further development in quantum computational efficiency.