Design parallel and sequential quantum algorithms via spectral element method on distributed quantum architectures

Area of Science:

• Quantum Computing
• Computational Science
• Numerical Analysis

Background:

• Near-term quantum hardware faces significant qubit capacity limitations, hindering complex simulations.
• The spectral element method (SEM) is a powerful numerical technique for high-accuracy simulations.
• Integrating advanced computational methods with quantum computing requires addressing hardware constraints.

Purpose of the Study:

• To develop a hybrid framework that overcomes qubit limitations in near-term quantum hardware.
• To enable high-accuracy simulations on current quantum devices by integrating SEM with distributed quantum computing.
• To demonstrate a scalable and practical solution for quantum-accelerated simulations.

Main Methods:

• A hybrid framework integrating the spectral element method (SEM) with distributed quantum computing.
• Domain decomposition techniques, including additive and multiplicative Schwarz methods, to divide global problems into smaller subproblems.
• Local application of the HHL algorithm to subproblems to achieve quantum speedups within hardware constraints.

Main Results:

• The proposed framework successfully reduces qubit requirements for complex simulations.
• Numerical results validate the effectiveness and scalability of the hybrid approach.
• High-accuracy simulations are achievable despite the qubit limitations of near-term quantum hardware.

Conclusions:

• The hybrid SEM and distributed quantum computing framework offers a practical solution for near-term quantum hardware.
• This approach effectively addresses the critical limitation of qubit capacity.
• The method enables quantum speedups for complex simulations without exceeding current hardware constraints.