Computational Speedups Using Small Quantum Devices.

Area of Science:

• Quantum Computing
• Computational Complexity
• Algorithm Design

Background:

• Current quantum computers possess a limited number of qubits (M).
• The potential for small quantum devices to outperform classical computers on large-scale problems remains an open question.
• The 3-satisfiability problem is a fundamental challenge in computational complexity.

Purpose of the Study:

• To investigate if small quantum computers can provide a genuine speedup for algorithms.
• To develop a hybrid quantum-classical approach for solving large 3-satisfiability problems.
• To demonstrate the practical utility of limited-qubit quantum devices.

Main Methods:

• Development of a novel hybrid quantum-classical algorithm.
• Application of the algorithm to 3-satisfiability problems with problem sizes (n) significantly larger than the number of qubits (M).
• Comparative analysis against fully classical algorithms.

Main Results:

• The hybrid algorithm achieves a significant speedup compared to its classical counterpart.
• The approach demonstrates effective problem-solving capabilities even when n >> M.
• Validation of the affirmative answer to whether small quantum devices can accelerate algorithms for larger problems.

Conclusions:

• Small quantum computers, when integrated into hybrid algorithms, can offer substantial computational advantages.
• The presented hybrid algorithm provides a viable method for tackling large 3-satisfiability instances.
• This work supports the ongoing development of practical quantum computing applications.