Realizing Shor's algorithm with topological acoustic phase bits.

Area of Science:

• Quantum-inspired computing
• Nonlinear acoustics
• Topological phase transitions

Background:

• Quantum algorithms offer new computational paradigms.
• Classical physical systems can achieve parallelism through correlations.
• Exploring alternative computing frameworks is crucial for advancing computational power.

Purpose of the Study:

• To introduce a quantum-inspired computing framework using phase bits (phibits).
• To demonstrate the factorization of composite integers using this novel acoustic platform.
• To validate the accuracy and robustness of the phibit implementation.

Main Methods:

• Development of a theoretical framework based on phase bits (phibits).
• Utilizing nonlinear topological acoustic waves to represent logical units.
• Implementation of the phase cache and operator spectra shift for computational operations.
• Experimental demonstration of Shor's algorithm's period-finding core.

Main Results:

• Successful factorization of composite integers 15 and 35.
• Experimental probability distributions closely matched theoretical predictions.
• Validation of the phibit implementation's accuracy.
• Demonstration of the nonlinear acoustic platform's robustness.

Conclusions:

• Phase bits (phibits) offer a viable approach for quantum-inspired computation.
• Nonlinear acoustic waves provide a robust platform for implementing phibit-based algorithms.
• This framework shows potential for tackling complex computational problems.
• The study validates a novel method for harnessing physical phenomena for computation.