Quantum interference enables constant-time quantum information processing

Area of Science:

• Quantum Computing
• Signal Processing
• Information Theory

Background:

• The Fast Fourier Transform (FFT) is crucial for signal processing but requires periodic inputs, limiting its applicability.
• The Kravchuk-Fourier Transform (KT) handles arbitrary-length finite strings, vital for image processing, but has a high runtime.
• Quantum effects may offer speedups for computational tasks, but efficient quantum algorithms for transforms are needed.

Purpose of the Study:

• To develop a one-step computation for a fractional quantum Kravchuk-Fourier transform (KT).
• To explore a quantum approach that overcomes the runtime limitations of classical KT.
• To leverage quantum architectures for efficient signal processing applications.

Main Methods:

• Utilized a quantum d-nary (qudit) architecture for computation.
• Employed a single quantum gate, potentially using the multiphoton Hong-Ou-Mandel effect.
• Focused on a one-step computation of the fractional quantum KT.

Main Results:

• Achieved a one-step computation of the fractional quantum KT.
• The quantum qudit architecture demonstrated processing time independent of input size.
• The proposed method offers a significant speedup over classical KT implementations.

Conclusions:

• The developed quantum KT computation provides a scalable and efficient alternative for signal processing.
• This quantum approach has the potential to accelerate applications in digital image processing, computer vision, and beyond.
• Existing quantum technologies can be scaled to implement this quantum KT for diverse real-world applications.