Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates

Area of Science:

• Quantum Information Science
• Data Processing
• Computational Mathematics

Background:

• Conventional uniform sampling in log-polar coordinates leads to central oversampling, resulting in inefficient data representation and computational waste.
• Adaptive sampling offers a potential solution to optimize data density and information content in log-polar coordinate systems.
• The integration of adaptive sampling into quantum data processing remains an underexplored area with significant potential.

Purpose of the Study:

• To introduce and develop an adaptive sampling method for quantum data processing in log-polar coordinates.
• To propose a quantum representation model for adaptively sampled data.
• To demonstrate the practicality of this model through a scaling up algorithm and its quantum circuit implementation.

Main Methods:

• Development of a quantum representation model where polar angle sampling limits are dependent on log-polar radius.
• Design of a scaling up algorithm utilizing biarcuate interpolation for quantum adaptive sampled data.
• Implementation of the algorithm in a quantum circuit.

Main Results:

• A novel quantum representation model for adaptive sampled data in log-polar coordinates was successfully proposed.
• A scaling up algorithm and its quantum circuit implementation were developed, demonstrating the model's practicality.
• The feasibility of the proposed adaptive sampling approach in quantum data processing was verified through numerical examples.

Conclusions:

• Adaptive sampling is a viable and efficient strategy for quantum data processing in log-polar coordinates, overcoming limitations of conventional methods.
• The proposed quantum representation model and scaling algorithm provide a foundation for more efficient quantum information processing.
• Further research into the complexities of adaptive sampling interpolation can lead to enhanced quantum algorithms.