Efficient decomposition methods for controlled-R _n using a single ancillary qubit.

Area of Science:

• Quantum Computing
• Quantum Information Science
• Theoretical Computer Science

Background:

• Controlled-R_n gates are essential in quantum computation.
• Existing decomposition methods often require numerous gates or complex architectures.
• An ancillary qubit approach offers a potential for gate reduction.

Purpose of the Study:

• To develop a more efficient decomposition method for controlled-R_n gates.
• To reduce the number of gates required for quantum Fourier transform circuits.
• To propose decompositions suitable for nearest-neighbor quantum architectures.

Main Methods:

• Extending existing ancillary qubit-based decomposition techniques.
• Analyzing gate counts for controlled-R_n decomposition.
• Investigating nearest-neighbor mapping with local CNOT gates.
• Minimizing circuit depth for specific architectures.

Main Results:

• A novel decomposition method achieving fewer gates than current best results for controlled-R_n.
• Confirmation of gate reduction in quantum Fourier transform circuits.
• An efficient decomposition mapped to nearest-neighbor architectures using local CNOT gates.
• Achieved a minimum circuit depth of 5 gate steps on nearest-neighbor architectures.

Conclusions:

• The proposed method offers significant improvements in gate efficiency for controlled-R_n decomposition.
• The findings contribute to the development of more practical and scalable quantum algorithms.
• The optimized decompositions are well-suited for current and future quantum hardware limitations.