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Phase Coordinate Uncomputation in Quantum Recursive Fourier Sampling.

Christoffer Hindlycke1, Niklas Johansson1, Jan-Åke Larsson1

  • 1Department of Electrical Engineering, Linköping University, 581 83 Linköping, Sweden.

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Summary
This summary is machine-generated.

Recursive Fourier Sampling (RFS) demonstrates quantum advantage. New phase space descriptions reveal uncomputation is key to RFS quantum advantage by removing phase coordinate garbage, explaining its limitations.

Keywords:
phase kickbackquantum advantagequantum algorithmsquantum oraclesuncomputation

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Area of Science:

  • Quantum computing
  • Computational complexity theory

Background:

  • Recursive Fourier Sampling (RFS) is an early problem demonstrating quantum advantage.
  • RFS is known to be outside the Merlin-Arthur complexity class.

Purpose of the Study:

  • To provide a new description of quantum algorithms using phase space terminology.
  • To enhance the understanding of the quantum advantage in RFS.

Main Methods:

  • Describing quantum computation in phase space terminology.
  • Analyzing the necessity of uncomputation for RFS.

Main Results:

  • Phase space terminology offers a clearer understanding of the quantum advantage in RFS.
  • Uncomputation is crucial for RFS quantum advantage, specifically removing phase coordinate garbage.

Conclusions:

  • The necessity of uncomputation in RFS is explained by phase space dynamics.
  • Phase coordinate garbage uncomputation is the reason for the limitations of the quantum advantage in RFS.