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Demonstration of quantum permutation algorithm with a single photon ququart.

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  • 1MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, and Department of Applied Physics, Xi'an Jiaotong University, Xi'an 710049, China.

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Summary
This summary is machine-generated.

We demonstrate a quantum algorithm for determining permutations using linear optics. This quantum permutation algorithm achieves faster computation by evaluating permutation parity in one step, outperforming classical methods.

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Area of Science:

  • Quantum computation
  • Linear optics
  • Quantum information science

Background:

  • Quantum algorithms offer potential speedups over classical algorithms for specific computational tasks.
  • Linear optical systems provide a platform for implementing quantum information processing.
  • Permutation determination is a fundamental problem with applications in various computational fields.

Purpose of the Study:

  • To experimentally demonstrate a quantum permutation determining algorithm using a linear optical system.
  • To realize quantum ququart states and essential permutation transformations.
  • To showcase the potential for speedup in quantum computation.

Main Methods:

  • Utilizing photon polarization and spatial modes to create quantum ququart states.
  • Implementing all necessary permutation transformations within the optical system.
  • Performing the quantum permutation determining algorithm at the single-photon level.

Main Results:

  • Successfully demonstrated a quantum permutation determining algorithm.
  • Achieved a one-step evaluation for permutation parity, compared to two steps for classical algorithms.
  • Confirmed the universality of the method for high-dimensional quantum computation.

Conclusions:

  • The experiment validates the feasibility of quantum permutation algorithms in linear optical systems.
  • The demonstrated approach offers a significant speedup for permutation parity determination.
  • This work highlights the potential of high-dimensional quantum computation using photonic systems.