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Efficient quantum walk on a quantum processor.

Xiaogang Qiang1, Thomas Loke2, Ashley Montanaro3

  • 1Centre for Quantum Photonics, H.H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, UK.

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Summary
This summary is machine-generated.

We developed efficient quantum circuits for continuous-time quantum walks on circulant graphs. This work links quantum walks to computational complexity, suggesting tasks for demonstrating quantum supremacy.

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Area of Science:

  • Quantum Computing
  • Computational Complexity Theory
  • Graph Theory

Background:

  • Random walk models are crucial in diverse fields like finance and genetics.
  • Quantum walks offer a powerful framework for novel quantum algorithms.
  • Circulant graphs represent a significant class of structures in graph theory.

Purpose of the Study:

  • To present efficient quantum circuits for continuous-time quantum walks on circulant graphs.
  • To enable efficient sampling from quantum walk output distributions on these graphs.
  • To establish a connection between quantum walks and computational complexity.

Main Methods:

  • Design and implementation of explicit quantum circuits for continuous-time quantum walks.
  • Analysis of the computational complexity of sampling from quantum walk distributions.
  • Experimental validation using a two-qubit photonics quantum processor.

Main Results:

  • Efficient quantum circuits for quantum walks on circulant graphs were developed.
  • Sampling from these quantum walks is shown to be intractable for classical computers.
  • A novel link between quantum walks and computational complexity theory is established.

Conclusions:

  • The developed quantum circuits provide a pathway for efficient quantum walk simulation.
  • This research highlights potential quantum supremacy demonstrations through sampling problems.
  • Experimental implementation confirms the feasibility of the proposed quantum circuits.