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Experimental study of Forrelation in nuclear spins.

Hang Li1, Xun Gao2, Tao Xin1

  • 1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; Collaborative Innovation Centre of Quantum Matter, Beijing 100084, China.

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|January 20, 2023
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Summary

Researchers experimentally probed Forrelation functions using nuclear spins, demonstrating a quantum query algorithm

Keywords:
ForrelationGradient ascent pulse engineeringNuclear magnetic resonanceQuery complexity

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Algorithms

Background:

  • Correlation functions quantify relationships in data.
  • Forrelation functions, a new class, are key to quantum query complexity.
  • A quantum algorithm offers exponential speedup for 2-fold Forrelation problems.

Purpose of the Study:

  • To experimentally investigate 2-fold and 3-fold Forrelation functions.
  • To assess the feasibility of quantum query algorithms in a realistic experimental setting.
  • To evaluate the potential for demonstrating quantum supremacy with current technology.

Main Methods:

  • Encoding Forrelation functions in nuclear spin systems.
  • Utilizing optimized GRAPE pulse sequences for precise spin control.
  • Managing and controlling spin fluctuations within a critical threshold.

Main Results:

  • Successful experimental probing of 2-fold and 3-fold Forrelations.
  • Demonstration of controlled spin fluctuations using optimized pulse sequences.
  • Validation of the quantum query algorithm's accuracy in the presence of experimental noise.

Conclusions:

  • The experimental implementation validates the quantum query algorithm for Forrelation.
  • The study indicates quantum supremacy is achievable for Forrelation problems with current technology.
  • This work paves the way for further experimental studies in quantum query complexity.