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Gaussian Boson Sampling.

Craig S Hamilton1, Regina Kruse2, Linda Sansoni2

  • 1FNSPE, Czech Technical University in Prague, Brêhová 7, 119 15, Praha 1, Czech Republic.

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Gaussian Boson sampling offers a new quantum computing approach using squeezed states. This method is a #P hard problem, providing advantages in photon generation probability over current protocols.

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Area of Science:

  • Quantum computing
  • Quantum optics
  • Computational complexity

Background:

  • Boson sampling is a key quantum computing task that leverages photonic platforms.
  • Current Boson sampling protocols do not require universal quantum control, making them suitable for photonic experiments.

Purpose of the Study:

  • To introduce Gaussian Boson sampling, a novel problem solvable with squeezed states.
  • To establish a theoretical framework for sampling from Gaussian states in quantum optics.
  • To demonstrate a #P hard problem using squeezed states for quantum computation.

Main Methods:

  • Utilizing squeezed states as the nonclassical resource.
  • Relating photon pattern probabilities in the Fock basis to the matrix Hafnian function.
  • Designing a Gaussian Boson sampling protocol.

Main Results:

  • The probability of measuring specific photon patterns from Gaussian states is determined by the Hafnian.
  • Gaussian Boson sampling is formulated as a #P hard problem.
  • The proposed method shows advantages in photon generation probability compared to existing protocols.

Conclusions:

  • Boson sampling from Gaussian states is feasible using squeezed states.
  • Gaussian Boson sampling presents a promising avenue for exploring quantum computational advantages.
  • The developed framework addresses the challenge of sampling from Gaussian states.