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Wigner Distribution Sets Universal Lower Bound for Quantum Advantage in Gaussian Boson Sampling.

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Quantum advantage in Gaussian boson sampling arises from Wigner quasiprobability distribution squeezing. This study establishes an easy-to-compute lower bound for quantum complexity, closely matching numerical results.

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Area of Science:

  • Quantum Computing
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Gaussian boson sampling is a prominent quantum computational task.
  • Understanding the physical origins of quantum advantage is crucial for advancing quantum computing.
  • The Wigner quasiprobability distribution is a key tool in quantum mechanics.

Purpose of the Study:

  • To identify the physical origin of quantum advantage in Gaussian boson sampling.
  • To establish a computable lower bound for the complexity dimension.
  • To analyze the properties of quantum advantage.

Main Methods:

  • Analysis of squeezing in the Wigner quasiprobability distribution.
  • Development of an analytical method to compute a universal lower bound for complexity.
  • Numerical convex optimization to determine the exact complexity dimension.

Main Results:

  • Quantum advantage in Gaussian boson sampling is directly linked to the squeezing of the Wigner quasiprobability distribution.
  • An easy-to-compute universal lower bound for the complexity dimension was established.
  • The Wigner lower bound was found to be in close agreement with values obtained through numerical optimization.

Conclusions:

  • The squeezing of the Wigner quasiprobability distribution is the physical source of quantum complexity in boson sampling.
  • The derived lower bound provides an efficient way to estimate quantum advantage.
  • The study reveals significant properties of quantum advantage through analytical and numerical investigations.