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Universal bound on sampling bosons in linear optics and its computational implications.

Man-Hong Yung1,2,3, Xun Gao4, Joonsuk Huh5

  • 1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.

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|October 25, 2021
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Summary
This summary is machine-generated.

Researchers found a fundamental limit for boson transition amplitudes in linear optical networks. This discovery enables efficient classical computation of quantum states and solves a long-standing problem in quantum information science.

Keywords:
boson samplingcomputational complexitylinear opticsquantum opticsquantum supremacy

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Area of Science:

  • Quantum Physics
  • Linear Optics
  • Quantum Information Science

Background:

  • Linear optical networks are crucial for quantum applications like interferometry and boson sampling.
  • Understanding boson behavior in these networks is key to advancing quantum technologies.

Purpose of the Study:

  • To establish the fundamental limit for transition amplitudes of bosons in any physical linear optical network.
  • To explore the implications of this bound for quantum computation and simulation.

Main Methods:

  • Theoretical analysis of boson scattering in passive optical elements.
  • Derivation of a general bound on transition amplitudes.

Main Results:

  • A fundamental transition amplitude bound for bosons in linear optical networks was established.
  • This bound leads to efficient classical algorithms for boson sampling and related problems.
  • It implies a polynomial-time randomized algorithm for estimating boson transition amplitudes, solving an open problem.

Conclusions:

  • The derived bound has broad applications, including Bose-Einstein condensate behavior and multi-photon interference.
  • It demonstrates that certain quantum computational decision problems in linear optics are efficiently solvable classically.
  • The results pave the way for classical algorithms to compute many-body wave functions and S-matrices for bosonic particles.