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Quantum supremacy in linear optics arises from the complexity of calculating transition amplitudes. A new measure, Fock state concurrence sum (CS), quantifies this complexity, directly impacting classical simulation runtime for boson sampling.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Linear Optical Quantum Computing

Background:

  • Understanding quantum supremacy in linear optical quantum computing is crucial.
  • Calculating multimode linear optical transition amplitudes is computationally hard, forming the basis of the boson sampling problem.

Purpose of the Study:

  • To identify a quantum measure that directly correlates with the classical runtime for computing transition amplitudes.
  • To introduce and define the 'Fock state concurrence sum' (CS) as a novel quantum measure.

Main Methods:

  • Developed generalized algorithms for computing transition amplitudes in Fock state boson sampling.
  • Introduced 'generalized Fock state concurrence' and its summation, CS.
  • Analyzed the relationship between CS and classical computational complexity.

Main Results:

  • The minimal classical runtime for known algorithms is directly dependent on CS.
  • CS acts as a collective measure controlling the computational complexity of Fock state boson sampling.
  • Demonstrated the role of Fock state concurrence in generalized algorithms for permanents.

Conclusions:

  • Fock state concurrence sum (CS) provides a unified viewpoint for interpreting the quantum computing power of linear optics.
  • CS offers a direct link between quantum properties and classical simulation difficulty.
  • The findings are expected to advance the understanding of quantum supremacy in physical systems.