Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

  title={Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices},
  author={Levon Chakhmakhchyan and Nicolas J. Cerf and Ra{\'u}l Garc{\'i}a-Patr{\'o}n},
  journal={Physical Review A},
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our… 

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Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices

A deterministic polynomial time cn approximation algorithm for the permanent of positive semidefinite matrices is designed and it is shown that the permanent is within a cn factor of the top eigenvalue of the Schur power matrix.

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Connection between BosonSampling with quantum and classical input states

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Connection between BosonSampling with quantum and classical input states.

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Quantum-inspired algorithms in practice

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