Quantum sampling problems, BosonSampling and quantum supremacy

@article{Lund2017QuantumSP,
  title={Quantum sampling problems, BosonSampling and quantum supremacy},
  author={Austin P. Lund and Michael J. Bremner and Timothy C. Ralph},
  journal={npj Quantum Information},
  year={2017},
  volume={3},
  url={https://api.semanticscholar.org/CorpusID:54628108}
}
This paper will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate, and two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and Instantaneous Quantum Polynomial-time Sampling.
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201 Citations
Highly Influential Citations
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Methods Citations
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201 Citations

The hardness of random quantum circuits

It is proved that estimating the output probabilities of random quantum circuits is #P-hard for any classical computer, and the results suggest that there is an exponential hardness barrier for the approximate classical simulation of most quantum circuits.

Quantum supremacy and random circuits.

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The Classical Complexity of Boson Sampling

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Boson Sampling with efficient scaling and efficient verification.

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Efficient classical simulation of noisy quantum computation

It is proved that under general conditions most of the quantum circuits at any constant level of noise per gate can be efficiently simulated classically with the cost increasing only polynomially with the size of the circuits.

Boson sampling with Gaussian input states: Toward efficient scaling and certification

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Power of quantum measurement in simulating unphysical operations

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Continuous-Variables Boson Sampling: Scaling and Verification

A new pathway to scale Boson Sampling experiments by combining continuous-variables quantum information and temporal encoding is presented and the performance of the device can be verified with a number of measurement samples growing polynomially in the number of photons.
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