Characterizing quantum supremacy in near-term devices

@article{Boixo2016CharacterizingQS,
  title={Characterizing quantum supremacy in near-term devices},
  author={Sergio Boixo and Sergei V. Isakov and Vadim N. Smelyanskiy and Ryan Babbush and Nan Ding and Zhang Jiang and Michael J. Bremner and John M. Martinis and Hartmut Neven},
  journal={Nature Physics},
  year={2016},
  volume={14},
  pages={595-600}
}
A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy… 

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The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.
...