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Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error.

Keisuke Fujii1,2,3, Hirotada Kobayashi4, Tomoyuki Morimae3,5,6

  • 1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.

Physical Review Letters
|June 5, 2018
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This summary is machine-generated.

This study proves that sampling quantum computation results from the one-clean-qubit model with one output qubit is classically hard. This finding strengthens complexity bounds for quantum computing models.

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Area of Science:

  • Quantum Computing
  • Computational Complexity Theory

Background:

  • The one-clean-qubit model is a restricted quantum computation model.
  • Classical sampling of its output distributions is linked to the polynomial-time hierarchy collapse.

Purpose of the Study:

  • To determine if the classical hardness of the one-clean-qubit model persists with only one output qubit.
  • To investigate potential strengthening of complexity class collapses for quantum computing models.

Main Methods:

  • Theoretical analysis of the one-clean-qubit model.
  • Investigating the relationship between quantum sampling and classical complexity classes.

Main Results:

  • The one-clean-qubit model with one output qubit remains classically hard to sample from.
  • The polynomial-time hierarchy collapse is strengthened from the third to the second level.
  • This strengthening applies to other subuniversal models like instantaneous quantum polynomial and boson sampling.

Conclusions:

  • The classical simulation of the one-clean-qubit model is proven hard even with a single output qubit.
  • Complexity class collapses are shown to be more severe than previously known for certain quantum models.