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Efficient classical simulation of continuous variable quantum information processes.

Stephen D Bartlett1, Barry C Sanders, Samuel L Braunstein

  • 1Department of Physics and Centre for Advanced Computing--Algorithms and Cryptography, Macquarie University, Sydney, New South Wales 2109, Australia.

Physical Review Letters
|February 28, 2002
PubMed
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We found conditions for efficiently simulating continuous variable quantum information on classical computers. This extends the Gottesman-Knill theorem, enabling classical simulation of specific quantum processes involving Gaussian states and quadratic Hamiltonians.

Area of Science:

  • Quantum Information Science
  • Computational Physics

Background:

  • The Gottesman-Knill theorem provides conditions for efficient classical simulation of quantum computations using stabilizer states.
  • Extending these conditions to continuous variable (CV) quantum systems is crucial for broader quantum information processing.

Purpose of the Study:

  • To establish sufficient conditions for the efficient classical simulation of continuous variable quantum algorithms.
  • To generalize the Gottesman-Knill theorem to the domain of continuous variable quantum information.

Main Methods:

  • Analysis of quantum processes involving harmonic oscillators and Gaussian states.
  • Identification of constraints on Hamiltonians (quadratic in canonical operators) and measurements (of canonical operators).
  • Development of a theorem outlining simulation feasibility based on these constraints.

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Main Results:

  • Sufficient conditions are derived for efficient classical simulation of CV quantum processes.
  • The theorem applies to systems of harmonic oscillators starting with unentangled Gaussian states.
  • Processes involving only quadratic Hamiltonian transformations and measurements of canonical operators (including losses) are efficiently simulable.

Conclusions:

  • The study successfully extends the Gottesman-Knill theorem to continuous variable quantum information.
  • Efficient classical simulation is possible for a significant class of CV quantum processes under specific conditions.
  • This work provides a theoretical foundation for understanding the computational power of certain CV quantum systems.