Chapter

Quantum Information with Continuous Variables

pp 47-55

Efficient Classical Simulation of Continuous Variable Quantum Information Processes

  • Stephen D. BartlettAffiliated withDepartment of Physics and Centre for Advanced Computing -Algorithms and Cryptography, Macquarie University
  • , Barry C. SandersAffiliated withDepartment of Physics and Centre for Advanced Computing -Algorithms and Cryptography, Macquarie University
  • , Samuel L. BraunsteinAffiliated withInformatics, Bangor University
  • , Kae NemotoAffiliated withInformatics, Bangor University

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Abstract

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.