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Related Experiment Videos

Quantum computation of a complex system: the kicked Harper model.

B Lévi1, B Georgeot

  • 1Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Paul Sabatier, F-31062 Toulouse 4, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

Quantum computers can efficiently simulate complex quantum systems like the kicked Harper model. Researchers developed algorithms showing polynomial speedups for quantum simulations, even with system imperfections.

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Area of Science:

  • Quantum Computing
  • Condensed Matter Physics
  • Quantum Simulation

Background:

  • The kicked Harper model is a well-studied system exhibiting diverse dynamics.
  • It can model phenomena like fractal spectra, localization, and anomalous diffusion.
  • This model is relevant for understanding electrons in magnetic fields.

Purpose of the Study:

  • To investigate the efficient simulation of complex quantum systems using quantum computers.
  • To analyze quantum algorithms for simulating the kicked Harper model.
  • To assess the impact of imperfections on quantum simulations.

Main Methods:

  • Developed and analyzed three distinct quantum algorithms for simulating the kicked Harper model's evolution operator.
  • Evaluated simulation efficiency and precision based on resource utilization.

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  • Investigated the effects of static imperfections on selected transport and spectral quantities.

    • Main Results:

    • Identified transport and spectral quantities computable more efficiently on quantum computers.
    • Achieved polynomial speedups (quadratic or less) compared to classical algorithms.
    • Observed varying sensitivity to imperfections across different parameter regimes and quantities.

    Conclusions:

    • Quantum computers offer efficient simulation capabilities for the kicked Harper model.
    • Polynomial gains are achievable, with performance varying by parameter regime.
    • Reliable measurements are possible with moderate imperfections, even on small quantum systems (7-8 qubits).