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Quantum chaos algorithms and dissipative decoherence with quantum trajectories.

Jae Weon Lee1, Dima L Shepelyansky

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

This study examines how environmental noise (dissipative decoherence) impacts quantum computer algorithms simulating quantum chaos. Results show computation fidelity degrades exponentially with system size and noise, leading to quantum attractors.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Chaos

Background:

  • Quantum algorithms are susceptible to environmental noise, leading to decoherence.
  • Understanding decoherence is crucial for building fault-tolerant quantum computers.
  • Quantum chaos regimes present unique challenges for quantum computation fidelity.

Purpose of the Study:

  • To investigate the impact of dissipative decoherence on quantum algorithms simulating quantum chaos.
  • To analyze fidelity decay rates and their dependence on system parameters and dissipation.
  • To explore the formation of quantum attractors under strong dissipation.

Main Methods:

  • Utilized quantum trajectories to model dissipative decoherence.
  • Simulated dynamics in quantum chaos regimes (dynamical localization, quantum ergodic, quasi-integrable).

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  • Employed the quantum sawtooth algorithm, implementable with a polynomial number of quantum gates.

    • Main Results:

    • Quantum computation fidelity decays exponentially with time.
    • Decay rate is proportional to the number of qubits, quantum gates, and per-gate dissipation rate.
    • Strong dissipation leads to the emergence of quantum attractors with potentially complex structures.

    Conclusions:

    • Dissipative decoherence significantly degrades quantum computation fidelity in quantum chaos simulations.
    • The quantum sawtooth algorithm's fidelity is sensitive to system size, gate count, and environmental noise.
    • Quantum attractors are a notable feature in the strong dissipation limit, distinct from static imperfections.