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Quantum to classical transition for random walks.

Todd A Brun1, Hilary A Carteret, Andris Ambainis

  • 1Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA. tbrun@ias.edu

Physical Review Letters
|October 4, 2003
PubMed
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We investigated two methods to achieve classical behavior in quantum random walks. Decoherence leads to classical linear growth in variance, while multi-coin walks maintain quantum quadratic growth, except in extreme cases.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Quantum random walks (QRWs) exhibit unique behaviors distinct from classical random walks due to quantum interference.
  • Understanding the transition from quantum to classical behavior is crucial for quantum computing and simulation applications.

Purpose of the Study:

  • To investigate two distinct mechanisms for inducing classical behavior in discrete quantum random walks on integers.
  • To analyze the role of decoherence and multi-coin strategies in the emergence of classicality.

Main Methods:

  • The study employs position variance as a quantitative measure to distinguish between quantum and classical diffusive behavior.
  • Analytical expressions for position variance in the long-time limit are derived for both decoherence and multi-coin scenarios.

Related Experiment Videos

  • The impact of varying degrees of decoherence and the number of coins used is examined.

    • Main Results:

    • Quantum random walks with decoherence demonstrate a transition to classical linear growth in position variance, even with minimal decoherence.
    • Multi-coin quantum random walks generally preserve the quadratic growth characteristic of quantum behavior.
    • The quadratic growth in multi-coin walks is only lost in the limiting case where a new coin is introduced at every step.

    Conclusions:

    • Decoherence provides an effective route to classical behavior in quantum random walks, altering their diffusive properties.
    • Multi-coin strategies offer a method to control quantum interference, but typically maintain quantum-like spreading.
    • The findings offer insights into controlling quantum dynamics and designing quantum algorithms with tunable classical-quantum transitions.