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Basis for a neuronal version of Grover's quantum algorithm.

Kevin B Clark1

  • 1Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System Los Angeles, CA, USA ; Complex Biological Systems Alliance North Andover, MA, USA.

Frontiers in Molecular Neuroscience
|May 27, 2014
PubMed
Summary
This summary is machine-generated.

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Grover's quantum algorithm offers a quadratic speed-up for searches. Similarly, neuronal calcium signaling exhibits a natural quadratic speed-up, enhancing cellular decision-making processes.

Area of Science:

  • Computational Science and Quantum Information Theory
  • Cellular Biology and Neuroscience

Background:

  • Grover's quantum algorithm provides a quadratic speed-up for searching unsorted databases, surpassing classical computational limits.
  • Eukaryotic cells, particularly neurons, exhibit rapid decision-making through intracellular calcium (Ca2+) signaling dynamics.

Purpose of the Study:

  • To draw parallels between Grover's quantum search algorithm and the natural Ca2+ signaling mechanisms in neurons.
  • To explore how neuronal Ca2+ dynamics achieve a quadratic speed-up analogous to quantum computation.

Main Methods:

  • Theoretical analysis comparing the computational principles of Grover's algorithm with cellular signaling pathways.
  • Utilizing a fire-diffuse-fire model for store-operated cytosolic Ca2+ signaling in glutamatergic neurons.
Keywords:
biotechnologycalcium-induced calcium reactions (CICRs)cellular decision makingclassical and quantum computationinositol 1,4,5-trisphosphate receptors (IP3Rs)intracellular calciumneuronal plasticityquantum molecular networks and memory

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  • Parameterizing model features to align with Grover's quantum algorithm requirements, including the Oracle Hadamard transform and Grover's iteration.

    • Main Results:

    • Neuronal Ca2+ waves demonstrate a quadratic decrease in inter-store travel time, proportional to the square-root of the diffusion coefficient (D (1/2)).
    • This cellular Ca2+ signaling speed-up matches the computational efficiency of Grover's quantum algorithm.
    • The spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release drive this enhanced cellular decision-making.

    Conclusions:

    • A neuronal analogue of Grover's quantum algorithm exists within cellular Ca2+ signaling.
    • This natural quantum-like mechanism in neurons enhances signal coincidence detection, integration, and synaptic plasticity.
    • Understanding this cellular computation can inform advancements in neuroscience and potentially bio-inspired computing.