In a 2005 book - now posted in Research Gate (see the link below) - the authors (led by Dr. Armando Freitas da Rocha) proposed an original model of quantum computing in the brain carried by calcium ions. Ten years later, the concept independently reappears in a convincing new paper (see Abstract below). I thank Chris Nunn for calling my attention to this paper, and congratulate Dr. Freitas da Rocha for his ingenious and visionary work!

Front. Mol. Neurosci., 16 April 2014 | doi: 10.3389/fnmol.2014.00029

Basis for a Neuronal Version of Grover's Quantum Algorithm

Kevin B. Clark1,2*

1Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System, Los Angeles, CA, USA

2Complex Biological Systems Alliance, North Andover, MA, USA

Abstract

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.

Book The Brain: From Fuzzy Arithmetics to Quantum Computing

More Alfredo Pereira Junior's questions See All
Similar questions and discussions