Basis for a Neuronal Version of Grover's Quantum Algorithm

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(N (1/2))) 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 Ca(2+) 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 Ca(2+)-induced Ca(2+) release and the search (or signaling) velocity of Ca(2+) wave propagation. As chemical processes, such as the duration of Ca(2+) mobilization, become rate-limiting over interstore distances, Ca(2+) waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca(2+) diffusion coefficient, D (1/2), 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 Ca(2+) 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.