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.
Highlights
Continued advances in systems biology, synthetic biology, and micro- and nanobiotechnology increasingly drive states-ofknowledge and -art in computational cell biology toward trends in logic gate, circuit, and algorithm designs (e.g., Ehrenfeucht et al, 2003; Amos, 2006; Baumgardner et al, 2009; Friedland et al, 2009; Adamatzky, 2010; Clark, 2010a,b,c,d, 2011, 2012b, 2013a; Norris et al, 2011; Karafyllidis, 2012; Mehta and Schwab, 2012; Daniel et al, 2013; Goñi-Moreno et al, 2013; Ji et al, 2013), especially for “programmable” group and solitary cellular decisions mediated by genetic, epigenetic, and somatic regulatory networks
Despite technological interests in neuronal information processing attributes, serious application of quantum computational approaches toward study of adaptive cybernetic-like neuron behavior and physiology remains disappointingly slow, except as it may broadly relate to more-or-less controversial debates over the statistical mechanics nature of consciousness, decision making, and other psychological states and functions of humans and animals
The principle is formally expressed in the strong condition as H(Q) + H(R) ≥ 2 log2[1/f (Q, R)], where H(Q) and H(R) are the Shannon entropies of respective spectrally decomposed measurements Q and R of quantum state |ψ with probability distributions p(q) and p(r) and maximum fidelity or inner product f (Q, R) = maxq,r | q|r | between eigenvectors |q and |r
Summary
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.
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