Basis for a neuronal version of Grover's quantum algorithm

By Kevin B. Clark. 2014

17 citations recorded by the source corpus.

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.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience, Electrical and Electronic Engineering, Quantum Computing

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Citations in the corpus

What can the brain teach us about building artificial intelligence? (2016, background): “& Clark, A. (2015) Words and the world: Predictive coding and the”
Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks (2023, background): “These kinds of local structural changes, such as those belonging to nonlinear Hebbian [41,50–53], dynamic stochastic synapse [54], spike timing-dependent plasticity [37,39,55], and quantum bidirectional plasticity learning models [10,13], are capable of mediating weak local correlative activity, whi”