Robust quantum walk search without knowing the number of marked vertices

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Efficient Quantum Walk on the Grid with Multiple Marked Elements

We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound...

Quantum Walk Based Search Algorithms

In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We present a rather detailed description of a somewhat simplified version of the MNRS algorithm. Finally, in the que...

MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES

The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...

Lococode Performs Nonlinear Ica without Knowing the Number of Sources

Low-complexity coding and decoding (Lococode), a novel approach to sensory coding, trains autoassocia-tors (AAs) by Flat Minimum Search (FMS), a recent general method for nding low-complexity networks with high generalization capability. FMS works by minimizing both training error and required weight precision. We nd that as a by-product Lococode separates nonlinear superpositions of sources wi...