14 citations · 39 across the 6 of their papers we have counts for
6 papers
Boolean Functions with Minimal Spectral Sensitivity
Krišjānis Prūsis, Jevgēnijs Vihrovs
We show examples of total Boolean functions that depend on variables and have spectral sensitivity , which is asymptotically minimal. Our main new function co…
Strong dispersion property for the quantum walk on the hypercube
Martins Kokainis, Krišjānis Prūsis, Jevgēnijs Vihrovs +2
We show that the discrete time quantum walk on the Boolean hypercube of dimension has a strong dispersion property: if the walk is started in one vertex, then the probability o…
Quantum Lower Bounds for 2D-Grid and Dyck Language
Andris Ambainis, Kaspars Balodis, Jānis Iraids +2
We show quantum lower bounds for two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of…
Stationary States in Quantum Walk Search
Krišjānis Prūsis, Jevgēnijs Vihrovs, Thomas G. Wong
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, a…
Full Characterization of Oscillatory Localization of Quantum Walks
Andris Ambainis, Krišjānis Prūsis, Jevgēnijs Vihrovs +1
Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion wi…
Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits
Andris Ambainis, Krišjānis Prūsis, Jevgēnijs Vihrovs +1
We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two verti…