Quantum Severalty: Speed-up and Suppress Effect in Searching Problem

TL;DR

This paper investigates quantum walk-based search problems, revealing speed-up and suppression effects that challenge classical intuition, and proposes a new method to analyze first passage probabilities for quantum simulations.

Contribution

It uncovers novel quantum effects in search processes on graphs with floating vertices and introduces an ancillary model to measure first passage probabilities.

Findings

Identified quantum speed-up and suppression effects in search problems.

Proposed a new method to analyze first passage probabilities.

Insights may lead to advanced quantum search algorithms and simulations.

Abstract

The idea that the search efficiency can be increased with the help of a number of autonomous agents is often relevant in many situations, which is known among biologists and roboticists as a stigmergy. This is due to the fact that, in any probability-based search problem, adding information provides values for conditional prpbabilities. We report new findings of speed-up and suppression effects occuring in the quantum search problem through the study of quantum walk on a graph with floating vertices. This effect is a completely counterintuitive phenomenon in comparison to the classical counterpert, and may faciliate new insight in the future information search mechanisms that were never been perceived in classical picture. In order to understand the first passage probability, we also propose a method via ancillary model to bridge the measurement of the time dependence of the total probability of the complementary part and the first passage probability of the original model. This is expected to provide new ideas for quantum simulation by means of qubit chips.