An Algebraic Model for Simulation of Percolation Decoherence on Quantum-Walk-Based Search Algorithms

Abstract

In this paper, we propose a linear algebra based model for percolation noise simulation in quantum-walk-based searches to analyze the impact on the success probability of the search. The model was built to allow an open and simultaneous simulation of any type of noise that represents an edge-break, which we show to be a well-behaved family of permutation matrices that maintain a particular set theory relation when acting as some system evolution operators. The simulation evolves using only linear algebra operations, opening avenues for easier analyses of unexpected observed convergence behaviour. As a use case, we investigate the simulation of a lackadaisical quantum walk with percolation noise.