Adam Glos

Limiting properties of stochastic quantum walks on directed graphs

The main results of our work is determining the differences between limiting properties in various models of quantum stochastic walks. In particular, we prove that in the case of strongly connected and a class of weakly connected directed graphs, local environment interaction evolution is relaxing, and in the case of undirected graphs, global environment interaction evolution is convergent. For other classes of directed graphs we show, that the character of connectivity large influence on the limiting properties. We also study the limiting properties for the non-moralizing global interaction case. We demonstrate that the digraph observance is recovered in this case.

Constructive quantum scaling of unitary matrices

In this work, we present a method of decomposition of arbitrary unitary matrix

The role of quantum correlations in Cop and Robber game

U\in \mathbf {U}(2^k)

Properties of quantum stochastic walks from the asymptotic scaling exponent.

U∈U(2k) into a product of single-qubit negator and controlled-

Impact of global and local interaction on quantum spatial search on chimera graph

\sqrt{\text{ NOT }}

Impact of the malicious input data modification on the efficiency of quantum algorithms.

NOT gates. Since the product results with negator matrix, which can be treated as complex analogue of bistochastic matrix, our method can be seen as complex analogue of Sinkhorn–Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively, and resulting circuit consists of