Przemysław Sadowski

Central limit theorem for reducible and irreducible open quantum walks

In this work we aim at proving central limit theorems for open quantum walks on

Various methods of optimizing control pulses for quantum systems with decoherence

{\mathbb {Z}}^d

Constructive quantum scaling of unitary matrices

Zd. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.

Micromechanical analysis of deformation and temperature inhomogeneities within rough contact layers

We introduce the model of generalized open quantum walks on networks using the Transition Operation Matrices formalism. We focus our analysis on the mean first passage time and the average return time in Apollonian networks. These results differ significantly from a classical walk on these networks. We show a comparison of the classical and quantum behaviour of walks on these networks.

Approximation of separable numerical range using simulated annealing

We design control setting that allows the implementation of an approximation of an unitary operation of a quantum system under decoherence using various quantum system layouts and numerical algorithms. We focus our attention on the possibility of adding ancillary qubits which help to achieve a desired quantum map on the initial system. Furthermore, we use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equation. We obtain results showing that applying the control pulses to the ancilla allows one to successfully implement unitary operation on a target system in the presence of noise, which is not possible which control field applied to the system qubits.

A model of thermal contact conductance at high real contact area fractions

We introduce a family of quantum walks on cycles parametrized by their liveliness, defined by the ability to execute a long-range move. We investigate the behaviour of the probability distribution and time-averaged probability distribution. We show that the liveliness parameter, controlling the magnitude of the additional long-range move, has a direct impact on the periodicity of the limiting distribution. We also show that the introduced model provides a method for network exploration which is robust against trapping.

Classical estimates of the effective thermoelastic properties of copper–graphene composites

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