Ph.D Thesis Defence by R.Uğraş Erdoğan on 16/01/2025

You are cordially invited to the Ph.D thesis defense by Ruha Uğraş Erdoğan

Title:

“Fractional Dynamics of Superconducting Transmon Qubit Circuits Interacting with Non-Markovian Environments”

Abstract:

We have developed the theory, based on the variable order fractional differential equations, for the evolution of open superconducting quantum circuits based on the Lévy process arising from the Mittag-Leffler correlations and fractional Random Telegraph Noise (fRTN) process that characterize the trapping and detrapping behavior of the two-level defect, in amorphous coating layer, coupled to the superconducting qubit circuit beneath the amorphous coating. It is assumed that the defect has a time dependent transition frequency, due to the AC-Stark shift, resulting from momentary coupling and decoupling of the defect with the other defects in its vicinity.

Fractional order differential equations have the potential to characterize the dissipation in Hamiltonian systems, otherwise which are non-dissipative in other words reversible. This concept has been shown in literature by constructing a fractional Hamiltonian formalism starting from the corresponding fractional Lagrangian equations. In our thesis, we have constructed a constant order fractional Heisenberg equation for a superconducting transmon qubit to observe the validity of the proposed theory in literature. The dependence of the relaxation on the characteristic exponent representing the memory of the environment has been observed in our simulations.

Noise might be a beneficial source, on the contrary to the common belief, in superconducting quantum systems to increase the relaxation and decoherence times. This might be one of the ways to run more complex quantum algorithms which require abstractions with wider and deeper quantum circuits to be run on actual quantum computers. In this respect, we have analyzed the effect of not only the Mittag Leffler correlated noise process but also the fRTN noise process that individually drives the qubit transversally coupled to a Markovian environment.

Since quantum simulation toolboxes do not exist for the variable order fractional quantum Lindblad master equations, Uğraş Erdoğan, himself, has developed these new codes to solve variable order fractional master equations to obtain the numerical solutions of the “variable order fractional master equation”. The codes for “constant order fractional Heisenberg equation” have also been developed by us to probe the effectiveness of fractional differential equation approach in modelling the quantum dissipation process without using the dissipator terms as in the case of Lindblad master equation. Necessary coding for “random number generation process from a fractional distribution” has also been done by us. This step has been needed to obtain different realizations of the noise processes characterizing the environment the superconducting quantum circuit has been coupled with.

We strongly believe that our study will attract interest in the “Quantum Engineering” Society

Advisor: Prof.Dr Ferit Acar Savacı

Time: 16/01/2025, Thursday,   2.00 pm

Place: Electrical-Electronics Engineering Department  Seminar Room   ( Second Floor )