A software framework for the realistic simulation and optimal control of solid-state qubits

Teske, Julian David; Bluhm, Jörg (Thesis advisor); Di Vincenzo, David (Thesis advisor)

Aachen : RWTH Aachen University (2022, 2023)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2022

Abstract

Realistic modeling of qubit systems including noise and constraints imposed by control hardware is required for performance prediction and control optimization of quantum processors. I introduce qopt, a software framework for simulating qubit dynamics and robust quantum optimal control considering common experimental situations. To this end, I model open and closed qubit systems with a focus on the simulation of realistic noise characteristics and experimental constraints. Specifically, the influence of noise can be calculated using Monte Carlo methods, effective master equations or with the efficient filter function formalism, which enables the investigation and mitigation of auto-correlated noise. To enable the use of gradient-based algorithms with fast convergence, I present derivatives for all simulation methods including most notably analytically derived filter function gradients with respect to control pulse amplitudes, for which I analyze the computational complexity of my results. When comparing pulse optimization using my derivatives to a gradient-free approach, I find that the gradient-based method is roughly two orders of magnitude faster for my test cases. I demonstrate the utility of the qopt package in the design of new concepts for a scalable quantum computing architecture by investigation ofthe flopping-mode, which is an alternative method to drive electron dipole spin resonance (EDSR) of an electron in a double quantum dot, where the large displacement between both dots increases the driving efficiency. I propose to operate the flopping-mode in the strong-driving regime to use the full magnetic field difference between the two dots. In simulations, the reduced required magnetic field gradients suppress the infidelity contribution of charge noise by more than two orders of magnitude, while providing Rabi frequencies of up to 60MHz. However, the near degeneracy of the conduction band in silicon introduces a valley degree of freedom that can degrade the performance. In addition, limitations of control electronics including finite bandwidth effects as well as transfer functions and drive-dependent noise can be considered using qopt. Vice-versa, the requirements for tailored control electronics for quantum computers can be estimated with qopt simulations, as I demonstrate by a study of the relation between pulse resolution and the achievable quantum process fidelity.