Today’s quantum processor architectures with more than 1000 superconducting qubits are getting closer to the goal of performing complicated calculations. However, the noisy
intermediate-scale quantum (NISQ) devices that exist at this time are challenged by phenomena like leakage, cross talking between qubits and decoherence. All three error
sources lead to a deterioration in the precision and accuracy of the quantum calculations performed on the quantum chips of NISQ devices and hence limit the ability to obtain
reliable results. However, the hardware implementation of qubits such as the transmon qubit system can suppress or compensate these effects using quantum optimal control
(QOC) methods through targeted and optimized microwave pulses. To realise Quantum-Gates and hence control the state of the transmon qubit an external magnetic field is applied to it. For the theory of what the Hamiltonians of one-qubit and two-qubit gates look like the knowledge about the time constant duffing oscillator and the drive Hamiltonian, which represents the time dependent part of the whole system Hamiltonian, plays a crucial role for the optimization process using QOC methods. In the last few years papers which address the problem of maximizing the fidelity of quantum gates by different QOC algorithms are now quite common. However, papers comparing those QOC algorithms in terms of the influence on the fidelity of qubit gates by testing them on IBM-devices are not so common.
Goal of this master’s thesis is to research the principle of QOC by using a transmon qubit system and QOC algorithms, which will be GRadient Ascent Pulse Engineering (GRAPE) and Chopped RAndom Basis (CRAB), by comparing them with regards to improved fidelity of two one-qubit gates and one two-qubit gate on the microwave pulse level.