Robust quantum control theory and demonstration with circuit QED

Performing higher fidelity and faster quantum gates in a multi-qubit system is the key to applicable quantum computation. Errors induced by dephasing, crosstalk among different elements in such system and pulse waveform deformation limit the quality of quantum gates. Because the time evolution operator associated with time-dependent Hamiltonian is too difficult to solve analytically, traditional quantum control approach relies on numerical search of time dependent control field and numerical optimization of pulse waveform, based on simple guess’s. The computation complexity grows as the system size grows, so it is computational expensive. On the other hand, by either making reasonable approximation or analysing symmetry, we established several theories to give analytical solutions of dynamical quantum gates which is robust to errors while keeping the gate time at the quantum speed limit. Our perturbative theory maps the field to geometric space and produces dynmaical decoupling and robust gates that could cancel arbitrary order noise. Our SWIPHT theory produces exact solution for high fidelity and fast quantum gates that could work even in strong crosstalk regime without any approximations. I will introduce the theory and some experimental results. I will also introduce some recent results from my new approach.