Charge Noise Limited Gate Fidelity > 99.9% of Spin Qubits with Si/SiGe Quantum Dots

Qubit number and error rate are both key parameters to characterize the power of quantum computing, but they are still challenging issues. The underlying physics for the error rate is dephasing due to coupling to the environment noise, magnetic or electrical for the case of spin qubits with quantum dots (QDs). Here I will discuss the spin dephasing measured for QDs made out of GaAs and Si/SiGe and how to suppress the dephasing to raise the gate fidelity well exceeding the threshold of fault tolerant qubit gates. In GaAs QDs the dephasing arises predominantly from the fluctuating nuclear spin bath. This noise is time-correlated and the variance increases with increasing correlation time from msec to 100 sec in the non-ergodic regime. We employ a micro-magnet technique for operating the single snd two spin qubits. We show that both fast gating and feedback control are useful to raise the fidelity exceeding 99 %. On the other hand, in Si QDs the magnetic noise is significantly reduced but electrical noise can be crucial instead. We apply the micro-magnet technique for natural and isotopically purified Si/SiGe QDs and obtain the fidelity exceeding 99.9 % for the isotopically purified Si/SiGe QDs by optimizing the gating speed, and find the fidelity is predominantly limited by charge noise. From this result we can also assign the fidelity of 99.6% obtained for the natural Si/SiGe to magnetic noise of remaining nuclear spins. I will discuss influences from charge fluctuations on the gate fidelity in the presence of a micro-magnet induced stray field.