Pulse shaping for a robust CZ gate in a silicon three-qubit device with always-on exchange

We theoretically consider a 3-qubit system of electron spins in a silicon triple quantum dot with always-on exchange coupling. We have shown how to perform local spin rotations and 2-qubit entangling gates between neighboring qubits in the absence of noise, these form a universal set. However, in practice, low fidelity due to noise is an important limitation of quantum devices, so it is necessary to create gates robust against noise. In this talk we will show how to make a CZ gate robust against charge noise, the most important noise in the silicon 3-qubit device. Using the fact that the hamiltonian accrues error in two separately controlled and commuting SU(2) subspaces we apply the pulse shaping method of Ref.[1] simultaneously in both spaces. Matching the pulse time in both spaces leads to a pulse that is robust to both fluctuations in exchange coupling and the electron g-factor induced by charge noise. The robust pulse maintains a fidelity of 10^-4 at 3.5% fluctuations in exchange or g-factor, an improvement over the 1% for the naive pulse.
[1]Barnes, et al., 2015. Robust quantum control using smooth pulses and topological winding. Scientific Reports,5(1).