Optimization of single-qubit gate fidelities in silicon quantum computers in the presence of crosstalk

Abstract

For scaling up the qubits in silicon quantum computers, it is vital to determine crosstalk effects that can lower the fidelity of the computer.
In this computational project, we examine single-qubit gate-fidelities in the presence of crosstalk for uncoupled spin qubits that are driven with X-gates via electron dipole spin resonance (EDSR). We introduce two models: the first model introduces the AC Stark shift and the novel second model expands on this by adding a resonance frequency shift on top. We assume the latter resonance frequency shift to be due to heating effects. We optimize the gate-fidelity for a qubit coupled to up to six drives as a function of the overall driving time and -frequency of a single drive for both models using the Nelder-Mead algorithm.

Using the AC Stark shift model, we still obtain 0.99999 fidelity if we do not account for the crosstalk. However, when using the second model, the fidelity drops to 0.69 in the presence of two drives when we do not correct for the heating-induced resonance frequency shift and the AC Stark shift. Furthermore, the fidelity decreases linearly with the number of drives coupled to the qubit, implicating that the resonance frequency shift will become a significant problem for the scalability of silicon quantum computers. We find that we can correct for the resonance frequency shift entirely by using optimized driving time and -frequency, where most gain comes from optimizing the driving frequency. Moreover, we discover that there is a linearly increasing dependence of the resonance frequency shift at the theoretical driving time as a function of the total drives. Up to a translation factor of 0.5 MHz, we discover the same linear relationship for the correction needed on the theoretical driving frequency to hit maximum fidelity as a function of the total drives.