Barrier-Controlled Multi-Qubit Exchange*

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for coherent qubit manipulation in spin-based quantum computing and quantum information processing. Various other phenomena such as many body localization and time crystals in semiconductor quantum dots also require tunable exchange couplings. However, controlling multiple exchange couplings in large quantum dot arrays proves to be challenging, due to non-linear and non-local dependence of the exchange couplings on the confinement gate voltages. In this work we demonstrate simultaneous control of multiple barrier-induced exchange couplings in a four-qubit processor. We model the dependence of the exchange couplings on all barrier gate voltages, which provides a means of precisely and simultaneously controlling multiple exchange couplings. We demonstrate two-, three-, and four-qubit exchange oscillations, and compare the experimental data to the simulated predictions.