  Several recent studies have demonstrated the utility of the quantum SWITCH as
an important resource for enhancing the performance of various information
processing tasks. In a quantum SWITCH, the advantages appear significantly due
to the coherent superposition of alternative configurations of the quantum
components which are controlled by an additional control system. Here we
explore the impact of increasing the Hilbert-space dimension of the control
system on the performance of the quantum SWITCH. In particular, we focus on a
quantifier of the quantum SWITCH through the emergence of non-Markovianity and
explicitly study their behavior when we increase the Hilbert-space dimension of
the control system. We observe that increasing the Hilbert-space dimension of
the control system leads to the corresponding enhancement of the non-Markovian
memory induced by it. Our study demonstrates how the dimension of the control
system can be harnessed to improve the quantum SWITCH-based information
processing or communication tasks
