  Many-body localization (MBL) can occur when strong disorders prevent an
interacting system from thermalization. To study the dynamics of such systems,
it is typically necessary to perform an ensemble average over many different
disorder configurations. Previous works have utilized an algorithm in which
different disorder profiles are mapped into a quantum ancilla. By preparing the
ancilla in a quantum superposition state, quantum parallelism can be harnessed
to obtain the ensemble average in a single computation run. In this work, we
modify this algorithm by performing a measurement on the ancilla. This enables
the determination of conditional dynamics not only by the ensemble average but
also by the quantum interference effect. Using a phenomenological analysis
based on local integrals of motion, we demonstrate that this protocol can lead
to an enhancement of the dephasing effect and a boost in the entanglement
growth for systems in the deep MBL phase. We also present numerical simulations
of the random XXZ model where this enhancement is also present in a smaller
disorder strength, beyond the deep MBL regime.
