Boosting entanglement growth of many-body localization by superpositions of disorder

Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, performing an ensemble average over many different disorder configurations is typically necessary. 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 entanglement growth for systems in the deep MBL phase. For a typical MBL system with short-range interactions, reaching saturation in entanglement usually takes an exponentially long time, which makes experimental explorations of long-time properties challenging. With our protocol, we demonstrate a significant reduction in the saturation time by several orders. This advancement facilitates easier access to the behavior in the long-time regime. 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.