Exploiting many-body localization for scalable variational quantum simulation

Abstract: Variational quantum algorithms have emerged as a promising approach to achieving practical quantum advantages using near-term quantum devices. Despite their potential, the scalability of these algorithms poses a significant challenge. This is largely attributed to the "barren plateau" phenomenon, which persists even in the absence of noise. In this work, we explore the many-body localization (MBL)-thermalization phase transitions within a framework of Floquet-initialized variational quantum circuits and investigate how MBL could be used to avoid barren plateaus. The phase transitions are observed through calculations of the inverse participation ratio, the entanglement entropy, and a metric termed low-weight stabilizer R\'enyi entropy. By initializing the circuit in the MBL phase and employing an easily preparable initial state, we find it is possible to prevent the formation of a unitary 2-design, resulting in an output state with entanglement that follows an area- rather than a volume-law, and which circumvents barren plateaus throughout the optimization. Utilizing this methodology, we successfully determine the ground states of various model Hamiltonians across different phases and show that the resources required for the optimization are significantly reduced. We have further validated the MBL approach through experiments carried out on the 127-qubit $ibm_brisbane$ quantum processor. These experiments confirm that the gradients needed to carry out variational calculations are restored in the MBL phase of a Heisenberg model subject to random unitary "kicks". These results provide new insights into the interplay between MBL and quantum computing, and suggest that the role of MBL states should be considered in the design of quantum algorithms.