Exploiting many-body localization for scalable variational quantum
  simulation
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.
Chenfeng Cao Yeqing Zhou Swamit Tannu Nic Shannon Robert Joynt