Simulating string-order melting in superconducting hardware with optimal control

Utilizing optimal control to achieve quantum simulation is an emerging strategy that combines intrinsic device physics with digital quantum simulation methods. Here we assess this strategy by designing protocols to probe the static and dynamic properties of symmetry-protected topological (SPT) states on superconducting transmon hardware. Specifically, we design methods to study string-order melting, in which a symmetry-breaking quench is applied to a prepared SPT state, leading to rapid decay in string order. To demonstrate feasibility we map a two-site AKLT Hamiltonian into a transmon device architecture and use numerical simulations to identify optimal controls which model string-order melting on near-term quantum hardware. We conclude by discussing additional opportunities to investigate SPT phases using quantum simulation with optimal control.