Preparation and exploitation of Trotter scars on near-term hardware

Determine whether Trotter-scar states—initial states supported on spectrally commensurate energy ladders that suppress Trotter-error growth and exhibit Loschmidt revivals—can be prepared and exploited on near-term quantum hardware to extend coherent simulation times and enhance the prospects for quantum advantage in digital quantum simulation.

Background

The paper introduces Trotter scars, a class of initial states whose spectral support lies on commensurate energy ladders, leading to suppressed Trotter-error growth and persistent Loschmidt revivals under Trotterized dynamics. Using interaction-picture perturbation theory, the authors connect error suppression to the spectral structure of the Hamiltonian and provide a variational approach to discover such states in specific spin models.

While numerical evidence demonstrates substantial error suppression and dynamical revivals for optimized states in the Heisenberg chain, Stark spin chain, and PXP model, practical utility depends on whether such states can be realized and leveraged on actual noisy intermediate-scale quantum (NISQ) devices. The authors explicitly identify as open the question of experimental preparation and exploitation of Trotter scars to extend coherent simulation times and potentially improve quantum advantage.