Variational counterdiabatic driving of the Hubbard model for ground-state preparation

Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited throughout the process. Usually, full spectrum original unassisted Hamiltonian is a prerequisite for constructing exact AGP, which implies CD are extremely difficult many-body systems. Here, we apply variational protocol recently proposed P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] two-component fermionic Hubbard model in one spatial dimension. This engages approximated AGP expressed as series nested commutators. We show optimal parameters satisfy set linear equations whose coefficients given squared Frobenius norms these devise algorithm escapes formidable iterative matrix-vector multiplications and evaluates commutators analytic representations. then examine one-dimensional up $L = 14$ sites with order $l \leqslant 3$. Our results demonstrate usefulness permit possible route towards ground-state preparation