Quantum Coherence and Counterdiabatic Quantum Computing

Counterdiabatic driving (CD) emerges as a valuable technique for implementing shortcuts to adiabaticity protocols, enhancing quantum technology applications. In this context, counterdiabatic quantum computing (CQC) represents a new paradigm with the potential to achieve quantum advantage for industrial problems. This work investigates the production of quantum coherence in adiabatic evolution accelerated by CD within the framework of CQC. Specifically, we analyze different orders in the nested commutator expansion for approximated CDs for three cases: a weighted max-cut problem, a four-local Hamiltonian, and a non-stoquastic Hamiltonian. Our findings reveal that the hierarchy introduced by coherence production correlates with the success probability in the impulse regime. This suggests that protocols increasing coherence during evolution enhance performance in adiabatic evolution driven by counterdiabatic techniques. We show that large quantum coherence also means large energy fluctuation during evolution, which is associated with the speed of evolution, paving the way for designing superior algorithms in CQC.