Universal Digitized Counterdiabatic Driving

Counterdiabatic driving realizes parameter displacement of an energy eigenstate of a given parametrized Hamiltonian using the adiabatic gauge potential. In this paper, we propose a universal method of digitized counterdiabatic driving, constructing the adiabatic gauge potential in a digital way with the idea of universal counterdiabatic driving. This method has three advantages over existing universal counterdiabatic driving and/or digitized counterdiabatic driving: it does not introduce any many-body and/or nonlocal interactions to an original target Hamiltonian; it can incorporate infinite nested commutators, which constitute the adiabatic gauge potential; and it gives explicit expression of rotation angles for digital implementation. We show the consistency of our method to the exact theory in an analytical way and the effectiveness of our method with the aid of numerical simulations.

💡 Research Summary

The manuscript introduces a novel framework called Universal Digitized Counterdiabatic Driving (UDCD) that enables the practical implementation of adiabatic gauge potentials (AGPs) in a fully digital quantum‑simulation setting. Counterdiabatic (CD) driving, also known as shortcuts to adiabaticity, requires the construction of an auxiliary Hamiltonian term— the AGP— that generates the exact infinitesimal displacement of an instantaneous eigenstate when a control parameter λ is varied. Traditional approaches to AGP synthesis face three major obstacles: (i) the need to introduce many‑body or non‑local operators that are absent from the target Hamiltonian, (ii) the exponential growth of operator bases when attempting to include higher‑order nested commutators, and (iii) the experimental burden of high‑frequency driving (in Floquet schemes) or deep quantum circuits (in digital schemes).

UDCD overcomes these limitations by (1) restricting all building blocks to the original Hamiltonian (\hat H(\lambda)) and its parameter derivative (\partial_\lambda \hat H(\lambda)), thereby avoiding any extra interaction terms; (2) employing a Fourier‑series representation of the function (-1/\omega) that appears in the exact AGP, which naturally generates an infinite series of nested commutators without explicit truncation; and (3) providing closed‑form expressions for the rotation angles that appear in the digital circuit, eliminating the need for costly numerical optimization.

The central construct is a composite unitary operator \