Geometrical scheduling of adiabatic control without information of energy spectra

A method for estimating the ground state of a given problem Hamiltonian using quantum devices that has been studied is adiabatic control [1]. In adiabatic control, one starts with a trivial Hamiltonian whose ground state is known, and gradually evolves it into the problem Hamiltonian over time to estimate the desired ground state. However, a challenge in adiabatic control is determining the optimal schedule to suppress non-adiabatic transitions. On the other hand, there is a technique called shortcuts to adiabaticity [2]. This method involves adding counter-diabatic terms to the Hamiltonian to suppress non-adiabatic transitions. It is known that counter-diabatic terms become stronger in regions where non-adiabatic transitions are more likely to occur. If we consider the counter-diabatic terms as an action to be minimized, the geodesic equation for the schedule can be derived [3]. Additionally, recent methods have been proposed to efficiently compute the counter-diabatic terms [4, 5]. In our research, we propose a method to pre-calculate the magnitude of the terms in the shortcuts to adiabaticity and determine a plausible schedule of adiabatic control.

[1] T. Kato, Journal of the Physical Society of Japan 5, 435 (1950).

[2] M. Demirplak and S. A. Rice, The Journal of Physical Chemistry A 107, 9937 (2003).

[3] A. T. Rezakhani, W.-J. Kuo, A. Hamma, D. A. Lidar, and P. Zanardi, Phys. Rev. Letters 103, 080502 (2009).

[4] B. Bhattacharjee, arXiv:2302.07228

[5] K. Takahashi and A. del Campo, Phys. Rev. X 14, 011032