Inverse engineering in quantum and classical systems via shortcut to adiabaticity

T. Kiran, M. Ponmurugan

In general, the conventional Lewis-Riesenfeld invariant-based inverse engineering is a nonadiabatic process that results in the adiabatic final states to achieve the shortcut to adiabaticity, which does not provide complete suppression of non-adiabaticity throughout the evolution. We propose a new method to accomplish the shortcut to adiabaticity through an entirely adiabatic path. This new method is developed using the number operator as an invariant of the Hamiltonian. This paper discusses the mathematical framework of the new method in two-level quantum system and analyzes its performance compared to the conventional Lewis-Riesenfeld invariant-based inverse engineering method.

Obinna Abah, Ricardo Puebla, Mauro Paternostro

Anthony Kiely

Si-Qi Chen, He Lu

Shortcuts to adiabaticity (STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse-engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy (N-$V$) center. The microwave pulses to drive inversely engineered STA are obtained with space-curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of N-$V$ system, and thus benefits quantum sensing and quantum computation based on the N-$V$ platform.

Kazutaka Takahashi

We discuss applications of shortcuts to adiabaticity (STA) to adiabatic quantum computation. After reviewing the fundamental properties and the present status of STA from the author's personal point of view, we apply the method to the adiabatic algorithm of the Grover's problem. We discuss two possible implementations of STA for the adiabatic quantum computations: the method of quantum adiabatic brachistochrone and the Lewis-Riesenfeld invariant-based inverse engineering.

Jincheng Shi, Yicheng Pan, Yue Ban +1 more

Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$θ$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.