We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is $\sim 10$ times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.

Achieving fast population transfer (FPT) in multiparticle systems based on the cavity quantum electronic dynamics is an outstanding challenge. In this paper, motivated by the quantum Zeno dynamics, a shortcut for performing the FPT of ground states in multiparticle systems with the invariant-based inverse engineering is proposed. Numerical simulation demonstrates that a perfect population transfer of ground states in multiparticle systems can be rapidly achieved in one step, and the FPT is robust to both the cavity decay and atomic spontaneous emission. Additionally, this scheme is not only implemented without requiring extra complex conditions, but also insensitive to variations of the parameters.

The “Lewis-Riesenfeld phases” which play a crucial role in constructing shortcuts to adiabaticity may be a resource for the implementation of quantum phase gates. By combining “Lewis-Riesenfeld invariants” with “quantum Zeno dynamics,” we propose an effective scheme of rapidly implementing $\pi$ phase gates via constructing shortcuts to adiabatic passage in a two-distant-atom-cavity system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is discussed. It is noted that this scheme is insensitive to both error sources. Additionally, a creation of $N$-atom cluster states is put forward as a typical example of the applications of the fast and noise-resistant phase gates. The study results show that the shortcuts idea is not only applicable in other logic gates with different systems, but also propagable for many quantum information tasks.

We propose an efficient method to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocols' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms—even only some of them—have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of fast population inversion. The results show that in both Hermitian and non-Hermitian systems, we can design different additional Hamiltonians to replace the traditional counterdiabatic driving Hamiltonian to speed up the process. This method provides many choices for designing additional terms of the Hamiltonian such that one can choose a realizable model in practice.

We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schrödinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schrödinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, $1/f$ noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.

In this paper, we propose a scheme for realizing nonadiabatic holonomic computation assisted by two atoms and the shortcuts to adiabaticity (STA). The blockade effect induced by strong Rydberg-mediated interaction between two Rydberg atoms provides us the possibility to simplify the dynamics of the system, and the STA helps us design pulses for implementing the holonomic computation with high fidelity. Numerical simulations show the scheme is noise immune and decoherence resistant. Therefore, the current scheme may provide some useful perspectives for realizing nonadiabatic holonomic computation.