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In this work, we derive universal nonadiabatic passages in an $M+N$-dimensional discrete system, where $M$ and $N$ denote the degrees of freedom for the assistant and working subspaces, respectively, that could be separated due to rotation or energy. A systematic method is provided to construct parametric ancillary bases for the nonadiabatic passages, which can set up connection between arbitrary initial and target states. In applications, a transitionless dynamics determined by the von Neumann equation with the time-dependent system Hamiltonian can be formulated to entangle distant qubits, as a vital prerequisite for the practical quantum networks. Using tunable longitudinal interaction between two distant qubits, the superconducting system evolves to the single-excitation Bell state with a fidelity as high as $F=0.997$ from the ground state. When the longitudinal interaction is switched off, the single-excitation Bell state can be further converted to the double-excitation Bell state with $F=0.982$ by parametric driving. Moreover, our protocol can be adapted to generate the Greenberger-Horne-Zeilinger state for $N$ qubits with $N$ steps. Our work develops a full-fledged theory for nonadiabatic state engineering in quantum information processing, which is flexible in target selection and robust against the external noise., Comment: 14 pages, 7 figures

A stable and fast path linking arbitrary pair of quantum states is commonly desired for the engineering protocols inspired by stimulated Raman adiabatic passage, such as shortcut to adiabaticity and holonomic transformation. It has immediate applications in quantum control and quantum computation and is fundamental about the exact solution of a time-dependent Schr\"odinger equation. We construct a universal control framework based on the system dynamics within an ancillary picture, in which the system Hamiltonian is diagonal so that no transition exists among the ancillary bases during the time evolution. Practically the desired evolution path can be obtained by the von Neumann equation for the parametric ancillary bases. We demonstrate that our control framework can be reduced to the nonadiabatic holonomic quantum transformation, the Lewis-Riesenfeld theory for invariant, and the counterdiabatic driving method under distinct scenarios and conditions. Also it can be used to achieve the cyclic transfer of system population that could be a hard or complex problem for the existing methods. For the state engineering over a finite-dimensional quantum system, our work can provide a full-rank nonadiabatic time-evolution operator.

A stable and high-quality single-magnon state is desired by the single-magnon source for quantum information application with a macroscopic spin system. We consider a hybrid system where a magnon mode is directly coupled to a nonresonant superconducting qubit via the exchange interaction. The magnon and qubit are under the driving and probing fields with the same frequency, respectively. We find that the single-magnon probability $P_1$ can be maximized when the product of the magnon-driving field detuning and the qubit-probing field detuning is equivalent to the square of the magnon-qubit coupling strength, $\Delta_q\Delta_m=J^2$. Then, the double-magnon probability $P_2$ can be minimized by tuning the ratio of the probing intensity to the driving intensity and the relative phase between the two fields. Under these optimized conditions with accessible strong driving intensity and low decay rate, strong magnon blockade gives rise to a stable single-magnon state with a high quality. It features a large brightness (the single-magnon probability) $P_1\approx0.40$ and a high purity (the equal-time second-order correlation function) $g^{(2)}(0)\sim10^{-5}$. The two indicators as a whole prevail over the existing results for photon, phonon, and magnon modes with respect to a stable single-quantum state. The optimized conditions with a scalable modification $\Delta_q\Delta_m\approx NJ^2$ apply to the situation when one focus on only one of the $N$ magnon modes that are simultaneously coupled to a common qubit., Comment: 10 pages, 7 figures

Nonadiabatic holonomic quantum gates are high-speed and robust. Nevertheless, they were found to be more fragile than the adiabatic gates when systematic errors become dominant. Inspired by the dark-path scheme that was used to partially relieve the systematic error in the absence of external noise, we construct a universal set of nonadiabatic holonomic $N$-qubit gates using the Rydberg-Rydberg interaction between atoms under off-resonant driving. Based on an effective four-level configuration in the Rydberg-atom system, the modified nonadiabatic holonomic geometric gates present a clear resilience to both systematic error in the whole parametric range and external noise. In our scheme, the conventional ultrastrong interaction between control atoms and the target atom for the nonadiabatic holonomic quantum computation is compensated by the detuning of the driving fields on the target atom. That idea yields a deeper understanding about the holonomic transformation. Moreover, our scheme is compact and scale-free with respect to $N$. It is interesting to find that the three-qubit gate is less susceptible to errors than the double-qubit one.

A hybrid system established by the direct interaction between a magnon mode and a superconducting transmon qubit is used to realize a high-degree blockade for magnon. It is a fundamental way toward quantum manipulation at the level of a single magnon and preparation of single magnon sources. Through weakly driving the magnon and probing the qubit, our magnon-blockade proposal can be optimized when the transversal coupling strength between the magnon and qubit is equivalent to the detuning of the qubit and the probing field or that of the magnon and the driving field. Under this condition, the equal-time second-order correlation function $g^{(2)}(0)$ can be analytically minimized when the probing intensity is about three times the driving intensity. Moreover, the magnon blockade could be further enhanced by proper driving intensity and system decay rate, whose magnitudes outrange the current systems of cavity QED and cavity optomechanics. In particular, the correlation function achieves $g^{(2)}(0)\sim10^{-7}$, about two orders lower than that for the photon blockade in cavity optomechanics. Also, we discuss the effects on $g^{(2)}(0)$ from thermal noise and the extra longitudinal interaction between the magnon and qubit. Our optimized conditions for blockade are found to persist in these nonideal situations.

We propose a nuclear-spin-polarization protocol in a general evolution-and-measurement framework. The protocol works in a spin-star configuration, where the central spin is coupled to the surrounding bath (nuclear) spins by flip-flop interaction of equal strength and is subject to a sequence of projective measurements on its ground state. Then a nondeterministic nuclear spin polarization could be implemented by entropy reduction through measurement. The optimized measurement-interval $\tau_{\rm opt}$ is analytically obtained in the near-resonant condition, which is relevant to the nuclear spins' polarization degree of the last-round measurement, the number of nuclear spins, and the coupling strength between the central spin and nuclear spins. Hundreds and even thousands of randomly aligned nuclear spins at the thermal state could be almost fully polarized with an optimized sequence of less than $20$ unequal-time-spacing measurements. In comparison to the conventional approaches, our protocol is not sensitive to the magnetic-field intensity, and it is robust against the extra counterrotating interaction in the near-resonant situation.