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Physical Review A

Shortcut engineering for accelerating topological quantum state transfers in optomechanical lattices

Jin-Kang Guo, Jin‐Lei Wu, Ji Cao, Shou Zhang, Shi‐Lei Su

Published Oct 15, 2024• 19 citations
Publisher

Abstract

We propose several schemes with diverse optional types of couplings to accelerate adiabatic topological quantum state transfers (QSTs) in optomechanical lattices (OMLs) by utilizing shortcut engineering, which hold significant promise for constructing topologically protected quantum networks. We first investigate the counterdiabatic (CD) schemes of shortcut to adiabatic topological QST in a small OML consisting of five sites. We show that a perfect QST can be achieved with either the full or the partial-CD terms, and the QST duration can be reduced to about one-tenth of that in the adiabatic version. To circumvent the next-nearest-neighbor couplings in the CD shortcut schemes, the detuning-induced transitionless-quantum-driving scheme is proposed and improved by incorporating the technique of soft quantum control, for which the auxiliary shortcut coupling becomes a nearest-neighbor hopping when considering a cyclic OML. We find that all shortcut schemes can maintain robustness of the adiabatic topological QST against disorders to a great extent, and more importantly, due to the much shorter duration, the shortcut schemes can guarantee a higher efficiency of QST when decay of the OML is taken into account. Finally, we expand the size of OML and propose a more general method by engineering an optimal coupling parameter to speed up the adiabatic topological QSTs, which can significantly shorten the QST duration, especially in large-scale OMLs.

DOI
10.1103/physreva.110.043510

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Quantum Review Letters•Jan 1, 2026•0 citations
We propose several schemes with diverse optional types of couplings to accelerate adiabatic topological quantum state transfers (QSTs) in optomechanical lattices (OMLs) by utilizing shortcut engineering, which hold significant promise for constructing topologically protected quantum networks. We first investigate the counterdiabatic (CD) schemes of shortcut to adiabatic topological QST in a small OML consisting of five sites. We show that a perfect QST can be achieved with either the full or the partial-CD terms, and the QST duration can be reduced to about one-tenth of that in the adiabatic version. To circumvent the next-nearest-neighbor couplings in the CD shortcut schemes, the detuning-induced transitionless-quantum-driving scheme is proposed and improved by incorporating the technique of soft quantum control, for which the auxiliary shortcut coupling becomes a nearest-neighbor hopping when considering a cyclic OML. We find that all shortcut schemes can maintain robustness of the adiabatic topological QST against disorders to a great extent, and more importantly, due to the much shorter duration, the shortcut schemes can guarantee a higher efficiency of QST when decay of the OML is taken into account. Finally, we expand the size of OML and propose a more general method by engineering an optimal coupling parameter to speed up the adiabatic topological QSTs, which can significantly shorten the QST duration, especially in large-scale OMLs.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
In noisy quantum systems, achieving high-fidelity state preparation using the adiabatic approach faces a dilemma: either extending the evolution time to reduce diabatic transitions or shortening it to mitigate decoherence effects. Here we present a quantum shortcut to adiabaticity for state preparation in a finite-sized Jaynes-Cummings lattice by applying counterdiabatic (CD) driving along given adiabatic trajectories. Leveraging the symmetry of eigenstates in our system, we convert the CD driving to an implementable Hamiltonian that only involves local qubit-cavity couplings for a two-site lattice with one polariton excitation. Additionally, we derive a partial analytical form of the CD driving for the lattice with two excitations. Our numerical results demonstrate that circuit errors and environmental noise have negligible effects on our scheme under practical parameters. We also show that our scheme can be characterized through the detection of qubit operators. This approach can lead to a promising pathway to high-fidelity state preparation in a significantly reduced timescale when compared to conventional adiabatic methods.
We propose a protocol to realize fast high-fidelity quantum state transfer between distant optomechanical interfaces connected by a continuum waveguide. The scheme consists of three steps: two accelerating adiabatic processes joined by a population conversion process. In comparison to the traditional adiabatic technique, our method reaches a higher transfer fidelity with a shorter time. Numerical results show that the fidelity of this transfer scheme in the dissipative system mainly depends on the protocol speed and the coupling strength of the waveguide and cavities. Assisted by inverting the pulse sequence, bidirectional transfer can be implemented, indicating the potential to build a quantum network.
Abstract The main challenge in deterministic quantum state transfer (QST) between remote mechanical resonators is the local decoherence and the transmission losses in the communication channel. In the path of overcoming this limitation, here we employ a shortcut to adiabatic passage protocol to devise a fast and reliable evolution path between two remote mechanical modes in separate optomechanical systems (OMSs). A QST between the two nodes is conceived by engineering their coupling to an intermediate fiber optical channel. The coupling pulses are operated such that the dark eigenmode of the system is decoupled from the fiber modes and transitions to the bright modes are compensated for by counterdiabatic drives. We show that one obtains a QST with high fidelity for various Gaussian states. The efficiency is compared to that of adiabatic passage (AP) protocol in the presence of losses and noises. Our results show that while the AP protocol is very sensitive to the decoherence, the shortcut to adiabaticity provides a robust and fast QST even for small values of the coupling strength. The performance of both protocols are also investigated for the case of multimode fiber through numerical and an effective single-model model which is found by the elimination of off-resonant fiber modes. Our findings may pave the way for using OMSs in the realization of continuous-variable Gaussian QST.
Abstract Robust quantum control is essential for the development of quantum computers, which rely on precise manipulation of qubits. One form of quantum control is stimulated Raman adiabatic passage (STIRAP), which ordinarily is a state transfer protocol but was extended by Kis and Renzoni (2002 Phys. Rev. A 65 032318) to perform qubit rotations. Shortcut methods to adiabaticity for STIRAP have been shown to speed up adiabatic processes, beyond the adiabatic criterion, with high fidelity. Here, we apply shortcut to adiabaticity methods to the STIRAP qubit rotation scheme to improve the performance of quantum logic gates. The scheme can be implemented via direct connections between ground states in a 4-level Λ system or effective connections in a 5-level Λ system with modified pulses that implement transitionless quantum driving via the addition of a counterdiabatic driving term. We show that the extended shortcut to adiabaticity method serves to improve the fidelity of qubit rotations in the diabatic regime.
Topological pumping has attracted great attention in topological physics and is highly valuable in the realization of robust quantum state transfer (QST). However, speeding up the topological QST under the requirement of adiabatic evolutions remains challenging. In this work, we propose a geometric adiabatic criterion with an effective quantum metric that characterizes non-adiabatic transitions during evolutions via the quantum metric, minimal energy gap and cycle time. Using two generalized Su–Schrieffer–Heeger models, we systematically validate our adiabatic criterion in optimizing topological pumping paths for transferring single-site states and two-site entangled states, respectively. With numerical simulations, we show that by designing pumping paths for minimizing the effective quantum metric, the fidelity and speed of the QST can be significantly improved. Our works provides a general framework for high-fidelity topological QST via quantum metric optimization.