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Optics Express

Optical control of entanglement and coherence for polar molecules in pendular states

Zuo-Yuan Zhang, Jin‐Ming Liu, Zhengfeng Hu, Yuzhu Wang

Published Sep 9, 2019• 12 citations
Publisher

Abstract

Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.

DOI
10.1364/oe.27.026588

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Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.
Quantum entanglement in high-dimensional Hilbert space offers broad prospects for quantum information science. Polar molecules have a rich internal structure and long coherence time, serving as an attractive candidate for quantum information processing. In this paper, we propose a theoretical scheme for creating high-dimensional entangled states based on ultracold SrO molecules. Qudits are encoded in the pendular states induced by an external electric field and coupled by the dipole-dipole interaction. With the assistance of optimal control theory, a series of optimal microwave fields is designed for the generation of an entangled qutrit-qubit state, qutrit-qutrit state, and ququart-ququart state through numerical iterations. We detail the relation of the fidelity and entanglement of the systemic final states with the number of iteration steps after the control fields are applied and analyze the population dynamics of the field-driven wave functions during time evolution. Moreover, three coupled SrO molecules arranged in an equilateral triangle configuration are employed as pendular qubits, and the trimolecular WWW and Greenberger-Horne-Zeilinger states are realized with high fidelities by optimal control. The specific molecule and experimental parameters used in our theoretical studies are chosen for computational convenience, but we include a discussion of how our results can be applied to realistic situations as well. In principle, our results could be extended to a situation with more pendular qudits, providing a significant step toward the achievement of high-dimensional quantum information processing with arrays of polar molecules.
Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system.
Abstract We consider two ultracold polar symmetric top molecules coupled by dipole-dipole interaction in an external electric field with appreciable intensity gradient, serving as the physical carrier of quantum information. Each molecule is induced to undergo pendular oscillations under the strong static electric field. Based on the pendular states of polar symmetric top molecules as candidate qubits, we investigate the bipartite quantum correlations of the two polar molecular system for the thermal equilibrium states, characterized by negativity and quantum discord, and then analyze the corresponding coherence, measured by relative entropy and l1 norm. Furthermore, we also examine the dynamics of the entanglement and coherence of the system in the presence of intrinsic decoherence, and explore the relations of their temporal evolution with various physical system parameters for two different initial Bell states. It is found that quantum correlations and coherence of the two polar molecules in pendular states can be manipulated by adjusting appropriate reduced variables including external electric field, dipole-dipole interaction, ambient temperature and decoherence factor. Our findings could be used for molecular quantum computing based on rotational states.
We propose a scheme for achieving basic quantum gates using ultracold polar molecules in pendular states. The qubits are encoded in the YbF molecules trapped in an electric field with a certain gradient and coupled by the dipole-dipole interaction. The time-dependent control sequences consisting of multiple pulses are considered to interact with the pendular qubits. To achieve high-fidelity quantum gates, we map the control problem for the coupled molecular system into a Markov decision process and deal with it using the techniques of deep reinforcement learning (DRL). By training the agents over multiple episodes, the optimal control pulse sequences for the two-qubit gates of NOT, controlled NOT, and Hadamard are discovered with high fidelities. Moreover, the population dynamics of YbF molecules driven by the discovered gate sequences are analyzed in detail. Furthermore, by combining the optimal gate sequences, we successfully simulate the quantum circuit for entanglement. Our findings could offer new insights into efficiently controlling molecular systems for practical molecule-based quantum computing using DRL.
Polar molecules are a promising platform for achieving scalable quantum information processing because of their long-range electric dipole-dipole interactions. Here, we take the coupled ultracold CaF molecules in an external electric field with gradient as qubits and concentrate on the creation of intermolecular entanglement with the method of deep reinforcement learning (RL). After sufficient training episodes, the educated RL agents can discover optimal time-dependent control fields that steer the molecular systems from separate states to two-qubit and three-qubit entangled states with high fidelities. We analyze the fidelities and the negativities (characterizing entanglement) of the generated states as a function of training episodes. Moreover, we present the population dynamics of the molecular systems under the influence of control fields discovered by the agents. Compared with the schemes for creating molecular entangled states based on optimal control theory, some conditions (e.g., molecular spacing and electric field gradient) adopted in this work are more feasible in the experiment. Our results demonstrate the potential of machine learning to effectively solve quantum control problems in polar molecular systems.
We present a systematic approach to implementation of basic quantum logic gates operating on polar molecules in pendular states as qubits for a quantum computer. A static electric field prevents quenching of the dipole moments by rotation, thereby creating the pendular states; also, the field gradient enables distinguishing among qubit sites. Multi-target optimal control theory is used as a means of optimizing the initial-to-target transition probability via a laser field. We give detailed calculations for the SrO molecule, a favorite candidate for proposed quantum computers. Our simulation results indicate that NOT, Hadamard and CNOT gates can be realized with high fidelity, as high as 0.985, for such pendular qubit states.