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arXiv:2605.03461

Analytical two-pulse control of universal single-qubit gates in rotational ultracold NaCs molecules

Qi Chen, Hao-Xuan Luo, Jin-Kang Guo, Qian-Qian Hong, Li-Bao Fan, Chuan-Cun Shu

quant-phSubmitted May 5, 2026• Announced May 6, 2026• 0 citations
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Abstract

Complex control protocols and sensitivity to experimental imperfections have limited the practical implementation of quantum gate operations. Here, we present an analytical framework for universal single-qubit gates using rotational states of ultracold NaCs molecules. By encoding qubits in the lowest rotational energy levels, we employ a first-order Magnus expansion to derive closed-form unitary evolution from an optimized two-pulse sequence. This approach establishes precise amplitude and phase conditions for arbitrary single-qubit rotations, achieving gate fidelities above 0.9999 in numerical simulations. We further demonstrate that complex multi-gate sequences, including phase-locked operations, can be executed with minimal population leakage into auxiliary states. The time-dependent molecular orientation is shown to faithfully encode both the gate truth table and coherence dynamics, enabling practical gate tomography via weak-field polarization detection. Our analytical method is also applicable to other molecules and physical platforms, offering a potential path to high-fidelity, scalable molecular quantum processors.

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Complex control protocols and sensitivity to experimental imperfections have limited the practical implementation of quantum gate operations. Here, we present an analytical framework for universal single-qubit gates using rotational states of ultracold NaCs molecules. By encoding qubits in the lowest rotational energy levels, we employ a first-order Magnus expansion to derive closed-form unitary evolution from an optimized two-pulse sequence. This approach establishes precise amplitude and phase conditions for arbitrary single-qubit rotations, achieving gate fidelities above 0.9999 in numerical simulations. We further demonstrate that complex multi-gate sequences, including phase-locked operations, can be executed with minimal population leakage into auxiliary states. The time-dependent molecular orientation is shown to faithfully encode both the gate truth table and coherence dynamics, enabling practical gate tomography via weak-field polarization detection. Our analytical method is also applicable to other molecules and physical platforms, offering a potential path to high-fidelity, scalable molecular quantum processors.
We present a theoretical framework for universal single-qutrit control in asymmetric-top molecules, advancing molecular quantum information processing. In this approach, the qutrit is encoded in three rotational eigenstates, with an auxiliary state providing independent phase control within the computational manifold. We explore an analytic protocol for arbitrary single-qutrit gates, combining directly addressable SU(2) rotations with auxiliary-state-mediated phase operations. To support this, we derive a multilevel pulse-area theorem that provides an explicit analytic mapping between gate parameters and control fields, enabling systematic design of high-fidelity microwave pulse sequences. Numerical simulations with 1,2-propanediol confirm the robustness of our approach, achieving Walsh-Hadamard gates with minimal leakage from the computational subspace. We further examine four SU(2) decomposition strategies and find that phase-error sensitivity depends on the decomposition sequence, while amplitude errors propagate along specific coherence pathways. Our results establish asymmetric-top molecules as a viable platform for qutrit-based quantum operations and offer an analytical method for precise quantum control of complex multilevel systems.
The lack of a direct map between control fields and desired control objectives poses a significant challenge in applying quantum control theory to quantum technologies. Here, we propose an analytical framework to precisely control a limited set of quantum states and construct desired coherent superpositions using a well-designed laser pulse sequence with optimal amplitudes, phases, and delays. This theoretical framework that corresponds to a multilevel pulse-area theorem establishes a straightforward mapping between the control parameters of the pulse sequence and the amplitudes and phases of rotational states within a specific subspace. As an example, we utilize this approach to generate 15 distinct and desired rotational superpositions of ultracold polar molecules, leading to 15 desired field-free molecular orientations. By optimizing the superposition of the lowest 16 rotational states, we demonstrate that this approach can achieve a maximum orientation value of | 〈 cos θ 〉 | max above 0.99, which is very close to the global optimal value of 1 that could be achieved in an infinite-dimensional state space. This work marks a significant advancement in achieving precise control over multilevel subsystems within molecules. It holds potential applications in molecular alignment and orientation, as well as in various interdisciplinary fields related to the precise quantum control of ultracold polar molecules, opening up considerable opportunities in molecular-based quantum techniques.
Ultracold polar molecules possess a manifold of long-lived molecular rotational states, which can be coherently controlled using microwave fields and entangled by the long-range dipole-dipole interactions between molecules. The ability to control these features at the individual molecule level provides a rich toolbox with which to engineer quantum simulations of exotic materials or build a molecular quantum computer. Until recently, this level of single molecule control has eluded researchers due to the challenges inherent in taming the complex internal structure of molecules. In this thesis, we demonstrate full control over the internal quantum states and coherent interactions of individual NaCs molecules in optical tweezers. This platform is based on coherent assembly of ultracold Na and Cs atoms trapped and cooled in separate arrays, before being magnetoassociated at a Feshbach resonance to form weakly-bound molecules. Using high-resolution spectroscopy of electronically excited molecular states, we identify an efficient two-photon pathway to the rovibrational ground state of NaCs that we use to prepare an array of ground state molecules in tweezers. We demonstrate a "magic ellipticity'' technique to eliminate differential light shifts between two molecular rotational states and achieve coherence times of up to 250(40) ms for a superposition of those states. We then show that we can rearrange molecules in an array to eliminate defects and perform single-shot readout of multiple rotational states using controlled molecule dissociation and imaging of constituent atoms at high magnetic field. Finally, we coherently control the dipole-dipole interactions between two molecules, producing a Bell state with a fidelity of 94(3) % and demonstrating a universal entangling iSWAP gate for qubits encoded in molecular hyperfine states.
The design of shaping pulse fields for controlling molecular orientation is of great importance in fields of stereochemical reactions, strong-field ionization, and quantum information processing. Traditional quantum optimal control algorithms typically solve the problem of molecular orientation in an infinite-dimensional rotational space, but they often overlook the constraints imposed by experimental limitations. In this work, a multi-objective and multi-constraint quantum optimal control algorithm is proposed to design a pulse field that conforms to the constraints of pulse area and energy. Specifically, the algorithm enforces a zero pulse area condition to eliminate the static field components and maintains constant pulse energy, ensuring compatibility with realistic experimental setups. Under these constraints, the algorithm optimizes the population and phase distribution of a selected number of low-lying rotational states in ultracold molecules to achieve maximum molecular orientation. The effectiveness of the proposed algorithm is demonstrated through numerical studies involving two- and three-state target subspaces, where the creation of a coherent superposition state with optimized population and phase distribution leads to the desired molecular orientation. Furthermore, its scalability is validated by applying it to a more complex 17-state subspace, where a maximum orientation value of 0.99055 is obtained, approaching the global optimal value of 1. Our findings demonstrate that by effectively managing these constraints, the influence of rotational states in the non-target state subspace can be substantially suppressed. The time-frequency analysis of the optimized pulses, combined with the Fourier transform spectrum of the time-dependent degree of orientation, indicates that the maximum molecular orientation is mainly achieved through ladder-climbing excitation of multi-color pulse fields, with the contributions from highly excited states being minimal. This work provides a valuable reference for designing experimentally feasible pulse fields using multi-constraint optimization algorithms, which helps to precisely control a limited number of rotational states to achieve maximum molecular orientation.
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.
We numerically investigate the possibilities of driving quantum algorithms with laser pulses in a register of ultracold NaCs polar molecules in a static electric field. We focus on the possibilities of performing scalable logical operations by considering circuits that involve intermolecular gates (implemented on adjacent interacting molecules) to enable the transfer of information from one molecule to another during conditional laser-driven population inversions. We study the implementation of an arithmetic operation (the addition of 0 or 1 on a binary digit and a carry in) which requires population inversions only and the Deutsch-Jozsa algorithm which requires a control of the phases. Under typical experimental conditions, our simulations show that high-fidelity logical operations involving several qubits can be performed in a time scale of a few hundreds of microseconds, opening promising perspectives for the manipulation of a large number of qubits in these systems.