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.
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.
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.
Physical quantum systems are commonly composed of more than two levels and offer the capacity to encode information in higher-dimensional spaces beyond the qubit, starting with the three-level qutrit. Here, we encode neutral-atom qutrits in an ensemble of ultracold 87Rb and demonstrate arbitrary single-qutrit SU(3) gates. We generate a full set of gates using only two resonant microwave tones, including synthesizing a gate that effects a direct coupling between the two disconnected levels in the three-level $\mathrm{\ensuremath{\Lambda}}$-scheme. Using two different gate sets, we implement and characterize the Walsh-Hadamard Fourier transform, and find similar final-state fidelity and purity from both approaches. This work establishes the ultracold neutral-atom qutrit as a promising platform for qutrit-based quantum information processing, extensions to d-dimensional qudits, and explorations in multilevel quantum state manipulations with nontrivial geometric phases.
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.
Qutrits offer the potential for enhanced quantum computation by exploiting an enlarged Hilbert space. However, the synthesis of high-fidelity and fast qutrit gates, particularly for single qutrits, remains an ongoing challenge, as it involves overcoming intrinsic constraints in quantum platforms. Here, we develop a novel framework for the efficient implementation of a single-qutrit gate set via coherent control, leveraging SU(3) dynamics while obviating platform-specific constraints such as those arising from the selection rule. As a proof-of-principle demonstration, we realize 35-ns qutrit hadamard and x gates using a superconducting transmon, achieving an average fidelity of 99.5%, as verified by randomized benchmarking. We further demonstrate two paradigmatic quantum circuits, which can be naturally extended to scalable qudit algorithms for phase estimation and parity check. In addition, we propose an SU(3)-based decomposition strategy for an arbitrary single-qutrit gate and numerically demonstrate its substantial efficiency improvement over conventional SU(2)-based protocols. By addressing the challenge of efficiently implementing single-qutrit gates, our protocol paves the way for realizing high-performance qutrit processors in diverse quantum platforms.
The capability to control molecular rotation for field-free orientation, which arranges molecules in specific spatial directions without external fields, is crucial in physics, chemistry, and quantum information science. However, conventional methods typically lead to transient orientations characterized by periodic directional reversals and necessitate the generation of coherent superpositions across a broad spectrum of rotational states of ultracold molecules. In this work, we develop a theoretical framework for achieving unidirectional field-free orientation by selectively manipulating two specific rotational states of symmetric top molecules. By leveraging the interplay between coherent superpositions and the precise selection of initial states, we demonstrate that both the maximum achievable orientation and its direction can be effectively controlled. To attain the desired two-state orientation, we present a quantum control strategy that utilizes a single control pulse, significantly simplifying the complexities of conventional multistate or multipulse schemes. Numerical simulations validate the effectiveness and feasibility of this approach for methyl iodide (CH3I) molecules, even when accounting for molecular centrifugal distortion.The results highlight the critical roles of initial-state selection and quantum coherence in achieving long-lasting, high unidirectional molecular orientation, opening new directions in stereochemistry, precision spectroscopy, and quantum computing.
Qudits, generalizations of qubits to multilevel quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the d -level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy-level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in SU ( d ) . Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Numerical validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for 10 − 4 error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.