We present a Physics-Informed Neural Quantum Control (PINQC) framework for rovibrational photoassociation in a Morse molecular system. The proposed method combines neural-network-based laser-field generation with differentiable quantum propagation, allowing optimized laser pulses to be obtained directly from the underlying quantum dynamics without requiring external training data. The optimized control fields efficiently transfer an initially continuum-like Gaussian wave packet into the vibrational ground-state level, promoting continuum-to-bound population transfer through coherent rovibrational dynamics. The resulting photoassociation process involves both vibrational stabilization and rotational redistribution arising naturally from dipole-induced couplings between neighboring rotational channels. A central result of the present work is the successful application of the PINQC framework to extended rovibrational models containing larger rotational levels than those previously accessible in our conventional photoassociation calculations. The optimization remains numerically stable despite the increased complexity of the molecular system, demonstrating that differentiable optimization provides an effective strategy for treating rovibrational models of increased dimensionality. These results establish the PINQC framework as a promising computational tool for molecular photoassociation and motivate future investigations of increasingly complex rovibrational quantum-control problems.
We present a Physics-Informed Neural Quantum Control (PINQC) framework for rovibrational photoassociation in a Morse molecular system. The proposed method combines neural-network-based laser-field generation with differentiable quantum propagation, allowing optimized laser pulses to be obtained directly from the underlying quantum dynamics without requiring external training data. The optimized control fields efficiently transfer an initially continuum-like Gaussian wave packet into the vibrational ground-state level, promoting continuum-to-bound population transfer through coherent rovibrational dynamics. The resulting photoassociation process involves both vibrational stabilization and rotational redistribution arising naturally from dipole-induced couplings between neighboring rotational channels. A central result of the present work is the successful application of the PINQC framework to extended rovibrational models containing larger rotational levels than those previously accessible in our conventional photoassociation calculations. The optimization remains numerically stable despite the increased complexity of the molecular system, demonstrating that differentiable optimization provides an effective strategy for treating rovibrational models of increased dimensionality. These results establish the PINQC framework as a promising computational tool for molecular photoassociation and motivate future investigations of increasingly complex rovibrational quantum-control problems.
A quantum shortcut to adiabaticity scheme based on physics-informed neural networks is proposed in this work. Compared with traditional shortcut to adiabaticity technology, our method innovatively integrates machine learning methods by employing parameterized physics-informed neural networks to solve parameterized differential equations. The neural networks serve as an approximating function for quantum adiabatic evolution processes, while incorporating parameter-dependent differential equations and various physical constraints as components of the loss function. Through networks training, we effectively simulate quantum system dynamics and derive the driving control field for population inversion. Numerical simulations show that the quantum system can achieve rapid population inversion within significantly reduced time while maintaining high fidelity and exceptional robustness against parameter fluctuations. The neural networks exhibit remarkable computational capabilities, particularly suitable for generating control functions in complex quantum systems. Compared with conventional counter-diabatic driving and transitionless quantum driving methods, this PINN-based framework not only achieves better control performance but also provides the improved practicality for experimental implementations. The success of this method demonstrates its promising applications in quantum control tasks, including but not limited to quantum state preparation, quantum gate optimization, and adiabatic quantum computing acceleration.
Quantum optimal control is a key tool for steering quantum dynamics, but its computational cost grows rapidly with the Hilbert space dimension. Here, we introduce a Fourier Neural Operator (FNO)-based framework for learning high dimensional molecular quantum dynamics and accelerating the inverse design of control protocols. Given an initial molecular population distribution, laser frequency, and polarization, the FNO predicts molecular-motional population dynamics up to 107 times faster than GPU-accelerated numerical propagation with CUDA-Q Dynamics. Using this fast and differentiable surrogate, we develop the FNO stochastic pulse-measurement planner (FNO-SPMP), which constructs pulse sequences to purify an initially mixed Boltzmann distribution. We demonstrate the protocol in an 888-dimensional subspace of the hydronium molecule at 20 K, achieving a target-state population of 0.98 with a sequence success rate of up to 86.2%. In a shared discrete control space, FNO-SPMP achieves nearly twice the success rate of a reinforcement-learning baseline while using roughly half as many quantum control pulses and reducing pulse-sequence generation time from approximately 10 hours to 10-20 minutes. These results show that operator-learning surrogates can enable inverse design in quantum systems whose Hilbert spaces are too large for conventional direct optimization.
Physics-informed neural networks (PINNs) represent a methodology that integrates physical equations into neural networks. By incorporating the residuals of physical equations as part of the loss function, PINNs enable the network to learn data features while simultaneously satisfying the constraints imposed by physical laws. The underlying principle of PINNs involves using optimization algorithms to iteratively update the network parameters until the value of a specified physics-informed loss function decreases to an acceptable level, thereby driving the network towards the solution of the differential equations. This approach is not merely a tool but serves as a bridge integrating scientific computing with artificial intelligence, offering novel paradigms for modeling and predicting complex systems. In this paper, we propose a non-Hermitian shortcut to adiabaticity (STA) scheme based on physics-informed neural networks. We utilize the physics-informed neural networks to solve parameterized differential equations, employing the neural networks as an approximating function for the quantum adiabatic evolution process. This provides an interpretable and end-to-end framework (termed STAPINNs) for control-field optimization, distinct from traditional gradient-based approaches like gradient ascent pulse engineering (GRAPE), which require pre-defined pulse parameterization. The parameterized differential equations, along with various physical constraints, are incorporated into the network's loss function. Training the networks allows them to fit the quantum system's evolution process and obtain the driving control function for population inversion. Compared to conventional STA techniques, our approach introduces machine learning into non-Hermitian quantum systems, enabling highly robust and high-fidelity population transfer. Numerical simulations demonstrate that the proposed method significantly outperforms traditional STA protocols under dissipative conditions, achieving fidelities above 0.99 even in the presence of substantial decoherence. Moreover, the framework demonstrates strong generalization across wide parameter ranges and is inherently scalable to multi-level and many-body systems due to the mesh-free, high-dimensional handling capability of PINNs. Neural networks possess strong computational capabilities suitable for generating driving control functions in complex systems, and are equally applicable to non-Hermitian STA techniques. The STAPINNs framework not only enhances control flexibility but also provides a powerful tool for optimizing quantum operations in open and noisy systems.
Physics-informed neural networks (PINNs) provide a pathway to reunify the simulation and control of quantum systems, in which these two tasks are typically decoupled in traditional strategies. However, most work remains confined to Markovian environments. When applied to non-Markovian systems, standard PINN architectures fail to converge reliably due to multi-objective optimization conflicts arising from the coupled differential equations. To address this fundamental limitation, we extend our previously proposed forked PINN (FPINN) by incorporating a dedicated control branch. By decoupling the optimization objectives at the gradient level via selective gradient flow, our method turns a previously intractable multi-task optimization into a well-conditioned one, allowing simulation and control to be optimized jointly without compromise. Numerical simulations on a two-qubit Heisenberg XXX model confirm that our framework faithfully reproduces the features of non-Markovian dynamics, including decoherence and information backflow. Taking a state-preparation task on the same model as an example, our FPINN achieves higher fidelity than gradient ascent pulse engineering, chopped random basis, and standard PINNs, with the advantage becoming more pronounced as the environment becomes more dissipative and more Markovian. The generated pulses are also noticeably smoother, which is advantageous for experimental implementation. Our framework thus provides a unified, end-to-end differentiable paradigm for simulation and control of open quantum systems, with potential implications for quantum computing, simulation, and control.
We have numerically examined optimization of the experimentally achievable shapes of mid-infrared femtosecond laser pulses to construct elementary quantum gates using molecular rovibrational states of a single molecule. Instead of optimizing the electric field by optimal control theory, the method generally used in theoretical studies of coherent control, the transmittance and the phase shift of conventional pulse shapers were optimized in the frequency domain by a genetic algorithm. The target molecular system we examined was the rotation-vibration states of CO in the $X({^{1}\ensuremath{\Sigma}}^{+})$ ground electronic state. Although the existence of the rotational degrees of freedom makes the quantum gate operation complicated, high fidelity of over 0.95 was achieved for one-rovibrational-qubit systems, which indicates that a molecular quantum computer may be feasible for at least one-qubit calculations on a diatomic molecule. On the other hand, two-qubit calculations are more difficult to achieve in a single CO molecule using rotational and vibrational degrees of freedom as different qubits. The importance of the control of the rotational in addition to the vibrational wave packet in order to realize a molecular quantum computer is discussed.
In this paper, authors present a physics-informed neural networks (PINN) approach for solving the optimal control problem (OCP) of the stochastic Schrödinger equation (SSE), with an emphasis on applications in quantum optics. The SSE models quantum systems under uncertainty, a scenario often encountered in open quantum systems where environmental interactions introduce randomness into the system dynamics. These stochastic dynamics are particularly relevant in quantum optics, where precise control over quantum states is crucial for applications such as quantum computing, secure communication, and measurement protocols. Traditional numerical methods for solving such problems face limitations due to high computational costs and the complexity associated with stochastic partial differential equations. The proposed approach utilises PINN, a type of deep learning model that integrates physical laws directly into the learning process by incorporating loss functions based on governing equations, initial and boundary conditions. The fidelity-based objective function is constructed to achieve the desired quantum state so as to develop an OCP solving algorithm. The proposed work is distinguished between deterministic drift-based training and post-training stochastic validation. Extensive numerical experiments are demonstrated near-unity deterministic fidelity. Further, a systematic architecture study validated that a moderately deep network yielded optimal performance with reduced computational cost. Fidelity dissipation analysis confirmed that the method maintained accuracy even under strong damping. These findings established the PINN as an efficient and physically consistent framework for quantum optimal control in open systems.