We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.

翻译：我们提出了一种新颖方法，利用物理信息神经网络（PINNs）的优势，来处理由$N_{Q}$量子比特系统构成的量子电路优化中的逆绝热（CD）协议。主要目标是利用物理启发的深度学习技术，精确求解量子系统中不同物理可观测量随时间的演化。为实现这一目标，我们将必要的物理信息嵌入底层神经网络，以有效攻克该问题。具体而言，我们对所有物理可观测量施加厄米性条件，并利用最小作用量原理，确保基于底层物理获取最恰当的逆绝热项。所提方法为解决CD驱动问题提供了一种可靠的替代方案，摆脱了以往依赖经典数值近似的技术中常见的限制。我们的方法提供了一个通用框架，用于从与该问题相关的物理可观测量中获得最优结果，包括外部时间参数化（即调度函数）、涉及非绝热项的规范势或算符，以及系统能级的时间演化等。该方法的主要应用对象为$\mathrm{H_{2}}$和$\mathrm{LiH}$分子，分别采用STO-3G基组表示为2量子比特和4量子比特系统。展示的结果成功推导出非绝热项的理想分解，该分解通过利用泡利算符的线性组合实现。这一特性为其在量子计算算法中的实际应用提供了显著优势。