Abstract

In recent years, Quantum Computing has revolutionized the field of physics by enabling researchers to tackle complex problems that were previously unsolvable. The ability to simulate and analyze phenomena at a quantum level has led to significant breakthroughs in our understanding of the universe. In this article, we describe and discuss how quantum computers are being used for cutting-edge research in quantum physics. The time-independent Schrödinger equation is a cornerstone of quantum mechanics, yet its solution for complex systems is a formidable computational challenge. Quantum Physics-Informed Neural Networks (QPINNs) have emerged as a promising paradigm, leveraging Quantum Neural Networks (QNNs) as a wavefunction ansatz within a physics-informed machine learning framework. A critical and often overlooked aspect of training these models is the management of the multi-term loss function, which balances adherence to the governing Partial Differential Equation (PDE) with physical constraints such as normalization. This paper presents a comprehensive implementation and comparative analysis of two distinct Dynamic Loss Weighting (DLW) strategies for training QPINNs to solve the 1D time-independent Schrödinger equation. The first strategy is an adaptive, gradient-based method that dynamically balances loss components based on their real-time impact on model parameters. The second is a pre-scheduled annealing method that follows a curriculum-like approach, prioritizing different physical constraints at different stages of training. We apply these methods to two benchmark systems: the Quantum Harmonic Oscillator (QHO) and the Finite Square Well. Our results demonstrate that the adaptive, gradient-based DLW, when paired with a physic informed wavefunction ansatz for the QHO, achieves remarkable accuracy, converging to the exact ground state energy of \(E\) = 0.5. Conversely, the scheduled annealing strategy applied to Square Well, using a more generic ansatz, converges to a plausible energy but with a higher residual loss. This comparative analysis reveals a crucial insight: the effectiveness of a DLW strategy is deeply intertwined with the physical-informedness of the underlying wavefunction ansatz. This suggests that a synergistic co-design philosophy, which considers the interplay between the quantum model's architecture and the adaptive training algorithm, is essential for developing robust and accurate QPINN-based solvers for quantum systems.