AI 中文总结
基于光子计算平台，通过求解不同领域的线性方程组验证广义变分量子线性求解器。在复数域引入扰动项处理病态问题，在有限域F2重新设计代价函数扩展VQLS，为其实际应用提供实验基础和方法指导。
AI 中文摘要
基于光子计算平台，我们通过系统求解不同领域的四维线性方程组，对广义变分量子线性求解器（VQLS）进行了实验验证。在复数域中，除了解决有唯一解的非奇异系统外，还研究了由奇异性引起的病态问题。为此引入受蒂霍诺夫正则化启发的扰动项并开发算法。此外，通过重新设计代价函数将VQLS扩展到有限域F2，该模2 VQLS无奇异性，适用于稳定器编码理论，可为量子计算实际应用提供基础和指导。
英文摘要
Based on a photonic computing platform, we experimentally validate a generalized variational quantum linear solver (VQLS) by systematically solving four-dimensional linear equation systems across different fields. In the complex field, in addition to solving non-singular systems that admit a unique solution, we investigate ill-conditioned problems arising from singularity--an issue frequently encountered in practical applications. To tackle these challenges, we introduce perturbation terms, a treatment inspired by Tikhonov regularization, and develop an algorithm capable of handling a wide range of systems. Furthermore, we extend the VQLS to the finite field F2 by redesigning the cost function to incorporate modulo 2 and imposing several constraints on the solution vector. This modulo 2 VQLS is inherently free from singularity. It is adapt to stabilizer coding theory and may find applications in areas such as decoders and the design of quantum gate sequences. Therefore, our work demonstrates the practical potential of VQLS in quantum computing, providing a solid experimental foundation and methodological guidance for its real-world applications.
