Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has
shown promising applications in machine learning, optimization, and
cryptography. Despite the progress, challenges persist due to system noise,
errors, and decoherence that complicate the simulation of quantum systems. The
depolarization channel is a standard tool for simulating a quantum system's
noise. However, modeling such noise for practical applications is
computationally expensive when we have limited hardware resources, as is the
case in the NISQ era. We propose a modified representation for a single-qubit
depolarization channel with two Kraus operators based only on X and Z Pauli
matrices. Our approach reduces the computational complexity from six to four
matrix multiplications per execution of a channel. Experiments on a Quantum
Machine Learning (QML) model on the Iris dataset across various circuit depths
and depolarization rates validate that our approach maintains the model's
accuracy while improving efficiency. This simplified noise model enables more
scalable simulations of quantum circuits under depolarization, advancing
capabilities in the NISQ era.

在噪声中间量子（NISQ）时代的量子计算在机器学习、优化和密码学等领域展示出了有前景的应用。然而，由于系统噪声、错误和退相干，这些挑战使得量子系统的模拟变得复杂。本文提出了一种改进的单比特去极化通道表示法，使用了仅基于 X 和 Z Pauli 矩阵的两个 Kraus 算子，从而将计算复杂度从每次通道执行的六个矩阵乘法降低为四个。在各种电路深度和去极化速率的条件下，对鸢尾花数据集上的量子机器学习（QML）模型进行的实验证实了我们的方法在提高效率的同时保持了模型的准确性。这种简化的噪声模型使得在去极化下更具可扩展性的量子电路模拟成为可能，推动了 NISQ 时代的技术发展。