This paper investigates the non-Markovian cost function in quantum error mitigation (QEM) and employs Dirac Gamma matrices to illustrate two-qubit operators, significant in relativistic quantum mechanics. Amid the focus on error reduction in noisy intermediate-scale quantum (NISQ) devices, understanding non-Markovian noise, commonly found in solid-state quantum computers, is crucial. We propose a non-Markovian model for quantum state evolution and a corresponding QEM cost function, using simple harmonic oscillators as a proxy for environmental noise. Owing to their shared algebraic structure with two-qubit gate operators, Gamma matrices allow for enhanced analysis and manipulation of these operators. We evaluate the fluctuations of the output quantum state across various input states for identity and SWAP gate operations, and by comparing our findings with ion-trap and superconducting quantum computing systems' experimental data, we derive essential QEM cost function parameters. Our findings indicate a direct relationship between the quantum system's coupling strength with its environment and the QEM cost function. The research highlights non-Markovian models' importance in understanding quantum state evolution and assessing experimental outcomes from NISQ devices.

本文研究了量子误差缓解 (QEM) 中的非马尔可夫成本函数，并采用狄拉克伽玛矩阵来说明双量子位算子，这在相对论量子力学中具有重要意义。在关注减少噪声中尺度量子 (NISQ) 设备中的误差的过程中，了解固态量子计算机中常见的非马尔可夫噪声至关重要。我们提出了一种量子态演化的非马尔可夫模型和相应的 QEM 成本函数，使用简单谐振子作为环境噪声的代理。由于伽玛矩阵与两个量子位门算子共享代数结构，因此可以增强对这些算子的分析和操作。我们评估了身份和交换门操作的不同输入状态下输出量子态的波动，并通过将我们的发现与离子阱和超导量子计算系统的实验数据进行比较，我们得出了基本的 QEM 成本函数参数。我们的研究结果表明量子系统与其环境的耦合强度与 QEM 成本函数之间存在直接关系。该研究强调了非马尔可夫模型在理解量子态演化和评估 NISQ 设备实验结果方面的重要性。