Quantum gate errors are a significant challenge for achieving precision measurements on noisy intermediate-scale quantum (NISQ) computers. This paper focuses on zero noise extrapolation (ZNE), a technique that can be implemented on existing hardware, studying it in detail and proposing modifications to existing approaches. In particular, we consider identity insertion methods for amplifying noise because they are hardware agnostic. We build a mathematical formalism for studying existing ZNE techniques and show how higher-order polynomial extrapolations can be used to systematically reduce depolarizing errors. Furthermore, we introduce a new method for amplifying noise that uses far fewer gates than traditional methods. This new approach is compared with existing methods for simulated quantum circuits. Comparable or smaller errors are possible with fewer gates, which illustrates the potential for empowering an entirely new class of moderate-depth circuits on near term hardware.

中文翻译：

---

零噪声外推可减少带有标识插入的量子门错误

量子门误差是在嘈杂的中级量子（NISQ）计算机上实现精确测量的一项重大挑战。本文着重于零噪声外推（ZNE），这是一种可以在现有硬件上实现的技术，对其进行详细研究并提出对现有方法的修改方案。特别地，我们考虑使用身份插入方法来放大噪声，因为它们与硬件无关。我们建立了一种数学形式主义来研究现有的ZNE技术，并展示了如何使用高阶多项式外推法来系统地减少去极化误差。此外，我们介绍了一种新的放大噪声的方法，该方法使用的门比传统方法少得多。将该新方法与用于模拟量子电路的现有方法进行了比较。