When compiling programs for fault-tolerant quantum computers, approximation errors must be taken into account. We propose a methodology that tracks such errors automatically and solves the optimization problem of finding accuracy parameters that guarantee a specified overall accuracy while aiming to minimize a custom implementation cost. The core idea is to extract constraint and cost functions directly from the high-level description of the quantum program. Then, our custom compiler passes optimize these functions, turning them into (near-)symbolic expressions for (1) the total error and (2) the implementation cost (e.g., total gate count). All unspecified parameters of the quantum program will show up as variables in these expressions, including accuracy parameters. After solving the corresponding optimization problem, a circuit can be instantiated from the found solution. We develop two prototype implementations, one in C++ based on Clang/LLVM, and another using the Q# compiler infrastructure. We benchmark our prototypes on typical quantum computing programs, including the quantum Fourier transform, quantum phase estimation, and Shor's algorithm.

中文翻译：

---

通过（近）符号资源估计自动管理量子程序的准确性

在为容错量子计算机编译程序时，必须考虑近似误差。我们提出了一种自动跟踪此类错误的方法，并解决了寻找精度参数的优化问题，以保证指定的整体精度，同时旨在最小化自定义实现成本。核心思想是直接从量子程序的高层描述中提取约束和代价函数。然后，我们的自定义编译器通过优化这些函数，将它们转换为 (1) 总错误和 (2) 实现成本（例如，总门数）的（接近）符号表达式。量子程序的所有未指定参数将在这些表达式中显示为变量，包括精度参数。求解相应的优化问题后，可以从找到的解决方案中实例化电路。我们开发了两种原型实现，一种使用基于 Clang/LLVM 的 C++，另一种使用 Q# 编译器基础结构。我们在典型的量子计算程序上对我们的原型进行了基准测试，包括量子傅立叶变换、量子相位估计和 Shor 算法。