Approximation errors must be taken into account when compiling quantum programs into a low-level gate set. We present a methodology that tracks such errors automatically and then optimizes accuracy parameters to guarantee a specified overall accuracy while aiming to minimize the implementation cost in terms of quantum gates.
The core idea of our approach is to extract functions that specify the optimization problem directly from the high-level description of the quantum program. Then, 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 quantum 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.