A Holistic Approach to Rotation Synthesis for Fault- Tolerant Quantum Computation

Rotation operations are essential ingredients in quantum algorithms. However, fault-tolerant quantum computation is intrinsically digital, based on a finite set of primitive gates, and thus cannot provide an analog rotation operation with arbitrary angles. It must resort to approximating a rotation operation using a basic universal gate set. Prior work on rotation synthesis either focuses on synthesizing individual rotations without considering a quantum circuit as a whole or is restricted to the specific quantum Fourier transform circuit. In this work, we develop a holistic and general approach to rotation synthesis, taking all rotation operations of a circuit into account for quantum cost minimization. Experimental results demonstrate the superiority of our method compared to the state-of-the-art methods in reducing the cost of synthesized Quantum algorithms with rotation operations.