Low-depth construction of Grover oracles from fully functional quantum circuits

Grover oracle is the core component of the Grover search algorithm. Instead of constructing a Grover oracle from scratch, we consider a common practice that how to construct a Grover oracle based on an existing fully functional quantum circuits (FFQCs). A FFQC typically performs computations for a primary target and includes ancillas (qubits for intermediate storage) restoration. Although these circuits can be directly integrated into an oracle, we find that this inevitably introduces circuit redundancy. To address this, we propose a low-depth transformation method that can convert an existing FFQC into a low-depth Grover oracle. Additionally, our method can further reduce the width while retaining the previously achieved low depth.