On the obfuscatability of quantum point functions

The goal of this work is to provide a positive result of quantum obfuscation. Point functions have been widely discussed in classical obfuscation theory but yet not formally defined in the quantum setting. To analyze the obfuscatability of quantum point functions, we start with preliminaries on quantum obfuscation, giving out the oracle-implementable relationship of two quantum circuit families and some obfuscations of combined quantum circuits. Then, we present the strict definition of a quantum point function and discuss its variants of multiple points and multiple qubits. Under the quantum-accessible random oracle model, we obtain the obfuscatability of quantum point function families by means of reduction. Finally, we discuss the application of quantum obfuscation in quantum zero-knowledge. As a start of study on quantum point functions, our work will be inspiring in the future development of quantum obfuscation theory.