Shallow Circuit Implementation for the Phase Form of Quantum Hashing and Local-Sensitive Hashing on IBMQ Noisy Emulators

In this work, we consider a well-known quantum hashing technique, and focus on its circuit representation. We implemented a shallow circuit for a phase form of the quantum hashing on a noisy emulator of IBMQ quantum devices using 8 qubits and showed that we can solve a problem MOD131 that cannot be solved classically using 8 bits. Our result demonstrates the power of the quantum algorithm in the case of restricted memory. Additionally, we suggest a local-sensitive hashing technique based on the phase form of the quantum hashing. The technique can be used for checking a distance between two integers x and y whether it is less than d. We present an example of the implementation of the algorithm for 5 qubits and d at most 5.