Efficient Algorithms for Quantum Hashing

Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is the number of control qubits. Our method outperforms existing approaches and reduces the circuit depth. Second, we propose an algorithm that provides a trade-off between the number of CNOT gates (and consequently, the circuit depth) and the precision of rotation angles. This is particularly important in the context of NISQ (Noisy Intermediate-Scale Quantum) devices, where hardware-imposed angle precision limit remains a critical constraint.