Efficient Algorithms for Quantum Hashing

TL;DR

This paper introduces efficient quantum hashing algorithms that optimize circuit depth and gate count, enhancing memory efficiency and security for quantum protocols, especially on NISQ devices.

Contribution

It presents a new quantum hashing circuit with reduced depth and a flexible algorithm balancing gate count and rotation precision for NISQ hardware.

Findings

Circuit uses 2^{n-1} CNOT gates, outperforming previous methods.

Algorithm offers a trade-off between gate number and rotation accuracy.

Improves feasibility of quantum hashing on noisy quantum devices.

Abstract

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.