Efficient Equivalent of Shallow Quantum Hashing

TL;DR

This paper demonstrates that shallow quantum hashing can be efficiently implemented with a depth-1 circuit, maintaining collision resistance, thus optimizing quantum hashing protocols.

Contribution

It establishes a connection between phase and amplitude forms of shallow quantum hashing and proposes a depth-1 circuit for amplitude form hashing.

Findings

Depth-1 circuit achieves the same collision resistance as depth-2 circuits.

Connection established between phase and amplitude forms of shallow quantum hashing.

Optimized quantum hashing circuits reduce complexity while maintaining security.

Abstract

Quantum hashing is a widely used technique in quantum computation that allows us to design space-efficient algorithms and protocols. Recently, Vasiliev has shown that the phase form of shallow quantum hashing can be implemented by a circuit of depth 2. In this paper, we establish a connection between shallow quantum hashing and single-qubit quantum hashing for the amplitude form. For a shallow circuit, we propose a circuit of depth 1 that achieves the same collision resistance.