Quantum Reports

Theory and Applications of Quantum Hashing

Farid Mansurovich Ablayev, Kamil Ravilevich Khadiev, Alexander Vasiliev, Mansur Ziiatdinov

Published May 15, 2025• 8 citations

Abstract

We review recent results on quantum one-way functions, including quantum fingerprinting or quantum hashing (we use these two terms as synonyms even though they have very small difference). This includes the analysis of their properties, different modifications, circuit implementation on an IBM Q platform, as well as on an experimental quantum setup. We discuss computational aspects of quantum hashing, its cryptographic properties and possible usage in communication protocols and algorithms.

DOI: 10.3390/quantum7020024

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Quantum Reports

Theory and Applications of Quantum Hashing

Farid Mansurovich Ablayev, Kamil Ravilevich Khadiev, Alexander Vasiliev, Mansur Ziiatdinov

Published May 15, 2025• 8 citations

Publisher

Abstract

DOI: 10.3390/quantum7020024

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quant-pharXiv:2608.09134Aug 11, 20260 citations

\mathtt{MOD_p}

, where $ \mathtt{MOD_p} = \{ a^{i \cdot p} \mid i \geq 0 \} $, for any prime number

p

. We consider 16-qubit and 27-qubit IBMQ computers with the special graphs of qubits representing nearest neighbor architecture that is not Linear Nearest Neighbor (LNN) one. We optimize quantum circuits for the quantum hashing algorithm with respect to minimizing the number of control operators as the most expensive ones. We apply the same approach for an optimized circuit implementation of Quantum Fourier Transform (QFT) operation on the aforementioned machines because QFT and hashing circuits have common parts.

MOD_p=\{a^\ell: \ell \bmod p=0\}

language, and the

EQ_p=\{a^\ell b^r: \ell \equiv r \pmod p\}

language. Given the enhancements that our algorithm provides~-- for instance, in one case it achieves a 16\%--17\% decrease in CNOT circuit cost~-- we believe it could also be useful in a broader quantum compilation context.