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International Conference on Quantum Communications, Networking, and Computing (QCNC)

Quantum Walk-Based Hash Function: Scalable Readout for Proof of Quantum Work

Shogo Shimada, Pulak Ranjan Giri, Rei Sato, Kazuhiro Saito

Published Apr 6, 2026• 1 citation

Abstract

We investigate quantum walk-based hash functions, which are generated from the count distribution generated by a quantum walker on graphs. The method is expected to be one of the promising approaches for generating robust hash functions; however, the quantum computation in small systems is susceptible to spoofing via classical imitation. To address this issue, it is necessary to perform calculations in a quantum space size that classical algorithms are difficult to simulate. In such cases, simply increasing the quantum space size leads to an increase in the number of quantum circuit measurements, thereby increasing the time required to generate the ideal measurement distribution. Based on these facts, we propose a quantum hybrid algorithm combining a quantum walk with a shot-based random projection architecture. This method compresses the output into a fixed-length 256-bit hash by weighting and binarizing the measurement counts of each node. We investigate the proposed method through the numerical simulations of quantum walks on the Hanoi Network (HN4) with$N=4096$. The results demonstrate no hash collisions and an avalanche effect of approximately 49%, which is close to the ideal value of 50%. Additionally, we achieved the consensus robustness of up to 94%, compared to the ideal value of 100%. These results suggest the feasibility of a scalable quantum hash function for Proof of Quantum Work (PoQ) on quantum devices.

DOI: 10.1109/qcnc69040.2026.00151

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Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.

We propose a Quantum inspired Hash Function using controlled alternate quantum walks with Memory on cycles (QHFM), where the

j

th message bit decides whether to run quantum walk with one-step memory or to run quantum walk with two-step memory at the

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th time step, and the hash value is calculated from the resulting probability distribution of the walker. Numerical simulation shows that the proposed hash function has near-ideal statistical performance and is at least on a par with the state-of-the-art hash functions based on quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property; and theoretical analysis indicates that the time and space complexity of the new scheme are not greater than those of its peers. The good performance of QHFM suggests that quantum walks that differ not only in coin operators but also in memory lengths can be combined to build good hash functions, which, in turn, enriches the construction of controlled alternate quantum walks.

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