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arXiv:2511.19292

Efficient Equivalent of Shallow Quantum Hashing

Ilnar Zinnatullin, Alexander Vasiliev

quant-phSubmitted Nov 24, 2025• Announced Nov 25, 2025• 0 citations
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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.

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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.
Abstract Quantum hashing is one of the techniques that allow to construct space-efficient quantum algorithms and protocols. We present a construction that allows to make it extremely time efficient. Our approach is based on the shallow implementation of the quantum fingerprinting technique but uses additional circuit identities specific to the quantum hash function for the cyclic group. The resulting algorithm is equivalent to the one we have implemented earlier using single-photon states with orbital angular momentum encoding.
Abstract In this work, we consider a well-known quantum hashing technique, and focus on its circuit representation. We implemented a shallow circuit for a phase form of the quantum hashing on a noisy emulator of IBMQ quantum devices using 8 qubits and showed that we can solve a problem MOD131 that cannot be solved classically using 8 bits. Our result demonstrates the power of the quantum algorithm in the case of restricted memory. Additionally, we suggest a local-sensitive hashing technique based on the phase form of the quantum hashing. The technique can be used for checking a distance between two integers x and y whether it is less than d. We present an example of the implementation of the algorithm for 5 qubits and d at most 5.
The integrity of evidence, a core principle of digital forensics, is essential for ensuring the reliability and admissibility of evidence in legal proceedings. Classical cryptographic hash functions have effectively ensured the integrity of digital evidence. However, they cannot be applied to quantum evidence emerging with the advent of the quantum computing era. This is due to fundamental principles of quantum mechanics such as superposition and entanglement. To address the challenge of ensuring quantum evidence integrity, this paper introduces a quantum amplitude hash function as a new paradigm. The function operates by directly hashing the entire amplitude, which represents the totality of information within the quantum evidence state, into a hash qubit. The proposed function is implemented as a quantum circuit of constant depth, ensuring excellent scalability. It is theoretically proven to satisfy key cryptographic properties such as preimage resistance, collision resistance, and sensitivity. Moreover, simulation experiments were conducted to validate the generation of hash qubits for representative quantum algorithms. This work is expected to lay a crucial technical foundation for advancing the field of quantum forensics and preparing for future investigative environments.
In the letter we define the notion of a quantum resistant ( -resistant) hash function which consists of a combination of pre-image (one-way) resistance ( ε -resistance) and collision resistance ( δ -resistance) properties. We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.
Abstract Current physical limitations require quantum circuits to be transformed to fit the nearest-neighbor architecture. To achieve this, we usually use different techniques such as nearest-neighbor decomposition. In this work, we optimize quantum circuits implementing quantum hashing for quantum computers with specific architecture provided by IBM Q Platform. The optimization is done by reducing the number of used CNOT gates. We show how to choose the best position for the target qubit to get optimal circuits for the considered architectures.