Implementation of Quantum Fourier Transform and Quantum Hashing for a Quantum Device with Arbitrary Qubits Connection Graphs

• URL: http://arxiv.org/abs/2501.18677v1
• Date: Thu, 30 Jan 2025 18:59:59 GMT
• Title: Implementation of Quantum Fourier Transform and Quantum Hashing for a Quantum Device with Arbitrary Qubits Connection Graphs
• Authors: Kamil Khadiev, Aliya Khadieva, Zeyu Chen, Junde Wu,
• Abstract summary: We consider quantum circuits for Quantum fingerprinting (quantum hashing) and quantum Fourier transform (QFT) algorithms. We present a generic method for constructing quantum circuits for these algorithms for quantum devices with restrictions.
• Score: 10.113567783910167
• License:
• Abstract: In the paper, we consider quantum circuits for Quantum fingerprinting (quantum hashing) and quantum Fourier transform (QFT) algorithms. Quantum fingerprinting (quantum hashing) is a well-known technique for comparing large objects using small images. The QFT algorithm is a very popular technique used in many algorithms. We present a generic method for constructing quantum circuits for these algorithms for quantum devices with restrictions. Many quantum devices (for example, based on superconductors) have restrictions on applying two-qubit gates. The restrictions are presented by a qubits connection graph. Typically, researchers consider only the linear nearest neighbor (LNN) architecture, but current devices have more complex graphs. We present a method for arbitrary connected graphs that minimizes the number of CNOT gates in the circuit. The heuristic version of the method is fast enough and works with $O(n^5)$ time complexity, where $n$ is the number of qubits. The certain version of the algorithm has an exponential time complexity that is $O(n^22^n)$. We compare quantum circuits built by our algorithm with quantum circuits optimized for specific graphs that are Linear-nearest-neighbor (LNN) architecture, ``sun'' (a cycle with tails, presented by 16-qubit IBMQ device) and ``two joint suns'' (two joint cycles with tails, presented by 27-qubit IBMQ device). Our generic method gives similar results with little bit more CNOT gates. At the same time, our method allows us to construct a circuit for arbitrary connected graphs.

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