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Using a Simplified Quantum Counter to Implement Quantum Circuits Based on Grover’s Algorithm to Tackle the Exact Cover Problem

Year: 2024

Type: article

Abstract: In this paper, we use a simplified quantum counter to implement Grover’s algorithm-based quantum circuits to tackle the NP-hard exact cover problem (ECP). The ECP seeks a subcollection of sets such that every element is covered by exactly one set. Leveraging Grover’s algorithm, our quantum circuits achieve a quadratic speedup, querying the oracle O(N) times, compared to O(N) for classical methods, where N=2n is the total number of unstructured input instances and n is the number of input (quantum) bits. For the whole quantum circuit, the simplified quantum counter saves (4mb−4m)⌊π/4N/M⌋ quantum gates and reduces the quantum circuit depth by (2mb)⌊π/4N/M⌋ compared to Heidari et al.’s design, where b=⌊logn⌋+1 is the number of counting qubits used in a counter. Experimental results obtained using IBM Qiskit packages confirm the effectiveness of our quantum circuits.

Source: Mathematics

DOI: 10.3390/math13010090

Authors: Jehn-Ruey Jiang, Yu-Jie Wang

Institution: National Central University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Ministry of Science and Technology, Taiwan, National Central University, National Taiwan University, National Science and Technology Council