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arXiv · 2411.15015

A Constant Measurement Quantum Algorithm for Graph Connectivity

Maximilian Balthasar Mansky·Chonfai Kam·Claudia Linnhoff-Popien
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Abstract

We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary abelian gates taken from ZX calculus. Due to the fusion rule, the two-qubit gates correspond to a large single action on the qubits. The algorithm is general and can handle any undirected graph, including those with repeated edges and self-loops. The depth of the algorithm is variable, depending on the graph, and we derive upper and lower bounds. The algorithm exhibits a state decay that can be remedied with ancilla qubits. We provide a numerical simulation of the algorithm.

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Maximilian Balthasar Mansky, Chonfai Kam, Claudia Linnhoff-Popien. 2024-11-22. A Constant Measurement Quantum Algorithm for Graph Connectivity. https://arxiv.org/abs/2411.15015

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