Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem

Abstract

In this paper, we propose a novel method of formulating an NP-hard wireless channel assignment problem as a higher-order unconstrained binary optimization (HUBO), where the Grover adaptive search (GAS) is used to provide a quadratic speedup for solving the problem. The conventional method relies on a one-hot encoding of the channel indices, resulting in a quadratic formulation. By contrast, we conceive ascending and descending binary encodings of the channel indices, construct a specific quantum circuit, and derive the exact numbers of qubits and gates required by GAS. Our analysis clarifies that the proposed HUBO formulation significantly reduces the number of qubits and the query complexity compared with the conventional quadratic formulation. This advantage is achieved at the cost of an increased number of quantum gates, which we demonstrate can be reduced by our proposed descending binary encoding.

11 pages, 9 figures

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Cited by in corpus (5)

• Accelerating Grover Adaptive Search: Qubit and Gate Count Reduction Strategies with Higher-Order Formulations
• Quantum Speedup of the Dispersion and Codebook Design Problems
• Towards an Automatic Framework for Solving Optimization Problems with Quantum Computers
• A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem
• Grover Adaptive Search with Spin Variables