Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem

TL;DR

This paper introduces a new quantum approach for wireless channel assignment that reduces qubit requirements and speeds up problem solving using Grover adaptive search, improving efficiency over traditional methods.

Contribution

It presents a novel HUBO formulation with binary encodings for quantum channel assignment, reducing qubits and query complexity compared to conventional quadratic formulations.

Findings

Significantly fewer qubits needed with the new HUBO formulation

Quadratic speedup achieved using Grover adaptive search

Descending binary encoding reduces quantum gate count

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.