Quantum Optimization in Wireless Communication Systems: Principles and Applications

TL;DR

The paper investigates how quantum optimization can address the NP-hard design challenges of next-generation wireless systems. It surveys two main paradigms—quantum annealing (QA) and gate-based QAOA—explaining their theoretical bases, operational differences, and limitations. Through a case study on passive RIS beamforming with binary phase shifts, it compares D-Wave QA and QAOA on IBM hardware, finding QA often achieves higher-quality solutions under current conditions. The authors argue that quantum optimization should be viewed as a powerful accelerator that complements classical methods, with practical impact contingent on continued hardware and algorithmic advances. Overall, the work highlights the potential and current constraints of applying quantum solvers to wireless optimization tasks.

Abstract

Quantum optimization is poised to play a transformative role in the design of next-generation wireless communication systems by addressing key computational and technological challenges. This paper provides an overview of the principles of adiabatic quantum computing, the foundation of quantum optimization, and explores its two primary computational models: quantum annealing and the gate-based quantum approximate optimization algorithm. By highlighting their core features, performance benefits, limitations, and distinctions, we position these methods as promising tools for advancing wireless communication system design. As a case study, we examine the design of passive reconfigurable intelligent surface beamforming with binary phase-shift resolution, supported by experimental results obtained from real-world quantum hardware.

Figures (5)

• Figure 1: QA schedule. The lower part of the figure shows examples of annealing schedule functions $A(s)$ and $B(s)$. $A(s)$ (resp. $B(s)$) drives the strength of the magnetic field of the initial Hamiltonian $H_\mathrm{I}$ (resp. the final Hamiltonian $H_\mathrm{F}$). The upper part of the figure shows how the qubits and couplers are affected by the magnetic field related to each Hamiltonian. At the beginning of the evolution, the system is in a disordered phase with all the qubits in superposition. At the end of the evolution, the system is in an ordered phase where qubits alignment is fixed. Between these two phases, the system goes through a phase transition likely to appear in the critical region when $A(s) \approx B(s)$. The precise location of the phase transition depends on the shape of the schedule and on the Hamiltonian. At the end of the evolution, measuring the qubits results in either the left half or the right half of each circle (the state being measured is in a superposition of the two optimal solutions to the MaxCut problem).
• Figure 2: Eigenenergy diagram of the schedule-dependent Hamiltonian $H(s)$ with a unique ground state. The quantum system is initialized in the ground state of the initial Hamiltonian $H_\mathrm{I}$. The qubits remain in the ground state during the whole evolution for closed systems (green dots). In case of noisy interaction, the quantum state might suffer from thermal excitations and become excited. The probability of observing the ground state diminishes, and the quantum state might finish in a superposition of several excited states (purple dots where transparent dots mean lower probability of observation). Passing through the critical region too rapidly also reduces the probability of observing the ground state at the end of the evolution.
• Figure 3: Discretization of the quantum adiabatic process in $p$ constant steps. The upper part shows a piecewise approximation of the annealing schedule. The medium part shows a quantum digital circuit where each qubit is associated with a wire. The qubits are prepared in a uniform superposition of states of the computational basis. Each constant time step $\Delta_k$ is used to build the unitary $U(\beta_k)$ (implementing the Hamiltonian $H_\mathrm{I}$) and the unitary $U(\gamma_k)$ (implementing the Hamiltonian $H_\mathrm{F}$). The schedule associated with each $H_\mathrm{I}$ and $H_\mathrm{F}$ is transmitted to the unitaries with the parameters $\beta_k$ and $\gamma_k$. The lower part displays a single layer of QAOA circuit corresponding to the MaxCut instance problem \ref{['fig:quantum_annealing']}. Each variable $s_i$ is associated with a qubit $q_i$. The $U(\beta_k)$ layer corresponds to a single wall of single rotation gates $R_x(-2\beta_k)$. In the layer associated to the problem $U(\gamma_k)$ each quadratic term is built from $2$ CNOTs and a single rotation gate $R_z(2\gamma_k)$.
• Figure 4: The system model for a RIS-aided communication system with binary phase-shift RIS resolution.
• Figure 5: D-Wave versus QAOA with $p=\{1,3\}$. (top) SNR for the ordered solutions; exhaustive search (dashed line). (bottom) Probability of occurrence for the ordered solutions.