⚡ electrical engineering

Efficient Quantum Algorithm for Phase Optimization of 1-Bit RIS-Assisted MIMO Communication System

This paper proposes a Quantum Approximate Optimization Algorithm with a deterministic linear ramp schedule (QAOA-LR) to efficiently solve the combinatorial phase optimization problem for 1-bit RIS-assisted MIMO systems, demonstrating near-optimal capacity performance and polynomial scaling on both simulations and real IBM Quantum hardware.

Original authors: Soumyadip Paul, Neel Kanth Kundu

Published 2026-07-17

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Soumyadip Paul, Neel Kanth Kundu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the internet as a giant, invisible river of data flowing through the air, carrying your favorite songs, videos, and messages. Usually, this river hits obstacles like tall buildings or thick walls, causing the signal to scatter, weaken, or get lost entirely. For decades, engineers have tried to fix this by building bigger, louder transmitters, but that uses a lot of energy and costs a fortune. Enter a new, clever idea: the Reconfigurable Intelligent Surface, or RIS. Think of an RIS as a giant, high-tech mirror made of thousands of tiny, smart tiles. Instead of just reflecting light like a bathroom mirror, these tiles can twist and turn the radio waves hitting them, steering the signal around corners and straight to your device. It's like having a team of invisible conductors directing a symphony of signals to ensure everyone hears the music perfectly.

However, making these mirrors work perfectly is a massive puzzle. Each tiny tile needs to decide exactly how to twist the signal. If the tiles are "1-bit" mirrors, they have a very simple choice: twist the signal one way or the exact opposite way. With just a few tiles, there aren't many ways to arrange them. But as you add more tiles, the number of possible combinations explodes. It's like trying to find the perfect combination for a safe with a billion dials; checking every single option one by one would take longer than the age of the universe. This is the "combinatorial optimization" problem that scientists have been struggling with. They need a way to find the best arrangement quickly, without checking every single possibility.

This is where a new paper steps in, bringing a futuristic tool to the table: a quantum computer. The authors, Soumyadip Paul and Neel Kanth Kundu, propose a new method called QAOA-LR to solve this puzzle. Instead of using a traditional computer to slowly grind through the math, they use a quantum algorithm that acts more like a guided hike. Imagine you are in a foggy mountain valley trying to find the lowest point (the best signal arrangement). A normal computer might take a step, check the ground, take another step, and repeat this thousands of times, getting tired and stuck in small dips. The authors' new method, QAOA-LR, is like having a map that tells you exactly how steep to walk at every step. It uses a "linear ramp," a simple rule that starts with big, exploratory steps and gradually gets smaller and more precise as you get closer to the bottom.

The researchers tested this idea in two ways. First, they ran massive simulations on powerful classical computers, modeling everything from small 2x2 antenna setups to huge 32x32 systems with up to 12 mirror tiles. They found that their "guided hike" method found solutions that were almost identical to the absolute best possible answer, even as the systems got bigger. Then, they took it for a real-world test on an actual quantum computer from IBM. They programmed the quantum machine to handle up to 100 mirror tiles. The results were promising: the quantum approach didn't just find good solutions; it did so much faster than traditional methods as the number of tiles grew. While the paper notes that this is still an early stage and the quantum hardware is currently "noisy" (a bit like a radio with static), the speed and accuracy suggest that this quantum-guided approach could be a game-changer for future 6G networks, helping our devices stay connected even in the most crowded and complex environments.

Technical Summary: Efficient Quantum Algorithm for Phase Optimization of 1-Bit RIS-Assisted MIMO Communication System

Problem Statement
The paper addresses the phase optimization challenge in Reconfigurable Intelligent Surface (RIS)-assisted Multiple-Input Multiple-Output (MIMO) communication systems. Specifically, it focuses on "1-bit" RIS configurations where each reflecting element is restricted to a binary phase shift of either $0$ or $\pi$ . This hardware constraint, while reducing circuit complexity and control overhead, transforms the Maximum Likelihood (ML) phase optimization problem into a combinatorial task with $2^N$ candidate configurations for an $N$ -element surface. This problem is equivalent to the Max-Cut problem and is NP-hard, rendering exhaustive search infeasible for large $N$ . While classical approaches like Semidefinite Programming (SDR) with Gaussian randomization offer near-optimal solutions, their computational complexity scales as $O(N^{3.5})$ , which becomes prohibitive for the large-scale surfaces envisioned in 6G deployments. Furthermore, existing quantum approaches, such as standard Quantum Approximate Optimization Algorithm (QAOA), rely on classical outer-loop optimizers to tune variational parameters, introducing significant overhead and repeated quantum circuit evaluations.

Methodology
The authors propose a novel algorithm termed QAOA-LR (Quantum Approximate Optimization Algorithm with a deterministic Linear Ramp schedule). The methodology proceeds through the following steps:

Problem Formulation: The ML capacity maximization problem is mapped to an Ising Hamiltonian. By maximizing the Frobenius norm of the effective channel matrix, the objective is reduced to a quadratic form $f(x) = x^T R x + p^T x$ , where $x$ represents the binary phase shifts. This is converted into a minimization problem suitable for QAOA, with the cost Hamiltonian $H_C$ derived from pairwise couplings and single-qubit biases.
QAOA Circuit Construction: The problem is encoded into a parameterized quantum circuit. The circuit alternates between a cost unitary ( $e^{-i\gamma_\ell H_C}$ ) and a mixer unitary ( $e^{-i\beta_\ell H_M}$ ) over $p$ layers. The cost unitary handles the Ising interactions using CNOT and $R_Z$ gates, while the mixer uses $R_X$ rotations.
Linear Ramp Schedule (QAOA-LR): Instead of employing a classical optimizer to iteratively tune the $2p$ $2 p$ variational parameters ( $\gamma$ $γ$ and $\beta$ $β$ ), the authors fix these parameters using a deterministic linear ramp schedule inspired by adiabatic quantum computing. The parameters are defined as:
- $\gamma_k = \frac{k}{p} \Delta$
- $\beta_k = \left(1 - \frac{k-1}{p}\right) \Delta$
  Here, $\Delta$ is a single scale parameter. The algorithm performs a simple one-dimensional grid search over $\Delta$ to find the value that minimizes the expected cost, thereby eliminating the iterative classical optimization loop.
Decoding: The optimal binary phase vector is decoded by measuring the expectation values of the Pauli-Z operators ( $\langle Z_n \rangle$ ) and applying a sign function.

Key Contributions
The paper makes three primary contributions:

Ising Mapping: It formulates the 1-bit RIS-assisted MIMO capacity problem as an Ising Hamiltonian, explicitly incorporating pairwise couplings and single-qubit bias terms induced by direct-path cross-coupling, enabling implementation via QAOA.
QAOA-LR Algorithm: It introduces an efficient variant of QAOA that replaces the complex, iterative classical parameter optimization with a fixed linear-ramp schedule requiring only a one-dimensional search over a single scale parameter. This significantly reduces optimization overhead.
Extensive Validation: The authors conduct extensive Monte Carlo simulations for MIMO configurations up to $32 \times 32$ and RIS elements up to $N=12$ . Crucially, they validate the approach on real quantum hardware (IBM Quantum's ibm_marrakesh processor) for up to 100 RIS elements, comparing performance against classical baselines.

Results

Simulation Performance: Monte Carlo simulations over Rayleigh-fading channels demonstrate that QAOA-LR closely tracks the optimum ML solution. For small RIS sizes ( $N \le 2$ ), the capacity performance matches the ML solution exactly across all tested MIMO configurations. As $N$ increases to 12, a slight performance gap appears for smaller antenna arrays but diminishes as the MIMO size grows; for $32 \times 32$ MIMO, QAOA-LR closely follows the ML capacity.
Hardware Execution: Experiments on the IBM Quantum processor confirm that QAOA-LR delivers high capacity (e.g., 68.2366 bits/s/Hz for $N=12$ in a $32 \times 32$ system) and scales effectively up to $N=100$ .
Complexity and Scaling: The execution time on the Quantum Processing Unit (QPU) scales linearly with the number of RIS elements ( $N$ ). In contrast, classical baselines like Randomized Restart Local Search (RRLS) and SDR exhibit superlinear growth. The complexity of QAOA-LR is $O(MpN)$ (where $M$ is the grid size), compared to $O(d p N)$ for standard QAOA (where $d$ is the number of classical iterations) and $O(N^{3.5})$ for SDR.
Parameter Sensitivity: Sensitivity analysis shows that the algorithm peaks at a specific scale parameter ( $\Delta = 1.0$ ) and outperforms Adam-optimized QAOA across the tested grid, confirming that a simple grid search suffices without iterative optimization.

Significance
The paper claims that QAOA-LR addresses critical gaps in scalability and practicality for gate-based quantum optimization in RIS systems. By removing the need for iterative classical parameter tuning, the approach reduces the computational overhead and is well-suited for noisy intermediate-scale quantum (NISQ) hardware. The results validate that quantum-assisted techniques can achieve near-ML capacity performance with polynomial scaling of execution time, offering a promising direction for optimizing large-scale 1-bit RIS configurations in future 6G networks. The authors note that future work will extend this framework to multi-bit RIS phase optimization.

More like this