Grover Adaptive Search for Maximum Likelihood Detection of Generalized Spatial Modulation

We propose a quantum-assisted solution for the maximum likelihood detection (MLD) of generalized spatial modulation (GSM) signals. Specifically, the MLD of GSM is first formulated as a novel polynomial optimization problem, followed by the application of a quantum algorithm, namely, the Grover adaptive search. The performance in terms of query complexity of the proposed method is evaluated and compared to the classical alternative via a numerical analysis, which reveals that under fault-tolerant quantum computation, the proposed method outperforms the classical solution if the number of data symbols and the constellation size are relatively large.

Quantum Speedup of the Dispersion and Codebook Design Problems

We propose new formulations of max-sum and max-min dispersion problems that enable solutions via the Grover adaptive search (GAS) quantum algorithm, offering quadratic speedup. Dispersion problems are combinatorial optimization problems classified as NP-hard, which appear often in coding theory and wireless communications applications involving optimal codebook design. In turn, GAS is a quantum exhaustive search algorithm that can be used to implement full-fledged maximum-likelihood optimal solutions. In conventional naive formulations however, it is typical to rely on a binary vector spaces, resulting in search space sizes prohibitive even for GAS. To circumvent this challenge, we instead formulate the search of optimal dispersion problem over Dicke states, an equal superposition of binary vectors with equal Hamming weights, which significantly reduces the search space leading to a simplification of the quantum circuit via the elimination of penalty terms. Additionally, we propose a method to replace distance coefficients with their ranks, contributing to the reduction of the number of qubits. Our analysis demonstrates that as a result of the proposed techniques a reduction in query complexity compared to the conventional GAS using Hadamard transform is achieved, enhancing the feasibility of the quantum-based solution of the dispersion problem.

AFDM Chirp-Permutation-Index Modulation with Quantum-Accelerated Codebook Design

We describe a novel index modulation (IM) scheme exploiting a unique feature of the recently proposed affine frequency division multiplexing (AFDM) in doubly-dispersive (DD) channels. Dubbed AFDM chirp-permutation-index modulation (CPIM), the proposed method encodes additional information via the permutation of the discrete affine Fourier Transform (DAFT) chirp sequence, without any sacrifice of the various beneficial properties of the AFDM waveform in DD channels. The effectiveness of the proposed method is validated via simulation results leveraging a novel reduced-complexity minimum mean-squared-error (MMSE)-based maximum-likelihood (ML) detector, highlighting the gains over the classical AFDM. As part of the work two interesting problems related to optimizing AFDM-CPIM are identified: the optimal codebook design problem, over a discrete solution space of dimension $\binom{N!}{K}$, where $N$ is the number of subcarriers and $K$ is the number of codewords; and the ML detection problem whose solution space is of dimension $KM^N$, where $M$ is the constellation size. In order to alleviate the computational complexity of these problems and enable large-scale variations of AFDM-CPIM, the two problems are reformulated as a higher-order binary optimization problem and mapped to the well-known quantum Grover adaptive search (GAS) algorithm for their solution.