Abstract Quantum computing shows promise for 6G networks due to its parallel computing capabilities. In the context of the Noisy Intermediate‐Scale Quantum era, the introduction of hybrid quantum‐classical algorithms like Quantum Approximate Optimization Algorithm (QAOA) offer powerful solutions to many combinatorial optimization problems in 6G. This paper focuses on Low‐Density Parity‐Check (LDPC) channel decoding and proposes an improved QAOA algorithm assisted by the learning‐to‐learn strategy. We also investigate the parameter concentration phenomenon in QAOA‐based LDPC decoding to assess the rationality. To evaluate effectiveness, a comprehensive numerical expression for the energy expectation of single‐layer QAOA and propose indicators for transfer performance evaluation is provided. Based on simulation results, the similarity in parameter distribution across specific LDPC configurations is investigated. This similarity facilitates the transfer of training outcomes from smaller to larger‐scale problems for optimization initialization, thereby avoiding the need for retraining. This approach offers insights and potential solutions for rapid, large‐scale channel decoding in 6G networks, despite the current limitations of quantum hardware.
Abstract Quantum computing shows promise for 6G networks due to its parallel computing capabilities. In the context of the Noisy Intermediate‐Scale Quantum era, the introduction of hybrid quantum‐classical algorithms like Quantum Approximate Optimization Algorithm (QAOA) offer powerful solutions to many combinatorial optimization problems in 6G. This paper focuses on Low‐Density Parity‐Check (LDPC) channel decoding and proposes an improved QAOA algorithm assisted by the learning‐to‐learn strategy. We also investigate the parameter concentration phenomenon in QAOA‐based LDPC decoding to assess the rationality. To evaluate effectiveness, a comprehensive numerical expression for the energy expectation of single‐layer QAOA and propose indicators for transfer performance evaluation is provided. Based on simulation results, the similarity in parameter distribution across specific LDPC configurations is investigated. This similarity facilitates the transfer of training outcomes from smaller to larger‐scale problems for optimization initialization, thereby avoiding the need for retraining. This approach offers insights and potential solutions for rapid, large‐scale channel decoding in 6G networks, despite the current limitations of quantum hardware.
With the development of 6G networks, the required computational power has been greatly increased, and quantum computing offers promising approaches for this purpose due to its properties such as superposition and entanglement. It has been proposed to combine the Quantum Approximation optimization Algorithm (QAOA) with the Learning-to-Learn (L2L) strategy using classical Recurrent Neural Networks (RNN) to solve the problem of channel decoding on Noisy IntermediateScale Quantum (NISQ) devices. In this paper, we build on this foundation to further investigate the impact of different RNNs on channel decoding. The experimental results show that by training the RNN model of Minimal Gated Unit (MGU) with fewer parameters, the initial parameters of the obtained QAOA have a certain degree of similarity with the Long Short Term Memory Network (LSTM), and the decoding results are comparable. The method of training RNNs improves the performance and saves the cost compared to the random initialization method. Despite the limitation by the current quantum hardware, this quantum computation approach provides the future for channel decoding in the 6G network a promising scheme.
Decoding Low-Density Parity-Check (LDPC) codes is a fundamental problem in coding theory, and Belief Propagation (BP) is one of the most popular methods for LDPC code decoding. However, BP may encounter convergence issues and suboptimal performance, especially for short-length codes and in high-noise channels. The Quantum Approximate Optimization Algorithm (QAOA) is a type of Variational Quantum Algorithm (VQA) designed to solve combinatorial optimization problems by minimizing a problem-specific cost function. In this paper, we present a QAOA-based decoding framework for LDPC codes by formulating a decoding cost function that incorporates both parity-check constraints and soft channel reliability information. The resulting optimization problem is solved using QAOA to search for low-energy configurations corresponding to valid codewords. We test the proposed method through extensive numerical experiments and compare its performance with BP decoding. The experimental results demonstrate that the QAOA-based decoder achieves a higher probability of correctly recovering the transmitted codeword than BP across multiple experimental settings.
Decoding low-density parity-check codes is critical in many current technologies, such as fifth-generation (5G) wireless networks and satellite communications. The belief propagation algorithm allows for fast decoding due to the low density of these codes. However, there is scope for improvement to this algorithm both in terms of its computational cost when decoding large codes and its error-correcting abilities. Here, we introduce the quantum-enhanced belief propagation (QEBP) algorithm, in which the Quantum Approximate Optimization Algorithm (QAOA) acts as a pre-processing step to belief propagation. We perform exact simulations of syndrome decoding with QAOA, whose result guides the belief propagation algorithm, leading to faster convergence and a lower block error rate (BLER). In addition, through the repetition code, we study the possibility of having shared variational parameters between syndromes and, in this case, code lengths. We obtain a unique pair of variational parameters for level-1 QAOA by optimizing the probability of successful decoding through a transfer matrix method. Then, using these parameters, we compare the scaling of different QAOA post-processing techniques with code length.
Forward Error Correction (FEC) provides reliable data flow in wireless networks despite the presence of noise and interference. However, its processing demands significant fraction of a wireless network's resources, due to its computationally-expensive decoding process. This forces network designers to compromise between performance and implementation complexity. In this paper, we investigate a novel processing architecture for FEC decoding, one based on the quantum approximate optimization algorithm (QAOA), to evaluate the potential of this emerging quantum compute approach in resolving the decoding performance-complexity tradeoff. We present FDeQ, a QAOA-based FEC Decoder design targeting the popular NextG wireless Low Density Parity Check (LDPC) and Polar codes. To accelerate QAOA-based decoding towards practical utility, FDeQ exploits temporal similarity among the FEC decoding tasks. This similarity is enabled by the fixed structure of a particular FEC code, which is independent of any time-varying wireless channel noise, ambient interference, and even the payload data. We evaluate FDeQ at a variety of system parameter settings in both ideal (noiseless) and noisy QAOA simulations, and show that FDeQ achieves successful decoding with error performance at par with state-of-the-art classical decoders at low FEC code block lengths. Furthermore, we present a holistic resource estimation analysis, projecting quantitative targets for future quantum devices in terms of the required qubit count and gate duration, for the application of FDeQ in practical wireless networks, highlighting scenarios where FDeQ may outperform state-of-the-art classical FEC decoders.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum approach for tackling combinatorial optimization problems. However, hardware constraints such as limited scaling and susceptibility to noise pose significant challenges when applying QAOA to large instances. To overcome these limitations, scalable hybrid multilevel strategies have been proposed. In this work we propose a fast hybrid multilevel algorithm with QAOA parameterization throughout the multilevel hierarchy and its reinforcement with genetic algorithms, which results in a high-quality, low-depth QAOA solver. Notably, we propose transferring parameters from the coarsest level to the finer level, demonstrating that the relaxation-based coarsening preserves the problem's structural information required for QAOA parametrization. Our strategy improves the coarsening phase and leverages both Quantum Relax & Round and genetic algorithms to incorporatep=1QAOA samples effectively. The results highlight the practical potential of multilevel QAOA as a scalable method for combinatorial optimization on near-term quantum devices.
Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.