The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number of qubits and low fidelity gates, application-based quantum solutions help us to understand and improve the performance of such technology even further. This paper introduces QGateD-Polar, a novel Quantum Gate-based Maximum-Likelihood Decoder design for Polar error correction codes, which are becoming widespread in today's 5G and tomorrow's NextG wireless networks. QGateD-Polar uses quantum gates to dictate the time evolution of Polar code decoding -- from the received wireless soft data to the final decoded solution -- by leveraging quantum phenomena such as superposition, entanglement, and interference, making it amenable to quantum gate-based computers. Our early results show that QGateD-Polar achieves the Maximum Likelihood performance in ideal quantum simulations, demonstrating how performance varies with noise.
The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number of qubits and low fidelity gates, application-based quantum solutions help us to understand and improve the performance of such technology even further. This paper introduces QGateD-Polar, a novel Quantum Gate-based Maximum-Likelihood Decoder design for Polar error correction codes, which are becoming widespread in today's 5G and tomorrow's NextG wireless networks. QGateD-Polar uses quantum gates to dictate the time evolution of Polar code decoding -- from the received wireless soft data to the final decoded solution -- by leveraging quantum phenomena such as superposition, entanglement, and interference, making it amenable to quantum gate-based computers. Our early results show that QGateD-Polar achieves the Maximum Likelihood performance in ideal quantum simulations, demonstrating how performance varies with noise.
We present the Hybrid Polar Decoder (HyPD), a hybrid of classical CMOS and quantum annealing (QA) computational structures for decoding Polar error correction codes, which are becoming widespread in today's 5G and tomorrow's 6G networks. HyPD considers CMOS for the Polar code's binary tree traversal, and QA for executing a Quantum Polar Decoder (QPD)-a novel QA-based maximum likelihood submodule. Our QPD design efficiently transforms a Polar decoder into a quadratic polynomial optimization form amenable to the QA's optimization process. We experimentally evaluate HyPD on a state-of-the-art QA device with 5,627 qubits, for Polar codes of block length 1,024 bits, in Rayleigh fading channels. Our results show that HyPD outperforms successive cancellation list decoders of list size eight by half an order of bit error rate magnitude at 1 dB SNR. Further experimental studies address QA compute time at various code rates, and with increased QA qubit numbers.
Channel Coding is the technique that enables reliable delivery of digital data over unreliable communication channels. For most high performance channel coding techniques, the existing classical algorithms are computationally expensive, making them impractical for throughput-demanding applications with large code sizes. Today’s Noisy Intermediate-Scale Quantum (NISQ) computers, although limited due to a modest number of qubits, short coherence time, and poor gate fidelity, are useful tools for exploring and experimenting with possible solutions to a wide variety of computational problems.In this paper we show how careful initialization of qubits combined with a simple quantum circuit, enables us to perform channel decoding for different linear block codes. We first explain our novel qubit initialization technique which we call "Quantum Soft Decision". We then show how to build a simple quantum circuit based on the Generator or Parity-check matrix using another technique called "Quantum Generator". Using these universal concepts, we implement Quantum Decoders for two different types of linear block codes, namely Hamming codes and Polar codes. Our simple quantum circuits achieve decoding performances comparable with best classical algorithms such as Maximum Likelihood (ML) for Hamming codes and Successive Cancellation (SC) and Successive Cancellation List (SCL) for Polar codes. Using Qiskit, we implemented and compared the decoding performance at different code sizes and noise levels on simulated (both ideal and noisy) quantum computers. Also using Amazon Braket, we verified the algorithm on real quantum computers.
We present the Hybrid Polar Decoder (HyPD), a hybrid classical-quantum decoder design for Polar error correction codes, which are becoming widespread in today’s 5G and tomorrow’s 6G networks. HyPD employs CMOS processing for the Polar decoder’s binary tree traversal, and Quantum Annealing (QA) processing for the Quantum Polar Decoder (QPD)-a Maximum-Likelihood QA-based Polar decoder submodule. QPD’s design efficiently transforms a Polar decoder into a quadratic polynomial optimization form, then maps this polynomial on to the physical QA hardware via QPD-MAP, a customized problem mapping scheme tailored to QPD. We have experimentally evaluated HyPD on a state-of-the-art QA device with 5,627 qubits, for 5G-NR Polar codes with block length of 1,024 bits, in Rayleigh fading channels. Our results show that HyPD outperforms Successive Cancellation List decoders of list size eight by half an order of bit error rate magnitude, and achieves a 1,500-bytes frame delivery rate of 99.1%, at 1 dB signal-to-noise ratio. Further studies present QA compute time considerations. We also propose QPD-HW, a novel QA hardware topology tailored for the task of decoding Polar codes. QPD-HW is sparse, flexible to code rate and block length, and may be of potential interest to the designers of tomorrow’s 6G wireless networks.
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible decoding strategies, maximum likelihood decoding (MLD) is provably optimal, since it identifies the logical group with largest likelihood by summing over all possible errors within logical class consistent with the observed syndrome. Despite its optimality, MLD is computationally intractable in general (#P-hard), motivating a rich landscape of exact and approximate algorithms. In this topical review, we provide a unified perspective on MLD by surveying recent advances through three complementary lenses: statistical mechanics, tensor networks, and artificial intelligence. From the statistical mechanics viewpoint, the MLD problem maps onto evaluating partition functions of disordered spin models, enabling exact solutions for certain codes and noise models as well as threshold estimation via phase-transition analysis. From the tensor network perspective, approximate contraction of tensor networks on the code's factor graph yields decoders that closely approach MLD accuracy with polynomial computational cost. From the artificial intelligence perspective, neural-network-based decoders, including autoregressive generative models and recurrent transformers, learn to approximate the MLD distribution from data, achieving high accuracy with the parallelism afforded by modern hardware accelerators. We discuss the connections among these three approaches, review their application to both simulated and experimental quantum hardware, and outline open challenges including real-time decoding, scalability to large code distances, and generalization to high-rate quantum low-density parity-check codes.
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.
We study the exact maximum-likelihood decoding of quantum error-correcting codes. Our primary focus is on the repetition code under circuit-level noise, which serves as a fundamental basis for quantum error correction experiments and is the only code that has achieved large distances and extremely low error rates. We uncover that the repetition code under circuit-level noise has an exact solution and propose an optimal maximum-likelihood decoding algorithm called "planar." This algorithm is based on the exact solution of the spin-glass partition function on planar graphs and has polynomial computational complexity. Through extensive numerical experiments, we demonstrate that our algorithm uncovers the exact threshold for depolarizing noise and realistic superconductor SI1000 noise. Furthermore, we apply our method to analyze data from recent quantum memory experiments conducted by Google Quantum AI, revealing that part of the error floor was attributed to the decoding algorithm used by Google. Finally, we implemented the repetition code quantum memory on superconducting systems using a 72-qubit quantum chip lacking reset gates, demonstrating that even with an unknown error model, the proposed algorithm achieves a significantly lower logical error rate than the matching-based algorithm. We also discuss the application of our approach to quantum codes whose maximum-likelihood decoding problem corresponds to a spin-glass problem, including the surface code under independent code-capacity noise.