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The near-capacity performance of classical low-density parity check (LDPC) codes and their efficient iterative decoding makes quantum LDPC (QLPDC) codes a promising candidate for quantum error correction. In this paper, we present a comprehensive survey of QLDPC codes from the perspective of code design as well as in terms of their decoding algorithms. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-four cycles. Our modified decoder outperforms the stateof-the-art decoders in terms of their word error rate performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic uniformly reweighted belief propagation for the sake of achieving an improved performance.INDEX TERMS Quantum error correction, low density parity check codes, quantum low density parity check codes, iterative decoding.

Routing in wireless multihop networks (WMHNs) relies on a delicate balance of diverse and often conflicting parameters, when aiming for maximizing the WMHN performance. Classified as a non-deterministic polynomial-time hard problem, routing in WMHNs requires sophisticated methods. As a benefit of observing numerous variables in parallel, quantum computing offers a promising range of algorithms for complexity reduction by exploiting the principle of quantum parallelism (QP), while achieving the optimum full-search-based performance. In fact, the so-called non-dominated quantum optimization (NDQO) algorithm has been proposed for addressing the multiobjective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of O(N ) and O(N √ N ) in the best and worst case scenarios, respectively. However, as the number of nodes in the WMHN increases, the total number of routes increases exponentially, making its employment infeasible despite the complexity reduction offered. Therefore, we propose a novel optimal quantum-assisted algorithm, namely, the non-dominated quantum iterative optimization (NDQIO) algorithm, which exploits the synergy between the hardware and the QP for the sake of achieving a further complexity reduction, which is on the order of O( √ N ) and O(N √ N ) in the best and worst case scenarios, respectively. In addition, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared with the near-optimal NDQO algorithm, while having the same order of power consumption.INDEX TERMS WMHNs, quantum computing, Pareto optimality, BBHT-QSA, DHA, NDQO.

Faster, ultra-reliable, low-power and secure communications has always been high on the wireless evolutionary agenda. However, the appetite for faster, more reliable, greener and more secure communications continues to grow. The stateof-the-art methods conceived for achieving the performance targets of the associated processes may be accompanied by an increase in computational complexity. Alternatively, a degraded performance may have to be accepted due to the lack of jointly optimized system components. In this survey we investigate the employment of quantum computing for solving problems in wireless communication systems. By exploiting the inherent parallelism of quantum computing, quantum algorithms may be invoked for approaching the optimal performance of classical wireless processes, despite their reduced number of cost-function evaluations. In this contribution we discuss the basics of quantum computing using linear algebra, before presenting the operation of the major quantum algorithms, which have been proposed in the literature for improving wireless communications systems. Furthermore, we investigate a number of optimization problems encountered both in the physical and network layer of wireless communications, while comparing their classical and quantumassisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.

Abstract-Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit.

Quantum Error Correction Codes (QECCs) can be constructed from the known classical coding paradigm by exploiting the inherent isomorphism between the classical and quantum regimes, while also addressing the challenges imposed by the strange laws of quantum physics. In this spirit, this paper provides deep insights into the duality of quantum and classical coding theory, hence aiming for bridging the gap between them. Explicitly, we survey the rich history of both classical as well as quantum codes. We then provide a comprehensive slow-paced tutorial for constructing stabilizer-based QECCs from arbitrary binary as well as quaternary codes, as exemplified by the dual-containing and non-dual-containing Calderbank-Shor-Steane (CSS) codes, non-CSS codes and entanglement-assisted codes. Finally, we apply our discussions to two popular code families, namely to the family of Bose-Chaudhuri-Hocquenghem (BCH) as well as of convolutional codes and provide detailed design examples for both their classical as well as their quantum versions.

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Low-complexity suboptimal multiuser detectors (MUDs) are widely used in multiple access communication systems for separating users, since the computational complexity of the maximum likelihood (ML) detector is potentially excessive for practical implementation. Quantum computing may be invoked in the detection procedure, by exploiting its inherent parallelism for approaching the ML MUDs performance at a substantially reduced number of cost function evaluations. In this contribution, we propose a soft-output (SO) quantum-assisted MUD achieving a near-ML performance and compare it to the corresponding SO ant colony optimization MUD. We investigate rank deficient direct-sequence spreading (DSS) and slow subcarrier-hopping aided (SSCH) spatial division multiple access orthogonal frequency division multiplexing systems, where the number of users to be detected is higher than the number of receive antenna elements used. We show that for a given complexity budget, the proposed SO-Dürr-Høyer algorithm (DHA) QMUD achieves a better performance. We also propose an adaptive hybrid SO-ML/SO-DHA MUD, which adapts itself to the number of users equipped with the same spreading sequence and transmitting on the same subcarrier. Finally, we propose a DSS-based uniform SSCH scheme, which improves the system's performance by 0.5 dB at a BER of 10 −5 , despite reducing the complexity required by the MUDs employed.