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The employment of quantum error correction codes (QECCs) within quantum computers potentially offers a reliability improvement for both quantum computation and communications tasks. However, incorporating quantum gates for performing error correction potentially introduces more sources of quantum decoherence into the quantum computers. In this scenario, the primary challenge is to find the sufficient condition required by each of the quantum gates for beneficially employing QECCs in order to yield reliability improvements given that the quantum gates utilized by the QECCs also introduce quantum decoherence. In this treatise, we approach this problem by firstly presenting the general framework of protecting quantum gates by the amalgamation of the transversal configuration of quantum gates and quantum stabilizer codes (QSCs), which can be viewed as syndrome-based QECCs. Secondly, we provide examples of the advocated framework by invoking quantum topological error correction codes (QTECCs) for protecting both transversal Hadamard gates and CNOT gates. The simulation and analytical results explicitly show that by utilizing QTECCs, the fidelity of the quantum gates can be beneficially improved, provided that quantum gates satisfying a certain minimum depolarization fidelity threshold (Fth) are available. For instance, for protecting transversal Hadamard gates, the minimum fidelity values required for each of the gates in order to attain fidelity improvements are 99.74%, 99.73%, 99.87%, and 99.86%, when they are protected by colour, rotated-surface, surface, and toric codes, respectively. These specific Fth values are obtained for a very large number of physical qubits (n → ∞), when the quantum coding rate of the QTECCs approaches zero (rQ → 0). Ultimately, the framework advocated can be beneficially exploited for employing QSCs to protect large-scale quantum computers.

Flexible modulation schemes and smart multiple-input multiple-output techniques, as well as low-complexity detectors and preprocessors may become essential for efficiently balancing the bit error ratio performance, throughput, and complexity tradeoff for various application scenarios. Millimeter-Wave systems have a high available bandwidth and the potential to accommodate numerous antennas in a small area, which makes them an attractive candidate for future networks employing spatial modulation and spacetime shift keying (STSK). Non-Orthogonal Multiple Access (NOMA) systems are capable of achieving an increased throughput, by allowing multiple users to share the same resources at the cost of a higher transmission power, or an increased detection (preprocessing) complexity at the receiver (transmitter) of an uplink (downlink) scenario. In this paper, we propose the new concept of joint-alphabet space time shift keying. As an application scenario, we employ it in the context of the uplink of NOMA mm-Wave systems. We demonstrate with the aid of extrinsic information transfer charts that a higher capacity is achievable when compared with STSK, while retaining the attractive flexibility of STSK in terms of its diversity gain and coding rate. Finally, we conceive quantum-assisted detectors for reducing the detection complexity, while attaining a near-optimal performance, when compared with the optimal iterative maximum A posteriori probability detector.

The provision of high-speed Internet access in an aircraft is mainly supported by satellite links at the time of writing, aided by links between the aircraft and the ground stations. It is anticipated that Air-To-Ground (A2G) communications between en-route aircraft and the ground stations will have a major role in providing the required quality of service, while complying with the low latency requirements of next-generation of communications networks. Non-orthogonal multiple access (NOMA) systems will increase the system throughput by allowing multiple aircraft to simultaneously communicate with the ground station, while requiring fewer resource slots. Given the limited number of orthogonal resource "slots" and the high number of aircraft to be supported, a potentially high level of interference is expected. In this contribution, we employ beamforming based on the angle of arrival of the signals and antenna arrays having multiple antenna elements, as well as a novel interference-exploiting sphere decoder, which detects the signals of the supported users, while beneficially exploiting those of the interfering users. We show that an improved performance may be achieved in both hard-input hard-output scenarios, as well as in iterative soft-input soft-output scenarios, when compared with the conventional sphere decoder, the maximum likelihood detector and the maximum a posteriori probability detector. We also characterize the complexity of the proposed receiver and evaluate its performance with the aid of bit error ratio simulations and extrinsic information transfer charts.

Inspired by the success of classical turbo codes, quantum turbo codes (QTCs) have also been conceived for near-hashing-bound transmission of quantum information over memoryless quantum channels. However, in real physical situations, the memoryless channel assumption may not be well justified, since the channel often exhibits memory of previous error events. Here, we investigate the performance of QTCs over depolarizing channels exhibiting memory and we show that they suffer from a performance degradation at low depolarizing probability values. In order to circumvent the performance degradation issue, we conceive a new coding scheme termed quantum turbo coding scheme exploiting error-correlation (QTC-EEC) that is capable of utilizing the error-correlation while performing the iterative decoding at the receiver. The proposed QTC-EEC can achieve convergence threshold at a higher depolarizing probability for channels with a higher value of correlation parameter and achieve performance near to the capacity. Finally, we propose a joint decoding and estimation scheme for our QTC-EEC relying on the correlation estimation (QTC-EEC-E) designed for more realistic quantum systems with unknown correlation parameter. Simulation results reveal that the proposed QTC-EEC-E can achieve the same performance as that of the ideal system of known correlation parameter and hence demonstrate the accurate estimation of the proposed QTC-EEC-E.

We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity. Specifically, from our simulation results, the threshold probability of the QBER curves for the color codes, rotated-surface codes, surface codes, and toric codes are given by $1.8 \times 10^{-2}$ , $1.3 \times 10^{-2}$ , $6.3 \times 10^{-2}$ , and $6.8 \times 10^{-2}$ , respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97, and 0.99 by employing the 1/7-rate color code, the 1/9-rate rotated-surface code, and 1/13-rate surface code, respectively.

Moore's law is expected to lead to the gates of the quantum world in 2017. Therefore, the emerging quantum computing research is expected to give rise to novel quantum search algorithms, which may replace the currently used classical ones in wireless communications, leading to performance improvements and complexity reduction. In this paper, we demonstrate the benefits of quantum-assisted multi-user detection (QMUD) in the uplink of a multi-user system, where the reference user conveys a multilayered video stream to the base station, while using adaptive modulation and different rates per video layer. This is the first study, where a QMUD is employed in a video application. The QMUD does not treat the rest of the users as interference, but rather detects the signals transmitted by all the users. We have evaluated the system's performance both in terms of its bit error ratio and peak signal-to-noise ratio versus the channel's signal-to-noise ratio, while quantifying the complexity reduction achieved by using the QMUD instead of the optimal classical maximum a posteriori probability MUD. The effect of the number of users on the system's performance is also quantified.

With the proliferation of millimeter-Wave (mm-Wave) systems and visible light communications (VLCs), indoor localization may find multiple applications. When high localization accuracy is required and triangulation is not possible due to the infrastracture and scenario limitations, the computational complexity of searching on a virtual grid may become excessive. In this paper, we amalgamate uplink mm-Wave-based and downlink VLC-based localization. We employ quantum search algorithms for reducing the computational complexity required for achieving the optimal full-search-based performance. Regarding the uplink mm-Wave-based localization, we employ a single anchor equipped with multiple antenna elements and we exploit the specular multipath components created by the room's walls. The proposed solutions outperform the state-of-the-art algorithms. Furthermore, various channel models are considered based on real indoors mm-Wave measurements. By using the VLC-based triangulation for downlink and the proposed mm-Wave-based localization algorithm for uplink, there was an average positioning error of 5.6 cm in the room considered, while requiring 261 database queries on average.

The tradeoff between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this tradeoff does not exist, but the corresponding lower and the upper bounds can be found in the literature. In this treatise, we survey the existing quantum coding bounds and provide new insights into the classical to quantum duality for the sake of deriving new quantum coding bounds. Moreover, we propose an appealingly simple and invertible analytical approximation, which describes the tradeoff between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a code word length of n = 128, the minimum distance is bounded by 11

Realistic public wireless channels and quantum key distribution (QKD) systems are amalgamated. Explicitly, we conceive network coding aided cooperative QKD over free space optical systems for improving the bit error ratio and either the key rate or the reliable operational distance. Our system has provided a 55% key rate improvement against the state-of-the-art benchmarker.

Large-scale quantum network coding (LQNC) is conceived for distributing entangled qubits over large-scale quantum communication networks supporting both teleportation and quantum key distribution. More specifically, the LQNC is characterized by detailing the encoding and decoding process for distributing entangled pairs of qubits to $M$ pairs of source-and-target users connected via a backbone route of $N$ hops. The LQNC-based system advocated is then compared with entanglement swapping-based systems for highlighting the benefits of the proposed LQNC.

The widespread use of mobile networking devices, such as smart phones and tablets, has substantially increased the number of nodes in the operational networks. These devices often suffer from the lack of power and bandwidth. Hence, we have to optimize their message routing for the sake of maximizing their capabilities. However, the optimal routing typically relies on a delicate balance of diverse and often conflicting objectives, such as the route's delay and power consumption. The network design also has to consider the nodes' user-centric social behavior. Hence, the employment of socially aware load balancing becomes imperative for avoiding the potential formation of bottlenecks in the network's packet-flow. In this paper, we propose a novel algorithm, referred to as the multi-objective decomposition quantum optimization (MODQO) algorithm, which exploits the quantum parallelism to its full potential by reducing the database correlations for performing multi-objective routing optimization, while at the same time balancing the teletraffic load among the nodes without imposing a substantial degradation on the network's delay and power consumption. Furthermore, we introduce a novel socially aware load balancing metric, namely, the normalized entropy of the normalized composite betweenness of the associated socially aware network, for striking a better tradeoff between the network's delay and power consumption. We analytically prove that the MODQO algorithm achieves the full-search based accuracy at a significantly reduced complexity, which is several orders of magnitude lower than that of the full search. Finally, we compare the MODQO algorithm to the classic non-dominated sort genetic algorithm II evolutionary algorithm and demonstrate that the MODQO succeeds in halving the network's average delay, while simultaneously reducing the network's average power consumption by 6 dB without increasing the computational complexity.

Quantum turbo codes (QTCs) are known to operate close to the achievable Hashing bound. However, the sequential nature of the conventional quantum turbo decoding algorithm imposes a high decoding latency, which increases linearly with the frame length. This posses a potential threat to quantum systems having short coherence times. In this context, we conceive a fully-parallel quantum turbo decoder (FPQTD), which eliminates the inherent time dependences of the conventional decoder by executing all the associated processes concurrently. Due to its parallel nature, the proposed FPQTD reduces the decoding times by several orders of magnitude, while maintaining the same performance. We have also demonstrated the significance of employing an odd-even interleaver design in conjunction with the proposed FPQTD. More specifically, it is shown that an odd-even interleaver reduces the computational complexity by 50%, without compromising the achievable performance.

Joint channel estimation (CE) and multi-user detection (MUD) have become a crucial part of iterative receivers. In this paper, we propose a quantum-assisted repeated weighted boosting search (QRWBS) algorithm for CE and we employ it in the uplink of multiple-input multiple-output orthogonal frequency division multiplexing systems, in conjunction with the maximum a posteriori probability (MAP) MUD and a near-optimal quantum-assisted MUD (QMUD). The performance of the QRWBS-aided CE is evaluated in rank-deficient systems, where the number of receive antenna elements (AEs) at the base station (BS) is lower than the number of supported users. The effect of the channel impulse response prediction filters, of the power delay profile of the channels, and of the Doppler frequency on the attainable system performance is also quantified. The proposed QRWBS-aided CE is shown to outperform the RWBS-aided CE, despite requiring a lower complexity, in systems where iterations are invoked between the MUD, the CE, and the channel decoders at the receiver. In a system, where U = 7 users are supported with the aid of P = 4 receive AEs, the joint QRWBS-aided CE and QMUD achieves a 2-dB gain, when compared with the joint RWBS-aided CE and MAP MUD, despite imposing 43% lower complexity.

With the research on implementing a universal quantum computer being under the technological spotlight, new possibilities appear for their employment in wireless communications systems for reducing their complexity and improving their performance. In this treatise, we consider the downlink of a rank-deficient, multi-user system and we propose the discrete-valued and continuous-valued quantum-assisted particle swarm optimization (PSO) algorithms for performing vector perturbation precoding, as well as for lowering the required transmission power at the base station (BS), while minimizing the expected average bit error ratio (BER) at the mobile terminals. We use the minimum BER criterion. We show that the novel quantum-assisted precoding methodology results in an enhanced BER performance, when compared with that of a classical methodology employing the PSO algorithm, while requiring the same computational complexity in the challenging rank-deficient scenarios, where the number of transmit antenna elements at the BS is lower than the number of users. Moreover, when there is limited channel state information feedback from the users to the BS, due to the necessary quantization of the channel states, the proposed quantum-assisted precoder outperforms the classical precoder.

In this contribution, the Hashing bound of entanglement-assisted quantum channels is investigated in the context of quantum devices built from a range of popular materials, such as trapped ion and relying on solid state nuclear magnetic resonance, which can be modeled as a so-called asymmetric channel. Then, quantum error correction codes (QECC) are designed based on extrinsic information transfer charts for improving performance when employing these quantum devices. The results are also verified by simulations. Our QECC schemes are capable of operating close to the corresponding Hashing bound.

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.

In large-dimensional wireless systems, such as cooperative multicell processing, millimeterwave, and massive multiple input multiple output systems, or cells having a high user density, such as airports, train stations, and metropolitan areas, sufficiently accurate estimation of all the channel gains is required for performing coherent detection. Therefore, they may impose an excessive complexity. As an attractive design alternative, differential modulation relying on noncoherent detection may be invoked for eliminating the requirement for channel estimation at the base station, although at the cost of some performance degradation. In this treatise, we propose low-complexity hard-input hard-output, hard-input soft-output, as well as soft-input soft-output quantum-assisted multiple symbol differential detectors (MSDDs) that perform equivalently to the optimal, but highly complex maximum a posteriori probability MSDDs in multiuser systems, where the users are separated both in the frequency domain and in the time domain. When using an MSDD, the detection of a user's symbols is performed over windows of differentially modulated symbols; hence, they exhibit an increased complexity with respect to the conventional differential detector while simultaneously improving the performance of the system, especially at high Doppler frequencies.

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.

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 state-of-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.

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.

Self-organizing networks act autonomously for the sake of achieving the best possible performance. The attainable routing depends on a delicate balance of diverse and often conflicting quality-of-service requirements. Finding the optimal solution typically becomes an nonolynomial-hard problem, as the network size increases in terms of the number of nodes. Moreover, the employment of user-defined utility functions for the aggregation of the different objective functions often leads to suboptimal solutions. On the other hand, Pareto optimality is capable of amalgamating the different design objectives by providing an element of elitism. Although there is a plethora of bioinspired algorithms that attempt to address this optimization problem, they often fail to generate all the points constituting the optimal Pareto front. As a remedy, we propose an optimal multiobjective quantum-assisted algorithm, namely the nondominated quantum optimization algorithm (NDQO), which evaluates the legitimate routes using the concept of Pareto optimality at a reduced complexity. We then compare the performance of the NDQO algorithm to the state-of-the-art evolutionary algorithms, demonstrating that the NDQO algorithm achieves a near-optimal performance. Furthermore, we analytically derive the upper and lower bounds of the NDQO algorithmic complexity, which is of the order of O(N) and O(N√(N)) in the best and worst case scenario, respectively. This corresponds to a substantial complexity reduction of the NDQO from the order of O(N2) imposed by the brute-force method.