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State-of-the-art noisy intermediate-scale quantum computers require low-complexity techniques for the mitigation of computational errors inflicted by quantum decoherence. Symmetry verification constitutes a class of quantum error mitigation (QEM) techniques, which distinguishes erroneous computational results from the correct ones by exploiting the intrinsic symmetry of the computational tasks themselves. Inspired by the benefits of quantum switch in the quantum communication theory, we propose beneficial techniques for circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the spatio-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain stabilizer formalism to circuit-oriented stabilizers. The applicability and implementational strategies of the proposed techniques are demonstrated by using practical quantum algorithms, including the quantum Fourier transform (QFT) and the quantum approximate optimization algorithm (QAOA)., 17 pages, 26 figures, submitted to IEEE Transactions on Signal Processing

Moore’s Law has prevailed since 1965, predicting that the integration density of chips will be doubled approximately every 18 months or so, which has resulted in nanoscale in- tegration associated with 7 nm technologies at the time of writing. At this scale however we are about to enter the transitory range between classical and quantum physics. Based on the brilliant proposition by Feynman a new breed of information bearers was born, where the quantum bits are mapped for example to the spin of an electron. As a benefit, the alluring properties of the nano-scale quantum world have opened up a whole spate of opportunities in signal processing and communications, as discussed in this easy-reading discourse requiring no background in quantum physics.

The unique and often-weird properties of quantum mechanics allow an information carrier to propagate through multiple trajectories of quantum channels simultaneously. This ultimately leads us to quantum trajectories with an indefinite causal order of quantum channels. It has been shown that indefinite causal order enables the violation of bottleneck capacity, which bounds the amount of the transferable classical and quantum information through a classical trajectory with a well-defined causal order of quantum channels. In this treatise, we investigate this beneficial property in the realm of both entanglement-assisted classical and quantum communications. To this aim, we derive closed-form capacity expressions of entanglement-assisted classical and quantum communication for arbitrary quantum Pauli channels over classical and quantum trajectories. We show that by exploiting the indefinite causal order of quantum channels, we obtain capacity gains over classical trajectory as well as the violation of bottleneck capacity for various practical scenarios. Furthermore, we determine the operating region where entanglement-assisted communication over quantum trajectory obtains capacity gain against classical trajectory and where the entanglement-assisted communication over quantum trajectory violates the bottleneck capacity., Accepted for publication in IEEE Transactions on Wireless Communications

To realize the Quantum Internet, quantum communications require pre-shared entanglement among quantum nodes. However, both the generation and the distribution of the maximally-entangled quantum states are inherently contaminated by quantum decoherence. Conventionally, the quantum decoherence is mitigated by performing the consecutive steps of quantum entanglement distillation followed by quantum teleportation. However, this conventional approach imposes a long delay. To circumvent this impediment, we propose a novel quantum communication scheme relying on realistic noisy pre-shared entanglement, which eliminates the sequential steps imposing delay in the standard approach. More precisely, our proposed scheme can be viewed as a direct quantum communication scheme capable of improving the quantum bit error ratio (QBER) of the logical qubits despite relying on realistic noisy pre-shared entanglement. Our performance analysis shows that the proposed scheme offers competitive QBER, yield, and goodput compared to the existing state-of-the-art quantum communication schemes, despite requiring fewer quantum gates., Accepted for publication in IEEE Transactions on Communications

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 state-of-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 quantum-assisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.

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.

Wireless Multihop Networks (WMHNs) have to strike a trade-off among diverse and often conflicting Quality-of-Service (QoS) requirements. The resultant solutions may be included by the Pareto Front under the concept of Pareto Optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as NP-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum Computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms have been proposed, namely the Non-Dominated Quantum Optimization (NDQO) and the Non-Dominated Quantum Iterative Optimization (NDQIO). However, their complexity is proportional to $\sqrt{N}$, where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in "polynomial time". As a remedy, we devise a dynamic programming framework and propose the so-called Evolutionary Quantum Pareto Optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude, when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction., Comment: Accepted in IEEE Transactions on Communications, 2018. In press

An ideal Visible Light Communication (VLC) system should facilitate reliable data transmission at high throughputs, while also providing flicker-free illumination at the user-defined dimming level. In this spirit, we conceive a unary code aided dimming scheme for On-Off Keying (OOK) modulated VLC systems. The proposed unary-coded scheme facilitates joint dimming and throughput control, while relying on iterative decoding. It is demonstrated that the proposed unary-coded dimming scheme provides attractive throughput gains over its contemporaries and it is also capable of approaching the theoretical throughput limit. Furthermore, we design novel joint dimming-Forward Error Correction (FEC) coding schemes, which significantly outperform their compensation time dimming based counterparts in terms of the attainable Bit Error Rate (BER) performance as well as the throughput. Finally, in the quest for approaching the capacity, we also optimize our system using EXtrinsic Information Transfer (EXIT) charts and demonstrate an SNR-gain of up to 6 dB over the compensation time dimming based classic benchmarker.

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 as 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 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.

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 space-time 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.

Quantum processors require Quantum Error Correction Codes (QECC's) for improving the fidelity of quantum logic gates. Fault tolerant QECC's are capable of providing error rate improvements in quantum processors as long as the components are operating below a certain gate error probability. In this contribution, we quantify the depolarization probability bound, below which transversal QECC's would give a better error probability than an uncoded gate. Both a low-complexity repetition code and Steane's 7-bit QECC are characterized.

Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce competition to both the turbo as well as the Low Density Parity Check (LDPC) codes, making its way into the 5G New Radio (NR). Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the polar encoder, decoders as well as the code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndrome-based quantum polar codes., 35 pages, accepted for publication in IEEE Communications Surveys and Tutorials

Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate, since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated quantum turbo code (QTC) design exhibiting a high quantum coding rate. The high quantum coding rate is achieved by combining the quantum-domain version of short-block codes (SBCs) also known as single parity check (SPC) codes as the outer codes and quantum unity-rate codes (QURCs) as the inner codes. Despite its design simplicity, the proposed QTC yields a near-hashing-bound error correction performance. For instance, compared to the best half-rate QTC known in the literature, namely the QIrCC-QURC scheme, which operates at the distance of $D = 0.037$ from the quantum hashing bound, our novel QSBC-QURC scheme can operate at the distance of $D = 0.029$. It is worth also mentioning that this is the first instantiation of QTCs capable of adjusting the quantum encoders according to the quantum coding rate required for mitigating the Pauli errors given the different depolarizing probabilities of the quantum channel., 19 pages, 12 figures

In this letter, we aim for maximizing the throughput of a visible light communication (VLC) system. Explicitly, we conceive a soft-in soft-out decoder providing soft feedback for the classic run length limited (RLL) codes, hence facilitating iterative decoding for exchanging valuable extrinsic information between the RLL and the error correction modules of a VLC system. Furthermore, we propose a unity rate code for our VLC system, which, hence, becomes capable of matching the ON–OFF keying capacity, while maintaining a flicker-free dimming value of 50%.

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.

Realistic public wireless channels and Quantum Key Distribution (QKD) systems are amalgamated. Explicitly, we conceive Network Coding aided Cooperative Quantum Key Distribution over Free Space Optical (NC-CQKD-FSO) systems for improving the Bit Error Ratio (BER) 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.

Inspired by the astounding performance of the unity rate code (URC) aided classical coding and detection schemes, we conceive a quantum URC (QURC) for assisting the design of concatenated quantum codes. Unfortunately, a QURC cannot be simultaneously recursive as well as non-catastrophic. However, we demonstrate that, despite being non-recursive, our proposed QURC yields efficient concatenated codes, which exhibit a low error rate and a beneficial interleaver gain, provided that the coding scheme is carefully designed with the aid of EXtrinsic Information Transfer (EXIT) charts.

In this letter, we conceive a multilayered coding scheme for the recently proposed layered asymmetrically clipped optical orthogonal frequency division multiplexing (LACO-OFDM) system, which exploits its layered structure for protecting the information bits transmitted in the base layer. Explicitly, we intrinsically integrate error correction into the layered structure of the LACO-OFDM system and invoke soft iterative decoding between the layers at the receiver. Our system operates within 2 dB of the capacity limit at a bit error ratio of $10^{-4}$ .

Pareto optimality is capable of striking the optimal trade-off amongst the diverse conflicting QoS requirements of routing in wireless multihop networks. However, this comes at the cost of increased complexity owing to searching through the extended multi-objective search-space. We will demonstrate that the powerful quantum-assisted dynamic programming optimization framework is capable of circumventing this problem. In this context, the so-called Evolutionary Quantum Pareto Optimization (EQPO) algorithm has been proposed, which is capable of identifying most of the optimal routes at a near-polynomial complexity versus the number of nodes. As a benefit, we improve both the the EQPO algorithm by introducing a back-tracing process. We also demonstrate that the improved algorithm, namely the Back-Tracing-Aided EQPO (BTA-EQPO) algorithm, imposes a negligible complexity overhead, while substantially improving our performance metrics, namely the relative frequency of finding all Pareto-optimal solutions and the probability that the Pareto-optimal solutions are indeed part of the optimal Pareto front, Accepted in Transactions on Vehicular Technology

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 topological error correction codes (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 colour 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 colour code, the $1/9$-rate rotated-surface code and $1/13$-rate surface code, respectively.

In this paper, we conceive novel symbol-based Color- Shift Keying (CSK)-aided concatenated coding schemes, which provide attractive performance gains over the comparable bitbased systems. Quantitatively, our 4CSK-aided and 16CSK-aided symbol-based concatenated systems require 0.8 dB and 0.45 dB lower SNR than the equivalent bit-based schemes. In terms of decoding complexity, the 4CSK-aided and 16CSK-aided systems reduce the decoding complexity by 67% and 33%, respectively. We have also analyzed the convergence behavior of our system with the aid of non-binary EXtrinsic Information Transfer (EXIT) charts adapted for symbol-based iterative CSK-assisted systems.

When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.

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 (QPSO) algorithms for performing Vector Perturbation (VP) 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 (MBER) criterion. We show that the novel quantum-assisted precoding methodology results in an enhanced BER performance, when compared to 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 (CSI) 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.

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.