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A universal decoding scheme is conceived for quantum stabilizer codes (QSCs) by appropriately adapting the ‘guessing random additive noise decoding’ (GRAND) philosophy of classical domain codes. We demonstrate that the generalized quantum decoder conceived is eminently suitable for different QSC decoding paradigms, namely for both stabilizer-measurement-based as well as the inverse-encoder-based decoding. We then harness the resultant decoder for both quantum Bose-Chaudhuri-Hocquenghem (BCH) codes and quantum polar codes and quantify both their quantum block error rate (QBLER), and QBLER per logical qubits as well as their decoding complexity. Furthermore, we provide a parametric study of the associated design trade-offs and offer design guideline for the implementation of GRAND-based QSC decoders.

We propose a novel quantum turbo short-block code, which subsumes multiple-rate quantum short-block codes (MR-QSBCs) as the outer codes and a quantum unity-rate code (QURC) as the inner code. The proposed design is denoted as MR-QSBC-QURC. More specifically, the proposed design exhibits multiple quantum coding rates despite relying only on a single quantum encoder. Moreover, the flexibility offered by the single-encoder MR-QSBCs enables us to leverage extrinsic information transfer (EXIT)-chart based heuristic optimization for determining the optimal weighting in the fractional encoding of MR-QSBCs. Our simulation results show that the MR-QSBC-QURC scheme conceived performs relatively close to the ultimate limit of the quantum hashing bound. Specifically, when considering the target quantum coding rates of $r_{Q} = \lbrace 0.3, 0.4, 0.5, 0.6, 0.7 \rbrace $ , the MR-QSBC-QURC operates at a distance of $D = \lbrace 0.042, 0.029, 0.030, 0.024, 0.017 \rbrace $ from the quantum hashing bound, respectively, at a quantum bit error ratio (QBER) of 10−3.

Experiments conducted on open-access cloud-based IBM Quantum devices are presented for characterizing their fault tolerance using [4, 2, 2]-encoded gate sequences. Up to 100 logical gates are activated in the Ibmq_Bogota and Ibmq_Santiago devices and we found that a [4, 2, 2] code’s logical gate set may be deemed fault-tolerant for gate sequences larger than 10 gates. However, certain circuits did not satisfy the fault tolerance criterion. In some cases the encoded-gate sequences show a high error rate that is lower bounded at ≈0.1, whereby the error inherent in these circuits cannot be mitigated by classical post-selection. A comparison of the experimental results to a simple error model reveal that the dominant gate errors cannot be readily represented by the popular Pauli error model. Finally, it is most accurate to assess the fault tolerance criterion when the circuits tested are restricted to those that give rise to an output state with a low dimension.

Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this work, we demonstrate that quantum low density parity check codes can be similarly bias-tailored. We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods beyond the family of 2D topological codes. We present examples of bias-tailored lifted product codes based on classical quasi-cyclic codes and numerically assess their performance using a belief propagation plus ordered statistics decoder. Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression relative to depolarising noise.

Quantum error mitigation (QEM) is a promising technique of protecting hybrid quantum-classical computation from decoherence, but it suffers from sampling overhead which erodes the computational speed. In this treatise, we provide a comprehensive analysis of the sampling overhead imposed by QEM. In particular, we show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels having the same average fidelity. Furthermore, we show that depolarizing errors incur the lowest sampling overhead among all kinds of Pauli errors. Additionally, we conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM. Especially, we observe that there exist a critical number of gates contained in quantum circuits, beyond which their amalgamation is preferable to pure QEM.

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.

An encoderless quantum code is capable of connecting quantum information by replacing the encoder circuit with a fault-tolerant single-qubit gate arrangement. As a further benefit, in contrast to state preparation techniques, our encoderless scheme requires no prior knowledge of the input information, therefore totally unknown states can be encoded fault-tolerantly. Our encoderless quantum code delivers a frame error rate that is three orders of magnitude lower than that of the corresponding scheme relying on a non-fault-tolerant encoder, when the gate error probability is as high as 10-3.

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. In addition, it is worth 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.

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.

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.

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.

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.