Quantum computing is considered to be a promising technology for some specific types of computing purposes. Modeling of quantum computing could help study and research of this field. In this dissertation, we approach quantum computing from a communication perspective that is to model quantum computing with a generalized noisy communication channel approach.
We proposed a generalized noisy communication channel approach (GNCom) for quantum computing. The proposed GNCom approach is applied to quantum computing as a universal quantum register. GNCom further extended the noisy communication channel framework by associating it with Quantum Electrodynamics (QED). Based on GNCom and QED, we proposed a quantum computer design technique.
Quantum computing is considered to be a promising technology for some specific types of computing purposes. Modeling of quantum computing could help study and research of this field. In this dissertation, we approach quantum computing from a communication perspective that is to model quantum computing with a generalized noisy communication channel approach.
We proposed a generalized noisy communication channel approach (GNCom) for quantum computing. The proposed GNCom approach is applied to quantum computing as a universal quantum register. GNCom further extended the noisy communication channel framework by associating it with Quantum Electrodynamics (QED). Based on GNCom and QED, we proposed a quantum computer design technique.
We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for eventual real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems. These are the first results concerning the quantum version of this problem, originally studied by Schulman in a classical setting [L. J. Schulman, Communication on noisy channels: A coding theorem for computation, in Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, IEEE, 1992, pp. 724--733], [L. J. Schulman, Deterministic coding for interactive communication, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, ACM, 1993, pp. 747--756]. We simulate a length N quantum communication protocol by a length O(N) protocol with arbitrarily small error. Under adversarial noise, our strategy can withstand, for arbitrarily small ε>0, error rates as high as 1/2−ε when parties preshare perfect entanglement, but the classical channel is noisy. We show that this is optimal. We provide extension of these results in several other models of communication, including when also the entanglement is noisy, and when there is no preshared entanglement but communication is quantum and noisy. We also study the case of random noise, for which we provide simulation protocols with positive communication rates and no preshared entanglement over some quantum channels with quantum capacity CQ=0, proving that CQ is in general not the right characterization of a channel's capacity for interactive quantum communication. Our results are stated for a general quantum communication protocol in which Alice and Bob collaborate, and these results hold in particular in the quantum communication complexity settings of the Yao and Cleve--Buhrman models.
In this research notebook on quantum computation and quantum communication protocol for quantum engineers, researchers, and scientists, we will discuss and summarize the practical challenges of implementing quantum computing algorithms and quantum communication protocols in today's real-world hardware systems. We will begin the discussion about the noise and its effect on quantum coherence and the mathematical models to represent the impact of noise on the physical systems. Furthermore, we will discuss the basic concepts of noise that practically limit quantum computation and quantum communication. We will discuss several mathematical methods to characterize, model, and represent the practical impact of noise. Next, we will discuss how photon loss impacts quantum communication protocols. We will summarize the current physical limitations and challenges facing quantum computation and quantum communication over optical fiber. We will also discuss technology options that can mitigate or eliminate the physical limitations for realizing quantum computation and quantum communication protocol. Later we will consider the methods being developed to mitigate such losses in larger-scale communication systems. We will investigate the current limitations of quantum computing algorithms and the need to develop near-term practical applications that can be successfully performed on noisy qubits. We will also review the challenges associated with implementing algorithms on the relatively noisy, intermediate-scale qubits used in today's technology domain. Finally, we will investigate how to benchmark qubits and quantum gates in the presence of noise. We will discuss several methods to benchmark quantum states and quantum gates and finally implement benchmarking of qubits in a real physical quantum computer on the IBM Q Experience.
The primary aim of the thesis is to introduce and investigate an original protocol for the design and the optimization of parameterized noisy quantum channels, with the goal of mitigating hardware-induced noise. Significant attention is also devoted to the design of noise models, which are essential for emulation purposes. The protocol begins with the derivation of a noise model for a hardware gate, represented as a quantum channel, that can be simulated classically. This task is achieved through process tomography, a procedure that enables the characterization of the channel. It should be noted that such simulation is feasible on classical computers, since the optimization task concerns low-dimensional gates typically acting on 2–3 qubits. The noisy channel is then engineered by embedding it into a probabilistic ensemble of circuits, in which additional single-qubit parameterized gates — assumed to be noiseless — are introduced. Through this procedure, the noisy channel becomes parameterized and can be optimized according to an appropriate metric. Following a worst-case, agnostic perspective, we choose the diamond distance between the noisy channel and the target unitary channel as the cost function. This metric is generally considered the most suitable for distinguishing quantum channels. The resulting optimal ensemble of circuits can be implemented on real hardware under fixed calibration conditions, yielding a channel that approximates the target more closely than the original noisy channel. This approach can be interpreted as a noise mitigation strategy based on pre-processing design and optimization: rather than correcting errors after the computation, less noisy channels are employed during the computation itself. In this context, the protocol — within the noise-aware variational quantum compiling framework — shares with the randomized compiling the principle of circuit dressing to tailor noise during execution. The methodology is validated on two toy models of the single-qubit identity with amplitude damping noise, combining both analytical and numerical approaches. The analysis highlights the role of convexity in the space of quantum channels, with explicit demonstrations of optimal convex combinations and connections to encoding-decoding and dynamical decoupling strategies. The analysis of these simple models is intended as a proof-of-principle of the protocol in a controlled and well-characterized environment. In addition, this thesis introduces the design of random noise models that are constrained to maintain a fixed diamond distance from a target quantum channel. The controlled addition of random noise to a unitary channel represents a significant and — to our knowledge — previously unexplored approach within noise modeling. Indeed, in principle, the currently available built-in noise models may limit the expressivity of the emulation. The task was achieved by enriching the noise spectrum through the addition of random Kraus operators and small systematic rotations. To assess the effects of hardware-induced noise, we proposed an experimental design aimed at simulating the time evolution of a triangular Ising model in a transverse field. Our approach employs Trotterization, adapted to the topology and connectivity of a certain quantum processing unit (QPU) profile. Building on the noisy native gates of the QPU profile, we propose the emulation, engineering and optimization of a noisy CZ gate, subsequently employed within sequences of non-native gates. Using the designed noise models, we perform several emulations aimed at evaluating the effectiveness of the protocol in the presence of progressively dominant systematic rotations, and at comparing it with Pauli twirling, a technique of randomized compiling.
Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
In this paper secure schemes for cryptographic key distribution - called quantum key distribution protocols - are investigated by means of computer simulation. For this, a general purpose quantum circuit designer and simulator program was developed and used. To be more realistic the protocols were ran on different noisy quantum channels. The aim is to determine the grade of security of the protocols in function of the channel parameters they are using; and also to propose a method for selecting the best protocol for a given channel.
Quantum cryptography is a promising way to secure communication in the era of quantum information technologies (Nx-ICT). However, ensuring the confidentiality and authenticity of quantum communication is challenging in the presence of noisy quantum channels and a lack of trust between communicating parties. Unconditional mistrustful quantum cryptography protocols address these challenges by providing security guarantees even when parties do not trust each other. This paper explores the fundamental concepts and methodologies behind unconditional mistrustful quantum cryptography protocols in Nx-ICT scenarios. We examine the theoretical underpinnings of these protocols, which are based on cryptographic techniques from quantum mechanics, such as quantum key distribution (QKD) and entanglement-based protocols. We also review the latest experimental developments and achievements in the implementation of unconditional mistrustful quantum cryptography protocols. We discuss the progress that has been made in mitigating noise-induced vulnerabilities, as noisy quantum channels are common in practical quantum communication systems. Finally, we discuss the future prospects and open research questions in this field. We emphasize the importance of continuous research to improve the efficiency, scalability, and security of unconditional mistrustful quantum cryptography protocols in the face of evolving Nx-ICT applications and advancements.