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Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether quantum computers are indeed producing correct results. This task, known as quantum verification, has been highlighted as a significant challenge on the road to scalable quantum computing technology. We review the most significant approaches to quantum verification and compare them in terms of structure, complexity and required resources. We also comment on the use of cryptographic techniques which, for many of the presented protocols, has proven extremely useful in performing verification. Finally, we discuss issues related to fault tolerance, experimental implementations and the outlook for future protocols.

Designing efficient techniques to search over encrypted data space has always been an intriguing security challenge, although many solutions based on classical searching methods have been proposed. Grover’s algorithm, a quantum counterpart of searching algorithms, has proven to provide quadratic speedup over any classical search technique on an unsorted database. However, this algorithm is unable to search over encrypted data space. This study proposed an extension of Grover’s algorithm to enable search over encrypted dataspace, allowing clients with limited-capability quantum resources to delegate complex search operations to an untrusted server. The blindness of data in this protocol is achieved by encrypting qubits using Pauli’s rotation gates that maximally mix the outgoing states. The empirical estimation of the overhead of the computation due to the introduction of this technique has been analyzed. This estimate has been used for comparative analysis, showing the efficiency of the proposed protocol. A practical application of the proposed searchable encryption technique has been utilized to estimate the increase in resources needed to carry out a brute-force attack on AES encryption using secure Grover’s algorithm. Furthermore, an extensive experimental analysis of the effect of noise has been studied using four different noise models: amplitude damping, phase damping, depolarizing noise, and bit-flip noise. The investigation provided useful insight into the behavior of the proposed algorithm under noisy conditions and also estimated the tolerance thresholds of the proposed algorithm under different noise models.

As quantum computing continues to reshape industries, learning its nuances is crucial for staying ahead in fields like cryptography, computing, and communication. Kickstart Quantum Computing and Communication Fundamentals is an essential guide for anyone eager to explore quantum technology. Designed for readers at all levels, especially academia, it starts with an accessible introduction to quantum computing and communication, explaining key concepts like superposition, entanglement, and measurement. The book covers quantum algorithms, including Shor's and Grover's algorithms, and dives into quantum circuits, gates, and the technologies behind quantum hardware like superconducting qubits and trapped ions. It also explores secure quantum communication protocols such as quantum key distribution and teleportation, providing hands-on examples with tools like Qiskit. Beyond the technical aspects, the book examines quantum computing's impact on cryptography, addressing current vulnerabilities and quantum-secure solutions. Concluding with emerging trends and challenges, this interdisciplinary resource blends physics, computing, and engineering, offering valuable insights for students, educators, and professionals entering the quantum age.

With over 450,000 users worldwide, Qiskit has become the go-to platform for building large-scale quantum applications on systems with hundreds of qubits. \"Ultimate Quantum Computing with Qiskit\" offers a comprehensive guide to mastering quantum computing using IBM's powerful open-source framework.This book begins by introducing the core concepts of mathematics, quantum mechanics, and computation, before diving into qubits and quantum logic gates for both single and multi-qubit systems. You'll then explore key features of Qiskit, including mapping, optimization, and transpilation, essential for building efficient quantum circuits.The book also covers a range of important topics, from foundational quantum algorithms like Grover's, Shor's and Fourier's to quantum communication protocols and variational quantum algorithms. Finally, advanced sections on quantum machine learning, error mitigation, and Qiskit Pulse will empower you to solve real-world problems and stay at the forefront of quantum computing innovation.Dive in today and unlock the power of quantum computing to build the applications of tomorrow. Let this book be your guide to mastering Qiskit and shaping the future of technology!.

Blind quantum computation (BQC) allows quantum-limited clients to delegate their quantum-computing tasks to a remote quantum server while keep their inputs, outputs, and algorithms private during the computation. Secure multi-party computation aims to solve the problem of collaborative calculations among a group of distrustful participants. Although BQC has been used to solve the problem of secure two-party quantum computation, the case of multiple clients carrying out collaborative calculations has not been considered. In this paper, a quantum secure three-party computation protocol is proposed based on BQC, and the protocol is further extended to a quantum secure multi-party computation protocol. Using the blindness of BQC, the problem of privacy of clients’ data in quantum secure multi-party computation is solved. Moreover, in the preparation stage of the protocols, the initial states only need to be encrypted once, which is simpler than previous protocols.

This book presents new and prospective approaches to quantum computing. It introduces the many possibilities to further develop the mathematical methods of quantum computation and its applications to future functioning and operational quantum computers. In this book, various extensions of the qubit concept, starting from obscure qubits, superqubits and other fundamental generalizations, are considered. New gates, known as higher braiding gates, are introduced. These new gates are implemented as an additional stage of computation for topological quantum computations and unconventional computing when computational complexity is affected by its environment. Other generalizations are considered and explained in a widely accessible and easy-to-understand way. Presented in a book for the first time, these new mathematical methods will increase the efficiency and speed of quantum computing. Part of IPEM-IOP Series in Coherent Sources, Quantum Fundamentals, and Applications.

The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with$T$gates whose underlying graph has a treewidth$d$can be simulated deterministically in$T^{O(1)}\\exp[O(d)]$time, which, in particular, is polynomial in$T$if$d=O(\\log T)$ . Among many implications, we show efficient simulations for log-depth circuits whose gates apply to nearby qubits only, a natural constraint satisfied by most physical implementations. We also show that one-way quantum computation of Raussendorf and Briegel (Phys. Rev. Lett., 86 (2001), pp. 5188-5191), a universal quantum computation scheme with promising physical implementations, can be efficiently simulated by a randomized algorithm if its quantum resource is derived from a small-treewidth graph with a constant maximum degree. (The requirement on the maximum degree was removed in [I. L. Markov and Y. Shi, preprint:quant-ph/0511069].)

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.

\"The objective of this book is to communicate advancements of knowledge and help disseminate results concerning recent applications and case studies in the area of quantum computing among working professionals and professionals in education and research, covering a broad cross-section of technical disciplines. This book will allow students to explore knowledge in quantum computing to produce serviceable and innocuous systems as well as purposeful systems with cutting-edge technology. To yield computer systems with decent usability, developers must attempt to understand the factors that determine how people use technology. This book will cater to an extensive cross-sectional and multi-disciplinary readership ranging from academics, business delegates, CEOs, communication designers, computer scientists, digital customers, e-decision makers, eLearning environment designers, industrial leaders, industry consultants, key workers, law enforce