Quantum computation has shown a lot of promise in being able to provide computational results not possible with the modern computer. However, the design of new algorithms has been slow. One reason for this could be that we simply do not understand this new paradigm of computation enough to fully utilize it. We present here is an improvement of our previous generalization the basic quantum gates and a new perspective on quantum computation and quantum information. The goal is to obtain a more abstract approach to quantum computation and quantum algorithms in which physical systems are viewed as the implementation for the computing paradigm and not the reason for the it
Quantum computation has shown a lot of promise in being able to provide computational results not possible with the modern computer. However, the design of new algorithms has been slow. One reason for this could be that we simply do not understand this new paradigm of computation enough to fully utilize it. We present here is an improvement of our previous generalization the basic quantum gates and a new perspective on quantum computation and quantum information. The goal is to obtain a more abstract approach to quantum computation and quantum algorithms in which physical systems are viewed as the implementation for the computing paradigm and not the reason for the it
In this research notebook on quantum computation and applications for quantum engineers, researchers, and scientists, we will discuss and summarized the core principles and practical application areas of quantum computation. We first discuss the historical prospect from which quantum computing emerged from the early days of computing before the dominance of modern microprocessors. And the re-emergence of that quest with the sunset of Moore's law in the current decade. The mapping of computation onto the behavior of physical systems is a historical challenge vividly illustrate by considering how quantum bits may be realized with a wide variety of physical systems, spanning from atoms to photons, using semiconductors and superconductors. The computing algorithms also change with the underline variety of physical systems and the possibility of encoding the information in the quantum systems compared to the ordinary classical computers because of these new abilities afforded by quantum systems. We will also consider the emerging engineering, science, technology, business, and social implications of these advancements. We will describe a substantial difference between quantum and classical computation paradigm. After we will discuss and understand engineering challenges currently faced by developers of the real quantum computation system. We will evaluate the essential technology required for quantum computers to be able to function correctly. Later on, discuss the potential business application, which can be touch by these new computation capabilities. We utilize the IBM Quantum Experience to run the real-world problem, although on a small scale.
A possible approach to tackling computationally demanding issues beyond the capabilities of conventional algorithms is the use of quantum circuits, which provide a fundamental foundation for utilizing the power of quantum computation. This abstract examines how quantum circuits are implemented, emphasizing important topics such as circuit optimization, gate operations, and qubit manipulation. We explore different methods of encoding quantum information into topological qubits, trapped ions, and superconducting circuits, among other physical qubit formats. Furthermore, we go over the function of gate operations in quantum circuits, emphasizing crucial gates like phase, Hadamard, and CNOT gates, which serve as the foundation for quantum algorithms. Additionally, we look at methods for maximizing the efficiency and dependability of quantum processing by designing quantum circuits to minimize gate counts, depth, and error rates. To enhance the capabilities of quantum computing, this abstract presents a novel synthesis of quantum neural networks (QNNs) and quantum parameterized circuits. Through the use of parameterized quantum circuits' inherent flexibility, our approach makes it easier to design and optimize quantum circuits with flexible parameters, providing a flexible foundation for a variety of quantum algorithms. Using this amalgamation, we unleash the capacity of quantum computers to address intricate optimization and machine learning assignments with unparalleled effectiveness and expandability. Our solution bridges the gap between traditional machine learning approaches and quantum computing paradigms by enabling the smooth integration of classical data processing techniques with quantum computation. We use quantum states as data representations in our implementation of quantum neural networks, and we optimize trainable parameters to meet predetermined goals. This new paradigm opens up the investigation of the inherent features of quantum states and provides new perspectives on their processing power compared to their classical counterparts. We show, by thorough testing and analysis, how effective quantum parameterized circuits and QNNs are at solving practical problems in a variety of fields. Our work sets the ground for revolutionary breakthroughs in quantum information processing by pushing the boundaries of quantum computation and machine learning integration, offering hitherto unseen insights and solutions to challenging challenges in science, engineering, and beyond.
This thesis lays down groundwork for researching towards heralding the age of useful quantum computers. It begins with background on quantum graphical calculi, which the work of this PhD has contributed to developing and utilizing. This leads into the first question this PhD research sought to answer: In what ways can quantum graphical calculi facilitate the discovery of new abstractions to close the gaps between algorithms and hardware, and theory and practice? We will focus on what I believe are two of the most promising and fundamental research avenues in this vein. One is quantum error correction, centering on the necessary protocols for quantum algorithms to be realizable on error-prone quantum devices. Building on a fully graphical reformulation of error correcting codes, we introduce a new normal form for Clifford isometries and show its correspondence to stabilizer tableaus. The other is qudit computation, the generalization of qubits (2-level quantum systems) to d-level quantum systems, bringing new possibilities for quantum information processing. To this end, we study the interesting properties of two novel qudit gate sets. One of these gate sets we show is the canonical generalization of the qubit Toffoli+Hadamard gate set to arbitrary prime qudit dimension. We further use these results to solve the multiqutrit exact synthesis problem, advancing the original solution for qubits by Giles and Selinger in 2013. In building upon the foundations in these areas, we seek to uncover paradigm shifts in how we process quantum information.
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N -bit classical and N -qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2 N for a quantum computer (e.g., 2 N qubits must be initialized and 2 N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2 N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024