The field of quantum computing is growing rapidly and there is a surprisingly large literature.Research in this area includes the design of quantum reversible circuits and developing quantum algorithms for the models of quantum computing.This paper is focused on representing quantum reversible gates in matrix form.In turn these matrices can be used to develop quantum circuits with help of K-Map.Also this paper gives the historical development of quantum algorithms and basics concepts in quantum compuation.
The field of quantum computing is growing rapidly and there is a surprisingly large literature.Research in this area includes the design of quantum reversible circuits and developing quantum algorithms for the models of quantum computing.This paper is focused on representing quantum reversible gates in matrix form.In turn these matrices can be used to develop quantum circuits with help of K-Map.Also this paper gives the historical development of quantum algorithms and basics concepts in quantum compuation.
This paper presents a decision diagram structure intended for the simulation and verification of reversible and quantum circuits. The structure is designed to efficiently represent the matrices describing reversible and quantum gate and circuit behaviour and takes advantage of key properties of those matrices. Algorithms are described for efficiently building the decision diagram representation directly from a gate without constructing the actual matrix and for performing matrix multiplication which is the fundamental operation to determine the function realized by a cascade of gates. Experimental results show the methods presented are applicable to large circuits at the state of the art in reversible and quantum synthesis and design.
Abstract — Reversible logic is one of the most vital issue at present time and it has different areas for its application, those are low power CMOS, quantum computing, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, computer graphics. It is not possible to realize quantum computing without implementation of reversible logic. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. This paper provides the basic reversible logic gates, which in designing of more complex system having reversible circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. This paper presents the data relating to the primitive reversible gates which are available in literature and helps researches in designing higher complex computing circuits using reversible gates.
Quantum computing fundamentals are based on Hilbert spaces and linear algebra, which allows to describe quantum gates as matrix representations. In this paper, a matrix approach is taken in order to analyze basic quantum circuits, composed of basic quantum gates of 1, 2, and 3 qubits. The most common cases of all those gates are analyzed. One-qubit gates are expressed as 2x2 matrices, accounting for a rotation around a determined axis. Two-qubit gates are described as 4x4 matrices, standing for controlled gates. Three-quibit gates are defined as 8x8 matrices, extending the concept of controlled gates and rotations.
Quantum computing has been attracting increasing attention in recent years because of the rapid advancements that have been made in quantum algorithms and quantum system design. Quantum algorithms are implemented with the help of quantum circuits. These circuits are inherently reversible in nature and often contain a sizeable Boolean part that needs to be synthesized. The logic design of such quantum circuits constitutes a non-trivial task and, hence, have heavily been investigated by researchers in the recent past. This paper provides a brief overview of these research. We review the major steps to be conducted in the logic design of quantum circuits and provide a sketch for each single step. These descriptions are enriched with discussions as well as references to the respective related work.
This chapter introduces Boolean quantum gates that allow us to map any Boolean circuit in such a way that the circuit becomes reversible. It describes quantum gates for one qubit, like for example Clifford gates that are the elements of the Clifford group and can be efficiently simulated with a classical computer. The chapter introduces the controlled-U gates and the unitary decomposition and formulate the process of transpilation. A Boolean quantum circuit represents a permutation in Hilbert space and can be represented by a unitary permutation matrix composed of the unitary matrices representing the quantum gates. Such a mapping does not alter the distribution of the amplitudes; the distribution remains unchanged during the execution of the quantum Boolean gates.
Quantum computing, a transformative field that emerged from quantum mechanics and computer science, has gained immense attention for its potential to revolutionize computation. This paper aims to address the fundamentals of quantum computing and provide a comprehensive guide for both novices and experts in the field of quantum computing. Beginning with the foundational principles of quantum computing, we introduce readers to the fundamental concepts of qubits, superposition, entanglement, interference, and noise. We explore quantum hardware, quantum gates, and basic quantum circuits. This study offers insight into the current phase of quantum computing, including the noisy intermediate-scale quantum (NISQ) era and its potential for solving real-world problems. Furthermore, we discuss the development of quantum algorithms and their applications, with a focus on famous algorithms like Shor’s algorithm and Grover’s algorithm. We also touch upon quantum computing’s impact on various industries, such as cryptography, optimization, machine learning, and material science. By the end of this paper, readers will have a solid understanding of quantum computing’s principles, applications, and the steps involved in developing quantum circuits. Our goal is to provide a valuable resource for those eager to embark on their quantum computing journey and for researchers looking to stay updated on this rapidly evolving field.