Abstract Quantum computing has gained attention in recent years due to the significant progress in quantum computing technology. Today many companies like IBM, Google and Microsoft have developed quantum computers and simulators for research and commercial use. The development of quantum techniques and algorithms is essential to exploit the full power of quantum computers. In this paper we propose a simple visual technique (we call Q-Map) for quantum realization of classical Boolean logic circuits. The proposed method utilizes concepts from Boolean algebra to produce a quantum circuit with minimal number of quantum gates.
Abstract Quantum computing has gained attention in recent years due to the significant progress in quantum computing technology. Today many companies like IBM, Google and Microsoft have developed quantum computers and simulators for research and commercial use. The development of quantum techniques and algorithms is essential to exploit the full power of quantum computers. In this paper we propose a simple visual technique (we call Q-Map) for quantum realization of classical Boolean logic circuits. The proposed method utilizes concepts from Boolean algebra to produce a quantum circuit with minimal number of quantum gates.
Today, quantum computers are still in development and are an area actively studied by researchers.Although quantum computers have high potential, there are significant technical difficulties and obstacles to achieving practical applications.Many research labs and companies are working on increasing the number of qubits, solving stability problems, and improving error correction techniques, and scalability.These efforts aim at advances such as the development of more stable and reliable qubits, the discovery of more precise control and reading techniques, and the design of more advanced algorithms.This study aims to establish a connection between quantum computers and classical computers.To achieve this, research and work have employed a Karnaugh-based approach.Karnaugh maps serve as highly useful tools in the analysis of complex logic circuits.Depending on one's needs and design requirements, different logic functions can be analyzed and simplified using Karnaugh maps.In this study, the Karnaugh map-based method is utilized to obtain the Boolean function from the state table of the Quantum circuit generated from the RCViewer+ synthesis tool.Subsequently, the obtained function is transformed into a combinational logic circuit.As a result, an optimal combinational circuit corresponding to the quantum circuit can be obtained.
Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research. Any viable computing system requires both hardware and software to work together harmoniously in order to perform useful computations. While the achievements of IBM and other companies represent a large step forward for quantum hardware, many gaps remain to be filled with respect to the corresponding software. Specifically, there is currently no clear path towards a complete process for translating quantum algorithms into physical operations that are directly executable on quantum hardware. Such a process is analogous to a compiler that translates programs written in a high-level language into executable machine instructions on a conventional digital computer, and it is necessary if quantum computers are to be harnessed to perform practically useful computations. Existing work has addressed individual components of this process, but so far no unified method for translating the whole of a quantum algorithm into executable operations has been described. I make substantial progress towards filling this gap by describing a set of high-level and low-level quantum circuit design techniques, which when taken together reduce the need of a circuit designer to be concerned with low-level details. On the high-level side, I describe an approach or strategy to designing quantum oracles for Grover's algorithm that allows it to be applied to several types of problems. This approach involves designing oracles in terms of high-level blocks such as counters, multiplexers, comparators, and arbitrary Boolean functions. The implementations of these blocks in terms of lower-level quantum gates are demonstrated in a way that makes it clear that scaled-up versions of them can be generated in a completely automated fashion. For a specific class of problems, which I call state-space path planning problems, I also introduce a paradigm for quantum oracle design that involves representing the problem in terms of individual states and moves. Problems of this sort have applications in robotics and games. Low-level techniques that I introduce
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.
Research on quantum computers has gained attention since they are able to solve certain tasks significantly faster than classical machines (in some cases, exponential speed-ups are possible). Since quantum computations typically contain large Boolean components, design automation techniques are required to realize the respective Boolean functions in quantum logic. They usually introduce a significant amount of additional qubits - a highly limited resource. In this work, we propose an alternative method for the realization of Boolean components for quantum logic. In contrast to the current state-of-the-art, we dedicatedly address the main reasons causing the additionally required qubits (namely the number of the most frequently occurring output pattern as well as the number of primary outputs of the function to be realized) and propose to manipulate the function so that both issues are addressed. The resulting methods allow to push the number of required qubits below what is currently considered the minimum.
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal form of Boolean function, and quantum logic circuits is described. It is shown that quantum information approach provides simple algorithm to construct Zhegalkin polynomial using truth table. Developed methods and algorithms have arbitrary Boolean function generalization with multibit input and multibit output. Such generalization allows us to use many-valued logic (k-valued logic, where k is a prime number). Developed methods and algorithms can significantly improve quantum technology realization. The presented approach is the baseline for transition from classical machine logic to quantum hardware.
The discovery of Shor's prime factorization and Grover's fast database search algorithm have made quantum computing the most rapidly expanding research field recently. Nanotechnology, in particular silicon-based nanoscale devices, have been proposed as one of the candidates that can be used to implement a quantum computer. In this paper, we have derived a systematic procedure to realize any general m-to-n bit combinational Boolean logic using elementary quantum gates. The quantum circuit layout under the locality constraint is then formulated, together with the gate count evaluation function, to reduce the total number of quantum gates required to implement the circuit.