This paper is meant to serve as an introductory guide on how to implement simple logic gates in a quantum environment. Uncompressed circuits for each statement can be found in the appendix.
Quantum computing is an emerging field that depends upon the basic properties of quantum physics and principles of classical systems. This leads a way to develop systems to solve complex problems that a classical system cannot do. In this article, we present simple methods to implement logic circuits using quantum gates. Logic gates and circuits are defined with quantum gates using Qiskit in Python. Later, they are verified with quantum circuits created by using IBM Quantum. Moreover, we propose a way of instantiating the basic logic circuits to design high-end logic expressions. As per our knowledge, the proposed simple approach may be helpful to solve the complex logical problems in near future.
Algorithms specifically designed for quantum computers have been developed. In quantum circuits, the Feynman, Toffoli, and Fredkin gates are employed instead of traditional inputs such as AND, OR, NAND, NOR, XOR, and XNOR in combinational logic gates. The ability to convert quantum circuits into combinational logic circuits, or vice versa, is of utmost importance. This essay study (or paper) aims to demonstrates the process of deriving combinational logic circuits from reversible quantum circuits. To achieve this, the Quine-McCluskey technique was utilized along with state tables generated from the quantum circuits to obtain an optimal logic expression that serves as the basis for constructing the combinational logic circuit. The resultant obtained combinational logic circuit was implemented within the MATLAB Simulink environment, and state tables were obtained. A comparison was made between the state tables derived from the quantum circuit and the combinational circuit, yielding successful results.
This chapter serves as a bridge from the introductory material to the sections on quantum algorithms. We start by implementing a classical circuit using quantum gates and show that quantum computers are at least as capable as classical computers. Then we discuss the term “beyond classical,” which is now the preferred term to describe computation that can be run efficiently on a quantum computer but would be intractable to run on a classical computer. For this, we discuss in detail Google’s seminal quantum supremacy paper.