Quantum Calculator on Circuit Optimization of Quantum Computing Using Qiskit

This paper introduces a comprehensive quantum calculator using Qiskit that integrates quantum arithmetic and logic functions into a single calculator. The calculator relies on quantum Fourier transforms (QFT), controlled-phase gates, and quantum modular arithmetic to perform basic arithmetic operations such as addition, subtraction, and multiplication. These arithmetic techniques used quantum parallelism and interference to perform calculations more efficiently, particularly for tasks involving large numerical inputs. Numerical values are stored in qubit registers and processed using QFT-based circuits, which enable efficient and reversible mathematical computations. In addition to arithmetic operations, the calculator also implements quantum logic algorithms, including Grover’s Search and the Deutsch-Jozsa algorithm. Grover’s algorithm is an unstructured search algorithm that operates by constructing an oracle and iteratively amplifying the probability amplitude of the target solution. This amplitude amplification significantly increases the likelihood of measuring the desired outcome. Due to this property, Grover’s algorithm has practical relevance in applications such as database searching and solving combinatorial optimization problems. The Deutsch-Jozsa algorithm determines whether or not a certain Boolean function is constant or balanced and offers an exponential speed up compared to classical methods for this class of problem. A key fundamental function of the calculator is the ability to generate hybrid quantum circuits that support both arithmetic and logical functions. That allows the exploration of simple as well as complex problem-solving strategies that take advantage of both quantum arithmetic and decision-making algorithms. For instance, combining Grover’s amplification with function characterizations from the Deutsch-Jozsa algorithm provides not only interesting circuit configurations but also adds value to the possibilities of the algorithms. This research offers a modular idea and allows exploring the fundamental principles of quantum computing generally speaking and will be a valuable resource for educational as well as research purposes in the rapidly growing field of quantum algorithm development.