Implementation and Performance Analysis of the Deutsch–Jozsa Quantum Algorithm Using Qiskit

Abstract

The quantum computing is a giant leap forward in comparison with our common computer models as it allows us to solve some problems with a much smaller number of steps. In this paper, we will demonstrate the design, development, and testing of the DeutschJozsa quantum algorithm using Qiskit. The algorithm can determine whether a Boolean function is identical or evenly divides with a single special query where traditional algorithms may require as many as 2n -1 +1 checks in the worst-case. We simulated the algorithm on an ideal simulator (Qiskit Aer) and IBM Quantum real hardware. Three aspects that we examined were the measurement accuracy, the depth of the quantum circuit, and how the noise of the real world, including decoherence and gate errors as well as readout errors, would influence the outcome of the NISQ devices. The simulator has nearly excellent precision, whereas the actual hardware has some visible disparities due to noise. These findings verify a undeniable quantum efficiency in query complexity and the cost decreases to a constant cost of O(1) quantum versus an exponential cost of O(2n) using a classical computer. Altogether, this paper is an example of quantum parallelism and quantum interference in a practical sense and serves as a good reference point to the capabilities of the current quantum hardware.