Execution of a quantum algorithm for calculating energies of some quantum mechanical systems

Abstract

Recently, quantum computing has come into the spotlight. This interest is fueled by the improvements in hardware, software, and algorithms needed for its practical application and the promise that it holds for the future acceleration of computational workloads compared to classical computing. Due to its true quantum nature, the quantum phase estimation (QPE) algorithm is one of many methods that has garnered much attention lately. Simulating it requires much memory and is unsolvable on systems with average system sizes. Another algorithm known as Kitaev’s algorithm or iterative quantum phase estimation algorithm (IQPE) functions with a single control qubit, which is its primary benefit over QPE. Recently another approximate IQPE (AIPE) approach was proposed in Shokri et al. (2021) for faster calculations than traditional IQPE. In order to evaluate the energy eigenvalues of several quantum mechanical systems, such as the finite square well potential (SWP) and harmonic oscillator(HO), by solving the Schrödinger equations, we developed both the traditional IQPE and AIPE techniques in this study using our own Python programs on IBM Qiskit. Our simulations of the systems with a fair inaccuracies relative to the actual values are supported by our findings from running the quantum circuits. Interestingly we found for SWP, AIPE performs better, whereas for the HO, traditional IQPE performs better than the AIPE approach. Our developed code is available at our GitHub page.