Simple Quantum Algorithms

Mikio Nakahara

Before we start presenting “useful” but rather complicated quantum algorithms, we introduce a few simple quantum algorithms which will be of help for readers to understand how quantum algorithms are different from and superior to classical algorithms. We follow closely Meglicki [1].

Madhusudan Singh Irish Singh, Bharat S. Rawal

Juan Gómez Mazorra

In this work, the underlying theory of variational quantum algorithms applied to the study of simple quantum systems has been reviewed. Using the Qiskit library, the VQE (Variational Quantum Eigensolver) algorithm has been implemented to obtain the ground state energy of three simple quantum systems: the hydrogen molecule, an electron in a Yukawa potential, and two electrons in an infinite potential well with contact interaction. The algorithm parameters that yielded the best results were the UCCSD ansatz, the COBYLA optimizer, and a high number of shots. Although the results of simulations using quantum algorithms did not achieve the same precision as classical algorithms, especially under noise models, the implementation of the VQE algorithm has been successful in exploring the current capabilities and limitations of quantum computing. These results demonstrate the ability of quantum algorithms to solve simple quantum systems, despite current challenges. Furthermore, they underscore their potential to surpass classical algorithms in solving complex quantum systems.

Daowen Qiu

Hongyuan Gao, Chenwan Li, Wen Quan Cui

To design a novel intelligence algorithm for discrete optimisation problem, a simple quantum-inspired bee colony algorithm (SQBCA) is proposed. The proposed SQBCA applies the quantum computing theory to bee colony optimisation (BCO), which is an effective discrete optimisation algorithm. Then the proposed simple quantum-inspired bee colony algorithm is used to solve benchmark functions and multiuser detection problems of code division multiple access (CDMA) system. By hybridising the bee colony optimisation and quantum computing theory, the quantum state and binary state of the quantum bees can be well evolved by simulated quantum rotation gate and simulated quantum not gate. The new robust multiuser detection based on SQBCA can search the global optimal solution. Simulation results for CDMA systems are provided to show that the proposed robust multiuser detection method is superior to the multiuser detection based on previous intelligence algorithms.