Quantum computing for atomic and molecular resonances

Abstract

The complex-scaling method can be used to calculate molecular resonances within the Born–Oppenheimer approximation, assuming that the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second quantization and then used the Jordan–Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the direct measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H2− molecule. The numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.

Approaching the theoretical limit in quantum gate decomposition

“…Even if currently available quantum computers are not advanced enough yet to outperform classical devices in solving these problems, a lot of progress has been made in demonstrating these algorithms on small quantum devices [3,4,5,6,7]. Beside these well known examples, various other promising schemes were developed to exploit quantum resources in solving computational problems, for example, variational quantum optimization [8], variational quantum eigensolvers [9], and quantum simulations of molecular and many-body phenomena [10,11,12,13,14] were successfully implemented on hardware, and at least qualitatively justified results were obtained.…”

A Universal Quantum Circuit Design for Periodical Functions

“…The blooming of hardware development by IBM, Google, IonQ and many others provokes tremendous enthusiasm developing quantum algorithms utilizing near term quantum devices and pursuit of application in various fields of science and engineering. Recently there arises a growing body of research focusing on quantum optimization [4,5], solving linear system of equations [6,7,8], electronic structure calculations [9,10,11,12,13,14,15], quantum encryption [16,17], variational quantum eigensolver (VQE) [18,19] for various problems [20,21,22] and open quantum dynamics [23,24] . Recently, quantum machine learning further explored and implemented quantum software that could show advantages compared with the corresponding classical ones [25,26,27,28,29,30,31,32].…”

Simulation of Chemical Reactions on a Quantum Computer

“…To mitigate this challenge, numerous quantum algorithms have been proposed in the literature for different applications, − with many relying on the Quantum Phase Estimation (QPE) algorithm. However, as QPE is a fault-tolerant algorithm, its implementation is currently unfeasible on utility-scale quantum processors.…”