Practical Quantum Computation of Chemical and Nuclear Energy Levels Using Quantum Imaginary Time Evolution and Lanczos Algorithms

TL;DR

This paper demonstrates practical quantum algorithms, QITE and QLanczos, for calculating chemical and nuclear energy levels on NISQ devices, achieving accurate results with fewer resources.

Contribution

It applies QITE and QLanczos algorithms to real quantum hardware, optimizing their efficiency and accuracy for nontrivial chemical and nuclear systems.

Findings

Accurate ground and excited state energies obtained on IBM-Q.

Significant reduction in quantum circuit complexity.

Effective error mitigation techniques improved results.

Abstract

Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in [1] eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to nontrivial quantum computation, using the deuteron binding energy and molecular Hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of time steps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM-Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.