Adaptive Basis Sets for Practical Quantum Computing

TL;DR

This paper introduces adaptive basis sets for quantum chemistry that depend on molecular structure, significantly improving accuracy on quantum devices without increasing qubit count, demonstrated on H₂ molecules.

Contribution

The development of adaptive basis sets that vary with molecular geometry to enhance quantum chemical calculation accuracy on NISQ devices.

Findings

Adaptive basis sets improve accuracy to double-zeta level

Achieved chemical accuracy for H₂ on IBM-Q devices

Method extends to larger molecules and basis sets

Abstract

Electronic structure calculations on small systems such as H$_2$, H$_2$O, LiH, and BeH$_2$ with chemical accuracy are still a challenge for the current generation of the noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allow one to keep the number of qubits employed in the calculations at minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provide an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H$_2$ molecule, in which exponents and contraction coefficients depend on the H-H distance, and apply it to the generation of H$_2$ potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.