  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.
