The influence of basis sets and ansatze building to quantum computing in chemistry

Abstract

Context

Quantum computing is an exciting area, which has grown at an astonishing rate in the last decade. It is especially promising for the computational and theoretical chemistry area. One algorithm has received a lot of attention lately, the variational quantum eigensolver (VQE). It is used to solve electronic structure problems and it is suitable to the noisy intermediate-scale quantum (NISQ) hardware. VQE calculations require ansatze and one of the most known is the unitary coupled cluster (UCC). It uses the chosen basis set to generate a quantum computing circuit which will be iteratively minimized. The present work investigates the circuit depth and the number of gates as a function of basis sets and molecular size. It has been shown that for the current quantum devices, only the smallest molecules and basis sets are tractable. The H\(_{\textbf{2}}\) molecule with the cc-pVTZ and aug-cc-pVTZ basis sets have circuit depths in the order of 10\(^6\) to 10\(^{\textbf{7}}\) gates and the C\(_{\textbf{2}}\)H\(_{\textbf{6}}\) molecule with 3–21G basis set has a circuit depth of \(\mathbf {2.2}\times \textbf{10}^{\textbf{8}}\) gates. At the same time the analysis demonstrates that the H\(_{\textbf{2}}\) molecule with STO-3G basis set, requires at least 500 shots to reduce the error and that, although error mitigation schemes can diminish the error, they were not able to completely negate it.

Methods

The quantum computing and electronic structure calculations were performed using the Qiskit package from IBM and the PySCF package, respectively. The ansatze were generated using the UCCSD method as implemented in Qiskit, using the basis sets STO-3G, 3–21G, 6–311G(d,p), def2-TZVP, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ. The operators and the Hamiltonian were mapped using the Jordan-Wigner scheme. The classical optimizer chosen was the simultaneous perturbation stochastic approximation (SPSA). The quantum computers used were the Nairobi and Osaka, with 7 and 127 qubits respectively.