Exploring the Scaling Limitations of the Variational Quantum Eigensolver with the Bond Dissociation of Hydride Diatomic Molecules: arXiv:2208.07411 [quant-ph]

The variational quantum eigensolver (VQE) allows prediction of chemically accurate total energies via variational minimization on a quantum device. The severe scaling of high-fidelity quantum chemical methods can be overcome due to qubit entanglement and an exponentially large computational space, potentially allowing for modeling of the electronic structure for larger systems to an accuracy of 1kcal/mol or better. Nevertheless, current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth. The largest chemical systems modeled to date using VQE include s and p block elements. Here we study the scaling of VQE on a quantum emulator to study the near-term feasibility of modeling a molecule containing d orbitals, specifically the TiH diatomic molecule, in order to better understand the hardware necessary to carry out this calculation on a real device. We model LiH, NaH, KH, and TiH diatomic molecules to demonstrate that the inclusion of d-orbitals and the UCCSD ansatz dramatically increase the cost of this problem. We show that a parallel implementation of VQE along with optimal choice of quantum circuit measurement basis set enable the study of larger systems on a classical emulator, but only provide approximately polynomial savings in the face of exponential growth in classical computational resources. The approximate error rates necessary to perform this calculation on trapped ion hardware are estimated and shown to likely prohibit the practical study of TiH on current devices using the UCCSD ansatz until significant improvements in both hardware and algorithms are available. The successful treatment of moderate-sized, d-electron molecules, such as TiH, using the VQE algorithm therefore stands as an important waypoint in the advancement of useful chemical applications of near-term quantum processors.