  Materials simulations involving strongly correlated electrons pose
fundamental challenges to state-of-the-art electronic structure methods but are
hypothesized to be the ideal use case for quantum computing. To date, no
quantum computer has simulated a molecule of a size and complexity relevant to
real-world applications, despite the fact that the variational quantum
eigensolver (VQE) algorithm can predict chemically accurate total energies.
Nevertheless, because of the many applications of moderately-sized, strongly
correlated systems, such as molecular catalysts, the successful use of the VQE
stands as an important waypoint in the advancement toward useful chemical
modeling on near-term quantum processors. In this paper, we take a significant
step in this direction. We lay out the steps, write, and run parallel code for
an (emulated) quantum computer to compute the bond dissociation curves of the
TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a
relatively simple chemical system that incorporates d orbitals and strong
electron correlation. Because current VQE implementations on existing quantum
hardware are limited by qubit error rates, the number of qubits available, and
the allowable gate depth, recent studies have focused on chemical systems
involving s and p block elements. Through VQE + UCCSD calculations of TiH, we
evaluate the near-term feasibility of modeling a molecule with d-orbitals on
real quantum hardware. We demonstrate that the inclusion of d-orbitals and the
use of the UCCSD ansatz, which are both necessary to capture the correct TiH
physics, dramatically increase the cost of this problem. We estimate the
approximate error rates necessary to model TiH on current quantum computing
hardware using VQE+UCCSD and show them to likely be prohibitive until
significant improvements in hardware and error correction algorithms are
available.

Quantum Physics;Emerging Technologies