Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes

A general framework for active space embedding methods with applications in quantum computing

We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by presenting a specific implementation of periodic range-separated DFT coupled to a quantum circuit ansatz, whereby the variational quantum eigensolver and the quantum equation-of-motion algorithm are used to obtain the low-lying spectrum of the embedded fragment Hamiltonian. The application of this scheme to study localized electronic states in materials is showcased through the accurate prediction of the optical properties of the neutral oxygen vacancy in magnesium oxide (MgO). Despite some discrepancies in the position of the main absorption band, the method demonstrates competitive performance compared to state-of-the-art ab initio approaches, particularly evidenced by the excellent agreement with the experimental photoluminescence emission peak.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

Excited State Properties of Point Defects in Semiconductors and Insulators Investigated with Time-Dependent Density Functional Theory

We present a formulation of spin-conserving and spin-flip hybrid time-dependent density functional theory (TDDFT), including the calculation of analytical forces, which allows for efficient calculations of excited state properties of solid-state systems with hundreds to thousands of atoms. We discuss an implementation on both GPU- and CPU-based architectures along with several acceleration techniques. We then apply our formulation to the study of several point defects in semiconductors and insulators, specifically the negatively charged nitrogen-vacancy and neutral silicon-vacancy centers in diamond, the neutral divacancy center in 4H silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. Our results highlight the importance of taking into account structural relaxations in excited states in order to interpret and predict optical absorption and emission mechanisms in spin defects.