Gabriel Greene-Diniz

Due to the wide range of technical applications of actinide elements, a thorough understanding of their electronic structure could complement technological improvements in many different areas. Quantum computing could greatly aid in this understanding, as it can potentially provide exponential speedups over classical approaches, thereby offering insights into the complex electronic structure of actinide compounds. As a first foray into quantum computational chemistry of actinides, this paper compares the method of quantum computed moments (QCM) as a noisy intermediate-scale quantum algorithm with a single-ancilla version of quantum phase estimation (QPE), a quantum algorithm expected to run on fault-tolerant quantum computers. We employ these algorithms to study the reaction energetics of plutonium oxides and hydrides. In order to enable quantum hardware experiments, we use several techniques to reduce resource requirements: screening individual Hamiltonian Pauli terms to reduce the measurement requirements of QCM and variational compilation to reduce the depth of QPE circuits. Finally, we derive electronic structure descriptions from a series of representative chemical models and compute the energetics from quantum experiments on Quantinuum's H-series ion trap devices using up to 19 qubits. We find our experiments to be in excellent agreement with results from classical electronic structure calculations and state vector simulations.

Quantifying correlation and entanglement between molecular orbitals can elucidate the role of quantum effects in strongly correlated reaction processes. However, accurately storing the wavefunction for a classical computation of those quantities can be prohibitive. Here we use the Quantinuum H1-1 trapped-ion quantum computer to calculate von Neumann entropies which quantify the orbital correlation and entanglement in a strongly correlated molecular system relevant to lithium-ion batteries (vinylene carbonate interacting with an O$_2$ molecule). As shown in previous works, fermionic superselection rules decrease correlations and reduce measurement overheads for constructing orbital reduced density matrices. Taking into account superselection rules we further reduce the number of measurements by finding commuting sets of Pauli operators. Using low overhead noise reduction techniques we calculate von Neumann entropies in excellent agreement with noiseless benchmarks, indicating that correlations and entanglement between molecular orbitals can be accurately estimated from a quantum computation. Our results show that the one-orbital entanglement vanishes unless opposite-spin open shell configurations are present in the wavefunction.

In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green's function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.

We have demonstrated a prototypical hybrid classical and quantum computational workflow for the quantification of protein-ligand interactions. The workflow combines the Density Matrix Embedding Theory (DMET) embedding procedure with the Variational Quantum Eigensolver (VQE) approach for finding molecular electronic ground states. A series of $β$-secretase (BACE1) inhibitors is rank-ordered using binding energy differences calculated on the latest superconducting transmon (IBM) and trapped-ion (Honeywell) Noisy Intermediate Scale Quantum (NISQ) devices. This is the first application of real quantum computers to the calculation of protein-ligand binding energies. The results shed light on hardware and software requirements which would enable the application of NISQ algorithms in drug design.