Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation.

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods.

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries.

Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator such that the cost of implementing is reduced compared to that of , yet acts on the subspaces of interest the same way as does.

Computational approaches to efficient generation of the stationary state for incoherent light excitation.

Light harvesting processes are often computationally studied from a time-dependent viewpoint, in line with ultrafast coherent spectroscopy experiments. Yet, natural processes take place in the presence of incoherent light, which induces a stationary state. Such stationary states can be described using the eigenbasis of the molecular Hamiltonian, but for realistic systems, a full diagonalization is prohibitively expensive.

On the breakdown of the Ehrenfest method for molecular dynamics on surfaces.

Due to a continuum of electronic states present in periodic systems, the description of molecular dynamics on surfaces poses a serious computational challenge. One of the most used families of approaches in these settings are friction theories, which up to a random fluctuating force term are based on the Ehrenfest approach. Yet, a mean-field treatment of electronic degrees of freedom in the Ehrenfest method makes this approach inaccurate in some cases.