We demonstrate the Einstein-Podolsky-Rosen (EPR) correlations in the Gaussian trial wavefunctional widely used in the Schrödinger representation of the self-interacting complex scalar fields (CSF). This demonstration is based on the explicit eigenstates ||ξ⟩, which possess the precise EPR entanglement and constitute a complete and orthonormal representation, of CSF ϕ and ϕ † in the Fock space. To show the entanglement of the Gaussian trial wavefunctional, we evaluate in the ⟨ξ||-representation its `entangled' Wigner functional resembling the Wigner function of the two-mode squeezed vacuum state, whose quantum entanglement is well known.
This work evaluates how well hybrid classical–quantum simulation methods capture not only the energy of small atomic and molecular systems, but also their other properties: contact densities, molecular structure, and state identity — the spin sector a computed state actually lives in. It employs explicitly correlated Gaussian (ECG) wavefunctions both as references for evaluating these properties and as classical seeds for sample-based quantum diagonalization (SQD), on the simulator and on IBM quantum hardware. Our testbeds — positronium hydride, the muonic heliumlike ions, the HD+ molecular ion, and the positronium anion and molecule — realize three typical failure regimes: boxes that lack the property no matter how configurations are selected, boxes that hold it exactly with no selection needed, and the middle regime where the selection itself decides. In every regime the property error dwarfs the energy error: a subspace can converge the energy to microhartrees while misstating an annihilation rate, a bond length, or the spin by whole percent. Property fidelity, not energy, is the discriminating test of a multicomponent simulation.
Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]R12-Correction
We provide an integration of the universal, perturbative explicitly correlated [2]R12-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. Our proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in VQE. The RDMs are then combined with a set of molecular integrals. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE+[2]R12 approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]R12. In particular the combination of MRA-PNOs with [2]R12 has turned out to be very promising -- persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a cubic complexity.