Parametric two-electron reduced-density-matrix method with application to diradical rectangular H4

Fast-forwarding molecular ground state preparation with optimal control on analog quantum simulators

We show that optimal control of the electron dynamics is able to prepare molecular ground states, within chemical accuracy, with evolution times approaching the bounds imposed by quantum mechanics. We propose a specific parameterization of the molecular evolution only in terms of interaction already present in the molecular Hamiltonian. Thus, the proposed method solely utilizes quantum simulation routines, retaining their favorable scalings. Due to the intimate relationships between variational quantum algorithms and optimal control, we compare, when possible, our results with state-of-the-art methods in the literature. We found that the number of parameters needed to reach chemical accuracy and algorithmic scaling is in line with compact adaptive strategies to build variational Ansätze. The algorithm, which is also suitable for quantum simulators, is implemented by emulating a digital quantum processor (up to 16 qubits) and tested on different molecules and geometries spanning different degrees of electron correlation.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

H4: A challenging system for natural orbital functional approximations

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D(2h) to D(4h) symmetry in H4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H4 D(4h)/D(2h) potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D(2h)-D(4h) transition of H4 has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.