Quantum-classical hybrid algorithm for the simulation of all-electron correlation

Abstract

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation—the static correlation—on the quantum computer and the non-exponentially scaling part—the dynamic correlation—on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

“…We now turn our attention to the wave function component of MC-PDFT. Although, in principle, PDFT may be combined with any wave function method or even density matrix methods, 27,28 the most explored direction so far for surpassing the capabilities of KS theory comes from combining PDFT with explicitly multicongurational wave functions, mainly MCSCF. The most popular version of MCSCF is complete active space SCF, 29 abbreviated CASSCF.…”

Emerging quantum computing algorithms for quantum chemistry

“…Furthermore, while molecular simulations generally require handling the N‐electron wavefunction, recently proposed approaches have instead focused on the expression of the ground‐state energy as a function of the two‐electron reduced density matrix 361,362 . While recent results have indicated that they represent a promising direction for efficient molecular quantum simulations, additional research is needed to assess their full potential.…”

Leveraging small scale quantum computers with unitarily downfolded Hamiltonians

“…Boyn el al. [9] obtained active-space 2-RDMs from quantum computations and post-processed them with two classical correlation methods, the anti-Hermitian contracted Schrödinger equation (ACSE) theory [10][11][12] and multiconfigurational pair-density functional theory (MC-PDFT) [13]. Fujii el al.…”