Toward Quantum-Centric Simulations of Extended Molecules: Sample-Based Quantum Diagonalization Enhanced with Density Matrix Embedding Theory

Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly suited to these computational platforms: they combine high-level calculations on active regions of a molecule with low-level calculations on the surrounding environment, thereby avoiding expensive high-level full-molecule calculations and allowing the distribution of computational cost across multiple and heterogeneous computing units. Here, we present the first density matrix embedding theory (DMET) simulations performed in combination with a sample-based quantum diagonalization (SQD) method. We employ the DMET-SQD formalism to compute the ground-state energy of a ring of 18 hydrogen atoms and the relative energies of the chair, half-chair, twist-boat, and boat conformers of cyclohexane. The full-molecule 41- and 89-qubit simulations are decomposed into 27- and 32-qubit active-region simulations, which we carry out on the ibm_cleveland device, obtaining results in agreement with reference classical methods. Our DMET-SQD calculations mark tangible progress in the size of active regions that can be accurately tackled by near-term quantum computers and are an early demonstration of the potential for quantum-centric simulations to accurately treat the electronic structure of large molecules, with the ultimate goal of tackling systems such as peptides and proteins.