Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition

Abstract

Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate errors required for their experimental realization. Here we propose a class of quantum-classical hybrid algorithms that compute the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, conditions for representing an $N$-electron wavefunction, that mitigates noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H${}_3$ into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of "chemical accuracy," even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.

References in corpus (12)

• Charge insensitive qubit design derived from the Cooper pair box
• Simulated Quantum Computation of Molecular Energies
• The Pauli principle revisited
• The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach
• Pinning of Fermionic Occupation Numbers
• Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
• Generalized Pauli constraints in reduced density matrix functional theory
• Quasipinning and its relevance for $N$-Fermion quantum states
• Quasipinning and selection rules for excitations in atoms and molecules
• The Python-based Simulations of Chemistry Framework (PySCF)
• Experimental Data from a Quantum Computer Verifies the Generalized Pauli Exclusion Principle
• Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom

Cited by in corpus (3)

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• Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer