The N-representability problem asks when does a reduced density matrix (RDM), like what might be obtained through tomography on a noisy quantum computer, represent a pure quantum state? It is sometimes overlooked that in algorithms for quantum computers where the expectation of a Hamiltonian is evaluated, such as with variational quantum eigensolvers, one often constructs the underlying RDMs. Aspects of the N-representability problem can be used in such a context to ascertain the quality of the state and potentially mitigate errors. One example of this is with the generalized Pauli constraints, which provide a necessary condition for the N-representability problem in 1-electron reduced density matrices (1-RDM). We will discuss our work experimentally verififying the generalized Pauli constraints for a 3-electron and 6-orbital system on a quantum computer by randomly preparing and measuring fermionic quantum states. Furthermore, we will use these constraints to develop a class of hybrid quantum-classical algorithms suitable for simulating small molecules. The constraints give rise to a natural form of error mitigation, and using this we perform the dissociation of molecular H3 into three hydrogen atoms on a quantum computer. The obtained energies are within 1 mHartree of the full configuration interaction method throughout the dissociation, and we also capture the Mott-Insulator transition in the 1-RDM. Finally we will show how the RDMs of a two-electron system can be used to generate an efficient linear ansatz on a quantum computer with constant scaling tomography that is ideal as a benchmark for molecular simulations. We will discuss our efforts to evaluate the performance of two quantum computers, highlighting the effect of errors on the RDMs and accentuating the need for robust error mitigation to allow for reliable near-term applications.

Reduced density matrix approaches for molecular simulation on near-term quantum computers

Macromolecular Chemistry: The Second Century

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ACS Spring 2020 National Meeting & Expo

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.