Modeling chemical reactions and complicated molecular systems has been proposed as the “killer application” of a future quantum computer. Accurate calculations of derivatives of molecular... Show moreModeling chemical reactions and complicated molecular systems has been proposed as the “killer application” of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential toward this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. Implementing these methods, we perform geometry optimization on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.0140.014 Å of the full configuration interaction value. Within the same experiment, we estimate the polarizability of the H22 molecule, finding agreement at the equilibrium bond length to within 0.060.06 a.u. (2%2% relative error). Show less
Sagastizabal, R.; Bonet Monroig, X.; Singh, M.; Rol, M.A.; Bultink, C.C.; Fu, X.; ... ; DiCarlo, L. 2019
Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by... Show moreVariational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy. Show less
Bonet-Monroig, X.; Sagastizabal, R.; Singh, M.; O'Brien, T.E. 2018
We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an... Show moreWe investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a third, zero-cost, post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symmetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost the mitigation of errors produced by different noise channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground-state dissociation curve. Show less
