Toward convergence of effective-field-theory simulations on digital quantum computers

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of ${E}_{4}=\ensuremath{-}2.220\ifmmode\pm\else\textpm\fi{}0.179$ MeV may be compared with the exact deuteron ground-state energy $\ensuremath{-}2.224$ MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.