Error Mitigation, Optimization, and Extrapolation on a Trapped Ion Testbed

Zero Noise Extrapolation (ZNE) is useful as an error mitigation technique because it is broadly applicable to a variety of quantum devices and applications. We test three implementations of ZNE on the Quantum Scientific Computing Open User Testbed (QSCOUT) ion-trap device at Sandia National Laboratories. We study ZNE in the context of the Variational Quantum Eigensolver (VQE), specifically using VQE to solve the electronic structure problem for HeH+. Our experimental results show that a naive implementation of ZNE via increasing the duration of our two-qubit gates does not scale our device noise enough for extrapolation. Similarly, scaling the two-qubit gate detuning only accounted for some of the noise present in our experiment. Instead, a gate-based, unitary folding noise scaling approach wherein two-qubit identity operations are added to the circuit proved amenable to error mitigation. Fitting a linear function to this data, we obtained noiseless energy estimates with 30x less error than an unmitigated estimate, 4 millihartree away from the ground state energy. This result shows that while ZNE can be used on almost any device, it is important to tailor noise scaling methods to the hardware. In addition, ZNE can be used as a practical benchmark for probing the most dominant sources of noise in experiment.