Quantum Computation of the Ground and Excited State Energies Using Quantum Imaginary Time Evolution and Quantum Lanczos Methods*

Various methods have been developed for quantum computation of the ground and excited states of physical systems, but many of them require either large numbers of ancilla or high dimensional optimization. The quantum imaginary time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in [1] eschew the aforementioned issues. In this study, we demonstrate the application of these algorithms on a nontrivial quantum computation, using the deuteron binding energy as an example. With the correct choice of initial and final states we showed that the number of time steps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We performed these calculations on cloud-accessible IBMQ quantum computers, and with the application of readout error mitigation and Richardson error extrapolation, we obtained ground and approximate excited state energies within 3% of the theory. These results show promise for using the algorithms in future field theory, scattering, and chemistry calculations.
[1] M. Motta, et.al., arXiv:1901.07653v2 [quant-ph] (2019)