Benchmarking quantum computers for real-time evolution of a $(1+1)$
  field theory with error mitigation
Quantum computers open the possibility of performing real-time calculations
for quantum field theory scattering processes. We propose to use an index
averaging the absolute value of the difference between the accurately
calculated Trotter evolution of site occupations and their actual measurements
on NISQ machines. The average is over all the qubits for a certain number of
Trotter steps. We use this metric to quantify the progress made in successive
state-of-the-art machines and error-mitigation techniques. We illustrate the
concept with the transverse Ising model in one spatial dimension with four
sites using three of IBM's quantum computers (Almaden, Boeblingen, and
Melbourne). We discuss the size of the Trotter steps needed to achieve physics
goals. Using the proposed metric, we show that readout mitigation methods and
Richardson extrapolations of mitigated measurements are very effective for
specific numbers of Trotter steps of a chosen size. This specific choice can be
applied to other machines and noise mitigation methods. On the other hand, a
reliable algorithmic mitigation would require a significantly larger number of
smaller Trotter steps.
Erik Gustafson Patrick Dreher Zheyue Hang Yannick Meurice