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.