  In addition to readout errors, two-qubit gate noise is the main challenge for
complex quantum algorithms on noisy intermediate-scale quantum (NISQ)
computers. These errors are a significant challenge for making accurate
calculations for quantum chemistry, nuclear physics, high energy physics, and
other emerging scientific and industrial applications. There are two proposals
for mitigating two-qubit gate errors: error-correcting codes and zero-noise
extrapolation. This paper focuses on the latter, studying it in detail and
proposing modifications to existing approaches. In particular, we propose a
random identity insertion method (RIIM) that can achieve competitive asymptotic
accuracy with far fewer gates than the traditional fixed identity insertion
method (FIIM). For example, correcting the leading order depolarizing gate
noise requires $n_\text{CNOT}+2$ gates for RIIM instead of $3n_\text{CNOT}$
gates for FIIM. This significant resource saving may enable more accurate
results for state-of-the-art calculations on near term quantum hardware.
