  Noisy intermediate-scale quantum (NISQ) devices offer unique platforms to
test and evaluate the behavior of non-fault-tolerant quantum computing.
However, validating programs on NISQ devices is difficult due to fluctuations
in the underlying noise sources and other non-reproducible behaviors that
generate computational errors. Efficient and effective methods for modeling
NISQ behaviors are necessary to debug these devices and develop programming
techniques that mitigate against errors. We present a test-driven approach to
characterizing NISQ programs that manages the complexity of noisy circuit
modeling by decomposing an application-specific circuit into a series of
bootstrapped experiments. By characterizing individual subcircuits, we generate
a composite model for the original noisy quantum circuit as well as other
related programs. We demonstrate this approach using a family of
superconducting transmon devices running applications of GHZ-state preparation
and the Bernstein-Vazirani algorithm. We measure the model accuracy using the
total variation distance between predicted and experimental results, and we
find that the composite model works well across multiple circuit instances. In
addition, these characterizations are computationally efficient and offer a
trade-off in model complexity that can be tailored to the desired predictive
accuracy.
