  Quantum computers (QCs) must implement quantum error correcting codes (QECCs)
to protect their logical qubits from errors, and modeling the effectiveness of
QECCs on QCs is an important problem for evaluating the QC architecture. The
previously developed Monte Carlo (MC) error models may take days or weeks of
execution to produce an accurate result due to their random sampling approach.
We present an alternative analytical error model that generates, over the
course of executing the quantum program, a probability tree of the QC's error
states. By calculating the fidelity of the quantum program directly, this error
model has the potential for enormous speedups over the MC model when applied to
small yet useful problem sizes. We observe a speedup on the order of 1,000X
when accuracy is required, and we evaluate the scaling properties of this new
analytical error model.
