The Discrete Noise Approximation in Quantum Circuits

When modeling the effects of noise on quantum circuits, one often makes the assumption that these effects can be accounted for by individual decoherence events following an otherwise noise-free gate. In this work, we address the validity of this model. We find that under a fairly broad set of assumptions, this model of individual decoherence events provides a good approximation to the true noise processes occurring on a quantum device during the implementation of a quantum circuit. However, for gates which correspond to sufficiently large rotations of the qubit register, we find that the qualitative nature of these noise terms can vary significantly from the nature of the noise at the underlying hardware level. The bulk of our analysis is directed towards analyzing what we refer to as the separability ansatz, which is an ansatz concerning the manner in which individual quantum operations acting on a quantum system can be approximated. In addition to the primary motivation of this work, we identify several other areas of open research which may benefit from the results we derive here.