Approximations in transmon simulation

Abstract

Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms which are too onerous to run in the loop with current-day quantum hardware, as well as for researchers without consistent access to said hardware. However, if the model used to represent the system is not selected carefully, an optimised control protocol may be rendered futile when applied to hardware. We present a series of models, ordered in a hierarchy of progressive approximation, which appear in quantum control literature. Significant model deviations are highlighted, with a focus on simulated dynamics under simple single-qubit protocols. The validity of each model is characterised experimentally by designing and benchmarking control protocols for an IBMQ cloud quantum device. This result demonstrates an error amplification exceeding 100%, induced by the application of a first-order perturbative approximation. Finally, an evaluation of simulated control dynamics reveals that despite the substantial variance in numerical predictions across the proposed models, the complexity of discovering local optimal control protocols appears invariant for a simple control scheme. The set of findings presented heavily encourage practitioners of this field to ensure that their system models do not contain assumptions that markedly decrease applicability to hardware in experimentally relevant control parameter regimes.