Approximations in transmon simulation

TL;DR

This paper evaluates various approximation models for simulating transmon quantum systems, demonstrating their validity and limitations through experiments on IBMQ hardware and analyzing the impact on control protocol optimization.

Contribution

It introduces a hierarchy of approximate models for transmon simulation and benchmarks their accuracy and effects on control protocols using experimental and simulation data.

Findings

First-order perturbative approximation causes error amplification.

Simple amplitude scaling cannot correct certain noncomputational errors.

Despite model variance, the complexity of finding optimal control remains consistent.

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 that are too onerous to run in the loop with current-day quantum hardware, as well as for researchers without consistent access to 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. The validity of each model is characterised experimentally by designing and benchmarking control protocols for an IBMQ cloud quantum device. This result demonstrates error amplification induced by the application of a first-order perturbative approximation. Furthermore, the emergence of errors that cannot be corrected by simple amplitude scaling of control pulses is demonstrated in simulation, due to an underlying mistreatment of noncomputational dynamics. 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 in the simple control scheme setting.