Characterization of control noise effects in optimal quantum unitary dynamics

Abstract

This work develops measures for quantifying the effects of field noise upon targeted unitary transformations. Robustness to noise is assessed in the framework of the quantum control landscape, which is the mapping from the control to the unitary transformation performance measure (quantum gate fidelity). Within that framework, a new geometric interpretation of stochastic noise effects naturally arises, where more robust optimal controls are associated with regions of small overlap between landscape curvature and the noise correlation function. Numerical simulations of this overlap in the context of quantum information processing reveal distinct noise spectral regimes that better support robust control solutions. This perspective shows the dual importance of both noise statistics and the control form for robustness, thereby opening up new avenues of investigation on how to mitigate noise effects in quantum systems.

PEET: a Matlab tool for estimating physical gate errors in quantum information processing systems

“…In PEET this is conducted by comparing their process matrices χ E and χ W , respectively. Other performance measures do exist, such as gate fidelity [1], or Hilbert-Schmidt norms between target unitary operators [31] in the case of unitary dynamics. Acting as an extension to the norm measures in the unitary case studied in Ref.…”

“…Acting as an extension to the norm measures in the unitary case studied in Ref. [31], the process matrix cost functional calculates the error in E(ρ) through the square of the Hilbert-Schmidt distance norm between χ W and χ E ,…”

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“…In [19] the authors use a noise model called "low frequency noise"( see section IV. C. of [12]): it is defined as the portion of the (control) amplitude noise that has a correlation time that is long (up to 10 3 times) compared to the timescale of the dynamics therefore it can be considered as constant in time. Additional noise models (additive or multiplicative) are presented in [24].…”

Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

“…In a related recent work the corresponding noise model is called "low frequency noise" (see section IV. C. of [36]): it is defined as the portion of the (control) amplitude noise that has a correlation time that is long (up to 10 3 times) compared to the timescale of the dynamics and as such it can be treated as constant in time. Additional noise models (additive or multiplicative) are presented in [37] in the general quantum control area.…”