Exact classical noise master equations: Applications and connections

Abstract

All quantum systems are subject to noise and imperfections due to stray fields, inhomogeneities or drifting experimental controls. An understanding of the effects of noise and decoherence is critical to the progress towards fully functional quantum devices. In this perspective, we focus on noise in quantum systems which are modelled by a dynamic stochastic parameter in the Hamiltonian. We will outline exact evolution equations describing the ensemble average dynamics for a variety of common noise types and their connections. We will also highlight an approximate evolution equation valid in the weak noise limit for an arbitrary classical stochastic field. This framework should serve as a starting point for identifying signatures of differing noise types and optimisation of robust control protocols.

Inverse engineering for robust state transport along a spin chain via low-energy subspaces

“…In addition, here we consider the special cases of white noise existing in the amplitudes of the disordered couplings. More complex types of noise [59], such as the Gaussian colored noise and non-Gaussian cases, can also be analyzed in principle. For instance, the influence of Ornstein-Uhlenbeck noise and flicker noise using STA for lattice transport have been studied [61,62].…”

“…Specifically, we assume there exists independent noise in two manipulated couplings J 1,2 (t), which can be expressed as the form λξ i (t)H i (t) with i = 1, 2. Here λ and H i (t) are the noise strength and the 'noisy' Hamiltonian, respectively; ξ i (t) denoting a given noise realization satisfies [59]…”

“…The corresponding correlation function is C(t − t ′ ) = δ(t − t ′ ), and the power spectrum is constant. Thus, the master equation (h = 1) can be derived [53,56,59,61,62]:…”

Employing typicality in optimal control theory: Addressing large Hilbert spaces

“…A GKLS master equation describes the quantum dynamics of both amplitude and phase noise. Extension of this study to non-Markovian noise model [24], and Poissonian noise is feasible.…”

Stochastic Operator Variance: An Observable to Diagnose Noise and Scrambling

“…In any experimental setting, tunable parameters such as Hamiltonian coupling constants may exhibit fluctuations due to interactions with the environment [3][4][5]. In this context, the dynamics of an ensemble of noisy realizations can be described in terms of the noise-averaged density matrix, which evolves according to a master equation describing nonunitary evolution [3,4,6,7]. Alternatively, noise can be utilized as a resource for the quantum simulation of open systems [4].…”