We carefully choose our cost functionCto have the following properties: (i)Cis faithful (i.e, it vanishes if and only ifρ~is diagonal), (ii)Cis efficiently computable on a quantum computer, (iii)Chas operational meanings such that it upper bounds the eigenvalue and eigenvector error (see ...
par(mar = c(5, 4, 1, 1)) matplot(c(Ns, Ns_xtra) * 3L, meds, lty = 1:3, type = "l", log = "xy", ylab = "seconds", xlab = "N", col = "black")Function Definitions# Stochastic gradient descent for mssm object. The function assumes that the # state vector is ...
As most of this work is concerned with qubits, we will make frequent use of the Bloch representation, stating that every qubit state \(\rho\) can be represented by a subnormalized vector \({\boldsymbol{r}}=({r}_{x},{r}_{y},{r}_{z})\) through \(\rho =({\mathbb{1}}+{\...
In much of modern control theory designs are based on the assumption that the state vector of the system to be controlled is available for measurement. In many practical situations only a few output quantities are available. Application of theories which assume that the state vector is known is...
A stoichiometric model specifies the relative quantities of reactants and products for each reaction within a network. There are two fundamental and commonly used computational techniques that utilize stoichiometric models to elucidate steady-state function. The first technique is Elementary Flux Mode (...
Three states of the model form the probability vector and while one of the states is measurable in real time the second is available only in integrated quantities. The observer designed here uses both information channels to increase precision of the reconstruction. The results are demonstrated on ...
Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 3 (Industry Papers), Association for Computational Linguistics, New Orleans, LA, USA (2018), pp. 52-59, 10.18653/v1/N18-3007 Google Scholar Vedantam...
Diverse Types of Measured Quantities Correlations Between Measurements Furthermore, the close relation between the evolution of this field as the technology advancement in a few other domains, such aspower-electronics-dominated power systems, integrated energy systems,cyber-physical systems, and Internet ...
We use (β2,γ) as partial but useful labeling of the basis vector. Theβ2-γplane is introduced as usual (see Fig.4c as an example): for a given pair (β2,γ), the corresponding point on the plane is located at the distanceβ2from the origin, and at the angleγfrom the horizo...
In the cases of quantities derived from expectations of multiple observables (i.e. spin and charge correlations) we make the simplifying assumption that the distribution of each of the observables combined to produce that quantity is independent to produce an overall error bar. Error bars for th...