Adaptive identification of coherent states

Abstract

We present methods for efficient characterization of an optical coherent state |α . We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of α. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of α in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).

Simultaneous model selection and parameter estimation: A superconducting qubit coupled to a bath of incoherent two-level systems

“…Furthermore, since the volume of the parameter space increases exponentially with its dimension, this makes the set of particles sparser. This "curse of dimensionality" decreases the effective sample size N ess = 1 i w 2 i , making it smaller than, e.g., in the considerations of [34,36,37], which may increase the numerical error. We attribute the observed floors in accuracy in Figs.…”

“…In [21], random, independently on data chosen, measurements were used for state estimation. While data-independent random controls are more easily realized experimentally and form, e.g., the basis of techniques such as randomized benchmarking [22][23][24][25], it has been shown theoretically [26][27][28][29][30][31][32][33][34][35][36][37] and experimentally [38][39][40][41][42][43] that in many situations adapting measurement settings during data collection can significantly speed up characterization.…”

Making sense of romantic jealousy in late 18th-century Sweden – the experiences of Pehr Stenberg

“…And it was curious; the same extent that I regained my peace of mind, the same extent the gout ceased to afflict my chest. 106 Viewed from a modern perspective, Stenberg's description resembles the anxiety and chest pains that sometimes accompany panic attacks. 107 However, for Stenberg, this interplay between a disease of the mind and of the body has a logical causality.…”

Practical adaptive quantum tomography

“…We will therefore follow the approach of Huszár and Houlsby [10] and use the particle filtering algorithm [52] to numerically implement Bayesian estimation. This approach has since been used by Ferrie [11,12] and by Granade et al [13] to develop useful applications of Bayesian tomography, by Stenberg et al [53] to learn coherent states, and has been successfully applied outside of tomography to efficiently learn Hamiltonians using classical [54] and quantum resources [55]. For our purposes here, we are primarily interested in the property that once a datum has been incorporated into a particle filter, it may be discarded, such that we do not incur computational costs that grow faster than the amount of data.…”

“…We will therefore follow the approach of Huszár and Houlsby [10] and use the particle filtering algorithm [52] to numerically implement Bayesian estimation. This approach has since been used by Ferrie [11,12] and by Granade et al [13] to develop useful applications of Bayesian tomography, by Stenberg et al [53] to learn coherent states, and has been successfully applied outside of tomography to efficiently learn Hamiltonians using classical [54] and quantum resources [55].…”