Related papers: Iterative phase estimation
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
Many satellite communication systems operating today employ low cost upconverters or downconverters which create phase noise. This noise can severely limit the information rate of the system and pose a serious challenge for the detection…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Given $N_{\textrm{tot}}$ applications of a unitary operation with an unknown phase $\theta$, a large-scale fault-tolerant quantum system can {reduce} an estimate's {error} scaling from $\mathcal{O} \left[ 1 / \sqrt{N_{\textrm{tot}}}…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Accurate phase estimation -- the process of assigning phase values between $0$ and $2\pi$ to repetitive or periodic signals -- is a cornerstone in the analysis of oscillatory signals across diverse fields, from neuroscience to robotics,…
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…
We propose a quantum-enhanced iterative (with $K$ steps) measurement scheme based on an ensemble of $N$ two-level probes which asymptotically approaches the Heisenberg limit $\delta_K \propto R^{-K/(K+1)}$, $R$ the number of quantum…
We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase,…
We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped $\textrm{Yb}^+$ ion qubit. We estimate these phases with uncertainties less than $4\cdot10^{-4}$ radians using…
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…
The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement---the estimation of a completely unknown phase---has been experimentally demonstrated with…
A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…
Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…