相关论文: Optimal, reliable estimation of quantum states
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover,…
The Bayes error rate (BER) is a fundamental concept in machine learning that quantifies the best possible accuracy any classifier can achieve on a fixed probability distribution. Despite years of research on building estimators of lower and…
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis.…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic read-out errors on quantum computers (QC). Currently used MEM strategies face a tradeoff: methods that scale well with the number of qubits…
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…
Quantum network protocols depend on the availability of shared entanglement. Given that entanglement generation and distribution are affected by noise, characterization of the shared entangled states is essential to bound the errors of the…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
Accurate calibration of control parameters in quantum gates is crucial for high-fidelity operations, yet it represents a significant time and resource challenge, necessitating periods of downtime for quantum computers. Robust Phase…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…