# Efficient adaptive MCMC implementation for Pseudo-Bayesian quantum tomography

@inproceedings{Mai2021EfficientAM, title={Efficient adaptive MCMC implementation for Pseudo-Bayesian quantum tomography}, author={T. T. Mai}, year={2021} }

We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradign for quantum tomography with attractive theoretical and empirical results. However, the computation of (Pseudo-)Bayesian estimators, due to sampling from complex and high-dimensional distribution, pose significant challenges that hampers their usages in practical settings. To overcome this problem, we…

## References

SHOWING 1-10 OF 45 REFERENCES

A practical and efficient approach for Bayesian quantum state estimation

- Physics, Computer Science
- 2020

An improved, self-contained approach for Bayesian quantum state estimation that relies on highly efficient preconditioned Crank--Nicolson sampling and a pseudo-likelihood is introduced.

Bayesian inference for quantum state tomography

- Computer Science
- 2018

A Bayesian approach to the problem of estimating density matrices in quantum state tomography, where a study of the convergence of the Monte Carlo Markov Chain algorithm is given, including a comparison with other estimation methods, such as maximum likelihood estimation and linear inversion.

Pseudo-Bayesian quantum tomography with rank-adaptation

- Mathematics, Physics
- 2017

Abstract Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the…

An invitation to quantum tomography

- Mathematics, Physics
- 2003

We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on…

3 Maximum-Likelihood Methods in Quantum Mechanics

- Mathematics
- 2004

Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum domain. For a given set of measurements, the most…

Experimental adaptive Bayesian tomography

- Physics
- 2013

We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for…

Quantum state tomography: Mean squared error matters, bias does not

- Physics, Mathematics
- 2014

Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may…

Reconstruction of Quantum States of Spin Systems : From Quantum Bayesian Inference to Quantum Tomography

- 1998

We study in detail the reconstruction of spin-1 2 states and analyze the connection between (1) quantum Bayesian inference, (2) reconstruction via the Jaynes principle of maximum entropy, and (3)…

Spectral thresholding quantum tomography for low rank states

- Physics, Mathematics
- 2015

The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states,…

Optimal large-scale quantum state tomography with Pauli measurements

- Mathematics
- 2016

Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this…