Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2501.17334 · New Journal of Physics

Unorthodox parallelization for Bayesian quantum state estimation

Hanson H Nguyen, Kody J. H. Law, Joseph M. Lukens

Published May 1, 2025• 1 citation
arXivHTMLPDF

Abstract

Abstract Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.

DOI
10.1088/1367-2630/add618

Related papers

Unorthodox Parallelization for Bayesian Quantum State Estimation

Hanson H. Nguyen, Kody J. H. Law, Joseph M. Lukens

Bayesian inference enables informationally efficient quantum state tomography (QST) yet is challenging to scale computationally. We demonstrate a parallelizable Bayesian QST method that, although unorthodox, proves remarkably practical, attaining significant speedups in multiqubit state estimation.

•Jan 1, 2025•0 citations

A practical and efficient approach for Bayesian quantum state estimation

Joseph M. Lukens, Kody J. H. Law, Ajay Jasra +1 more

Abstract Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.

arXiv:2002.10354•New Journal of Physics•Apr 30, 2020•121 citations

Quantum State Vector Reconstruction via Bayesian Inference

Jincheng Zhang

Quantum state vector reconstruction is a fundamental problem in quantum information theory, crucial for tasks like quantum state tomography and quantum error correction. Traditional methods often struggle with noisy measurements and lack a principled framework for uncertainty quantification. This paper introduces a novel algorithm, Quantum State Vector Reconstruction via Bayesian Inference, that leverages Bayesian inference to reconstruct a quantum state vector from a set of measurements, enhancing accuracy and offering a more robust approach compared to existing methods. We detail the core mechanism, emphasizing the integration of Bayesian estimation for uncertainty quantification and refinement of the reconstruction process. The algorithm incorporates a probabilistic approach to estimate the state vector distribution, improving reconstruction by incorporating uncertainty estimates directly into the reconstruction process. This results in a more reliable and accurate state vector reconstruction, particularly when dealing with noisy measurements. This work addresses the limitations of conventional methods by providing a principled Bayesian framework for state vector reconstruction, offering a significant advancement in this field.

•Sep 3, 2026•0 citations

Quantum-Enhanced Bayesian Inference for Uncertainty Quantification

Jincheng Zhang

Quantum-enhanced Bayesian inference offers a promising approach to address the computational challenges associated with uncertainty quantification, particularly in situations demanding high accuracy and speed. This paper explores the design and implementation of a quantum algorithm, quantum state tomography, to enhance Bayesian inference, aiming to mitigate the inherent cost of traditional methods. We detail the theoretical framework underpinning this approach, highlighting its potential to significantly improve reliability and speed. The core claim centers on leveraging quantum state tomography to achieve a more precise estimate of the system state, thereby bolstering the accuracy of Bayesian inference. This work represents a novel investigation into the application of quantum mechanics to Bayesian inference, with the potential to deliver substantial improvements in computational efficiency and robustness.

•Sep 1, 2026•0 citations

Bayesian inference for quantum state tomography

Douglas Soares Gonçalves, Caio Azevedo, Carlile Lavor +1 more

We present a Bayesian approach to the problem of estimating density matrices in quantum state tomography. A general framework is presented based on a suitable mathematical formulation, 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. This analysis indicates that our approach not only recovers the underlying parameters quite properly, but also produces physically acceptable punctual and interval estimates. A prior sensitive study was conducted indicating that when useful prior information is available and incorporated, more accurate results are obtained. This general framework, which is based on a reparameterization of the model, allows an easier choice of the prior and proposal distributions for the Metropolis–Hastings algorithm.

Journal of Applied Statistics•Nov 15, 2017•9 citations

Quantum-Inspired Bayesian Inference for High-Dimensional Regression

Jincheng Zhang

High-dimensional regression problems, prevalent in diverse fields like genomics, finance, and medical diagnostics, pose a significant challenge to classical Bayesian inference. The computational cost of calculating posterior distributions often scales exponentially with the number of parameters, rendering many real-world applications intractable. This paper introduces a novel Bayesian inference algorithm inspired by the principles of quantum mechanics, specifically superposition and interference. We represent the prior distribution as a superposition of states, allowing for simultaneous exploration of the entire parameter space. Inference is then performed through a "quantum-inspired" sampling process that mimics the probabilistic nature of quantum measurements. This approach offers a potential pathway to circumvent the computational bottlenecks inherent in traditional Bayesian methods, particularly in the context of high-dimensional data. We outline the key components of the algorithm, provide a theoretical framework, and discuss its potential advantages and limitations. The core of the method lies in effectively harnessing the parallel exploration capability suggested by quantum mechanics to drastically reduce the computational burden associated with estimating the posterior distribution.

•Aug 28, 2026•0 citations
Abstract Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.
Abstract Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.
Quantum state vector reconstruction is a fundamental problem in quantum information theory, crucial for tasks like quantum state tomography and quantum error correction. Traditional methods often struggle with noisy measurements and lack a principled framework for uncertainty quantification. This paper introduces a novel algorithm, Quantum State Vector Reconstruction via Bayesian Inference, that leverages Bayesian inference to reconstruct a quantum state vector from a set of measurements, enhancing accuracy and offering a more robust approach compared to existing methods. We detail the core mechanism, emphasizing the integration of Bayesian estimation for uncertainty quantification and refinement of the reconstruction process. The algorithm incorporates a probabilistic approach to estimate the state vector distribution, improving reconstruction by incorporating uncertainty estimates directly into the reconstruction process. This results in a more reliable and accurate state vector reconstruction, particularly when dealing with noisy measurements. This work addresses the limitations of conventional methods by providing a principled Bayesian framework for state vector reconstruction, offering a significant advancement in this field.
Quantum-enhanced Bayesian inference offers a promising approach to address the computational challenges associated with uncertainty quantification, particularly in situations demanding high accuracy and speed. This paper explores the design and implementation of a quantum algorithm, quantum state tomography, to enhance Bayesian inference, aiming to mitigate the inherent cost of traditional methods. We detail the theoretical framework underpinning this approach, highlighting its potential to significantly improve reliability and speed. The core claim centers on leveraging quantum state tomography to achieve a more precise estimate of the system state, thereby bolstering the accuracy of Bayesian inference. This work represents a novel investigation into the application of quantum mechanics to Bayesian inference, with the potential to deliver substantial improvements in computational efficiency and robustness.
We present a Bayesian approach to the problem of estimating density matrices in quantum state tomography. A general framework is presented based on a suitable mathematical formulation, 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. This analysis indicates that our approach not only recovers the underlying parameters quite properly, but also produces physically acceptable punctual and interval estimates. A prior sensitive study was conducted indicating that when useful prior information is available and incorporated, more accurate results are obtained. This general framework, which is based on a reparameterization of the model, allows an easier choice of the prior and proposal distributions for the Metropolis–Hastings algorithm.
High-dimensional regression problems, prevalent in diverse fields like genomics, finance, and medical diagnostics, pose a significant challenge to classical Bayesian inference. The computational cost of calculating posterior distributions often scales exponentially with the number of parameters, rendering many real-world applications intractable. This paper introduces a novel Bayesian inference algorithm inspired by the principles of quantum mechanics, specifically superposition and interference. We represent the prior distribution as a superposition of states, allowing for simultaneous exploration of the entire parameter space. Inference is then performed through a "quantum-inspired" sampling process that mimics the probabilistic nature of quantum measurements. This approach offers a potential pathway to circumvent the computational bottlenecks inherent in traditional Bayesian methods, particularly in the context of high-dimensional data. We outline the key components of the algorithm, provide a theoretical framework, and discuss its potential advantages and limitations. The core of the method lies in effectively harnessing the parallel exploration capability suggested by quantum mechanics to drastically reduce the computational burden associated with estimating the posterior distribution.