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:2012.03104 · Machine Learning Science and Technology

Machine learning pipeline for quantum state estimation with incomplete measurements

Onur Danaci, Sanjaya Lohani, Brian T. Kirby, Ryan T. Glasser

Published Feb 12, 2021• 24 citations
arXivHTMLPDF

Abstract

Abstract Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.

DOI
10.1088/2632-2153/abe5f5

Related papers

Quantum State Estimation from Partial Tomography Data Using a Stack of Machine Learning Models and Imputation

Onur Danaci, Sanjaya Lohani, Brian T. Kirby +2 more

Reconstruction of two-qubit systems typically performed using 36 coincidence measurements. We trained an ensemble of CNN & XGBoost ML models, employed imputation to demonstrate high-fidelity state estimation when multiple measurements are missing.

Frontiers in Optics•Jan 1, 2020•1 citation

Learning Entanglement Quasiprobability from Noisy and Incomplete Data

Yu-Zhuo Li, Li-Chao Peng, Ke-Mi Xu

Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a $30\times$ reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems.

quant-pharXiv:2603.18414•Mar 20, 2026•0 citations

Machine learning assisted quantum state estimation

Sanjaya Lohani, Brian T Kirby, Michael Brodsky +2 more

Abstract We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.

arXiv:2003.03441•Machine Learning Science and Technology•Jun 5, 2020•101 citations

Efficient Quantum Tomography with Fidelity Estimation.

Zhaoyu Han, Jun Wang, Songbo Wang +4 more

We propose a quantum tomography scheme for pure states which adopts machine learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic state. We prove the validity of the scheme theoretically and perform numerically simulated experiments on several typical target quantum states such as W, cluster and dimer states. We find that the required number of measurements to meet the convergence criterion does not grow exponentially in the number of qubits, thus the scheme achieves high efficiency that is crucial for large-scale quantum states tomography in a laboratory.

•Dec 8, 2017•3 citations

Quantum state estimation based on deep learning

Haowen 皓文 Xiao 肖, Zhiguang Han

Abstract We used deep learning techniques to construct various models for reconstructing quantum states from a given set of coincidence measurements. Through simulations, we have demonstrated that our approach generates functionally equivalent reconstructed states for a wide range of pure and mixed input states. Compared with traditional methods, our system offers the advantage of faster speed. Additionally, by training our system with measurement results containing simulated noise sources, the system shows a significant improvement in average fidelity compared with typical reconstruction methods. We also found that constraining the variational manifold to physical states, i.e., positive semi-definite density matrices, greatly enhances the quality of the reconstructed states in the presence of experimental imperfections and noise. Finally, we validated the correctness and superiority of our model by using data generated on IBM Quantum Platform, a real quantum computer.

Chinese Physics B•Sep 10, 2024•1 citation

Machine learning models for quantum state tomography

Marko Čechovič

This thesis asks whether modern machine-learning model families and restoration ideas that have driven progress in computer graphics can also improve quantum state tomography, the reconstruction of an unknown quantum state from repeated measure- ments. We study four broad families-feed-forward neural networks, conditional genera- tive adversarial networks, iterative generative models from diffusion to flow matching, and transformers-across three practical regimes: incomplete near-clean measurements, com- plete finite-shot measurements, and measurements that are both incomplete and noisy. Five selected point-estimation pipelines are developed through validation-guided exper- iments and evaluated on the same synthetic two-qubit state partitions and paired test records. The common formulation treats missing settings as masked data, represents shot-dependent reliability through confidence, and uses a normalised Cholesky map to ensure a physical output. Combined with set-based aggregation and Bures-based train- ing, this formulation reduces the complete high-shot mean Bures distance of a naive multilayer perceptron from 0.079 to 0.022. On this common in-distribution benchmark, RhoTransformer has the lowest mean Bures distance at all four headline operating points, reaching 0.015 with all sixteen settings at 105...

•Jan 1, 2026•0 citations
Abstract Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.
Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a 30×30\times30× reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems.
Abstract We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.
We propose a quantum tomography scheme for pure states which adopts machine learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic state. We prove the validity of the scheme theoretically and perform numerically simulated experiments on several typical target quantum states such as W, cluster and dimer states. We find that the required number of measurements to meet the convergence criterion does not grow exponentially in the number of qubits, thus the scheme achieves high efficiency that is crucial for large-scale quantum states tomography in a laboratory.
Abstract We used deep learning techniques to construct various models for reconstructing quantum states from a given set of coincidence measurements. Through simulations, we have demonstrated that our approach generates functionally equivalent reconstructed states for a wide range of pure and mixed input states. Compared with traditional methods, our system offers the advantage of faster speed. Additionally, by training our system with measurement results containing simulated noise sources, the system shows a significant improvement in average fidelity compared with typical reconstruction methods. We also found that constraining the variational manifold to physical states, i.e., positive semi-definite density matrices, greatly enhances the quality of the reconstructed states in the presence of experimental imperfections and noise. Finally, we validated the correctness and superiority of our model by using data generated on IBM Quantum Platform, a real quantum computer.
This thesis asks whether modern machine-learning model families and restoration ideas that have driven progress in computer graphics can also improve quantum state tomography, the reconstruction of an unknown quantum state from repeated measure- ments. We study four broad families-feed-forward neural networks, conditional genera- tive adversarial networks, iterative generative models from diffusion to flow matching, and transformers-across three practical regimes: incomplete near-clean measurements, com- plete finite-shot measurements, and measurements that are both incomplete and noisy. Five selected point-estimation pipelines are developed through validation-guided exper- iments and evaluated on the same synthetic two-qubit state partitions and paired test records. The common formulation treats missing settings as masked data, represents shot-dependent reliability through confidence, and uses a normalised Cholesky map to ensure a physical output. Combined with set-based aggregation and Bures-based train- ing, this formulation reduces the complete high-shot mean Bures distance of a naive multilayer perceptron from 0.079 to 0.022. On this common in-distribution benchmark, RhoTransformer has the lowest mean Bures distance at all four headline operating points, reaching 0.015 with all sixteen settings at 105...