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Frontiers in Optics

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

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

Published Jan 1, 2020• 1 citation
Publisher

Abstract

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.
DOI
10.1364/fio.2020.ftu8d.5

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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.
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...
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