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arxiv: 2407.01734 · v4 · pith:ANYSXWP2new · submitted 2024-07-01 · 🪐 quant-ph · cs.AI

Optical Quantum Mixed-State Reconstruction With Multiple Deep Learning Approaches

Nhan Trong Luu , Tuyen Quang Nguyen , Duong Trung Luu , Thang Cong Truong This is my paper

Pith reviewed 2026-05-23 22:58 UTC · model grok-4.3

classification 🪐 quant-ph cs.AI
keywords quantum state tomographyneural networksmixed statesdeep learningquantum reconstructionoptical quantum states
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The pith

Neural networks achieve state-of-the-art quantum state tomography by using class information for both pure and mixed states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes two neural network approaches for reconstructing quantum states from measurement data. The Restricted Feature Based Neural Network and the Mixed States Neural Network both incorporate class information about the state type during the reconstruction process. This allows them to handle pure states and mixed states effectively. If successful, these methods could make quantum state characterization more accurate and efficient for applications in quantum technologies.

Core claim

By leveraging class information during reconstruction, the two neural network methods achieve state-of-the-art performance of tomography for both pure and mixed quantum states.

What carries the argument

Restricted Feature Based Neural Network and Mixed States Neural Network that use class information to improve reconstruction accuracy.

Load-bearing premise

The neural networks can generalize across different reconstruction scenarios for pure and mixed states when class information is provided, without needing retraining or overfitting.

What would settle it

Testing the networks on quantum states from new classes without providing class information and observing if the reconstruction accuracy drops significantly below state-of-the-art levels.

Figures

Figures reproduced from arXiv: 2407.01734 by Duong Trung Luu, Nhan Trong Luu, Thang Cong Truong, Tuyen Quang Nguyen.

Figure 1
Figure 1. Figure 1: Samples of Fock state 2) Coherent state: Displaced vacuum states, characterized by the complex displacement amplitude α |ψcoherent(α)⟩ = |α⟩ = D(α)|0⟩, D(α) = exp(α × a † − α × a) (11) D(α) is the displacement operator where a is the annihilation and (a † ) is the creation operator of the bosonic mode [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Samples of Coherent state 3) Thermal state: Mixed states where the photon number distribution follows super-Poissonian statistics ρthermal(n th) = N Xc−1 n=0 1 nth + 1 ( n th nth + 1 ) n |n⟩ ⟨n| (12) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Samples of Thermal state 4) Cat state: Bosonic-code states consisting of superpo￾sitions of coherent states up to a normalization N with projections Πr given by |ψ µ cat⟩ = 1 N Π(S+1)µ{ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 7
Figure 7. Figure 7: Samples of GKP state Name Constraint Fock state 1 ≤ nphoton ≤ 16 Coherent state 10−6 ≤ |α| 2 ≤ 3 Thermal state 1 ≤ nth ≤ 16 Cat state S ∈ [0, 2], |α| ∈ [1, 3], r ∈ [0, 2S + 1] Num state n ∈ {1.56, 2.67, 2.77, 4.15, 4.34} Binomial state 2 ≤ N ≤ NC /(S + 1) − 1 GKP state n1, n2 ∈ {−20, 20}, δ ∈ [0.2, 0.5] TABLE I: Constraints for states in dataset B. Experimented noise models Noise is an unavoidable element … view at source ↗
Figure 4
Figure 4. Figure 4: Samples of Cat state 5) Num state: Specific set of bosonic-code states, con￾sisting of superpositions of a few Fock states, numerically optimized for quantum error correction, and characterized by their average photon number n [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Samples of Num state 6) Binomial state: Bosonic-code states constructed from a superposition of Fock states weighted by the binomial coefficients |ψ µ binomial⟩ = 1 √ 2N+1 N X +1 m=0 (−1)µms N + 1 m  |(S + 1)m⟩ (14) [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Samples of Binomial state 7) GKP state: Finite Gottesmann-Kitaev-Preskill states, limits the lattice and adds a Gaussian envelope to make the state normalizable |ψ µ GKP ⟩ = P α∈K(µ) e −δ 2 |α| 2 e −iRe[α]Im[α] |α⟩, K(µ) = pπ 2 (2n1 + µ) + i pπ 2 n2 (15) [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Architecture of RFB-Net. state by taking 3-length value vectors as input and generating the predicted states. We train our model using a linear combination of cross￾entropy loss for the label and the sum of MAE loss for the real and imaginary parts of the regression output F as a feature vector: loss = − PN c=1 labelreal,N log(labelpred,N )+ PN i=1 [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Architecture of MS-NN. generate a density operator that encompasses positive semi￾definite, negative semi-definite, and even indefinite outcomes. This approach is particularly relevant in situations where the creation of an odd cat state is required, and can be achieved through the subtraction of two coherent states |α⟩ and |−α⟩: |ψ µ cat⟩ = 1 q 2(1 − e−2|α| 2 ) (|α⟩ − |−α⟩) (19) Model’s loss function is a… view at source ↗
Figure 11
Figure 11. Figure 11: Training loss progression of RFB-Net [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Validation fidelity progression per 100 iterations of [PITH_FULL_IMAGE:figures/full_fig_p007_12.png] view at source ↗
Figure 15
Figure 15. Figure 15: Training fidelity progression of QST-CGAN [28] [PITH_FULL_IMAGE:figures/full_fig_p008_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Samples of QST-CGAN [28] predictions. Model name Fidelity RFB-Net 0.97 MS-NN 0.91 QST-CGAN [28] 0.19 TABLE II: Validation fidelity of investigated models on gen￾erated dataset [PITH_FULL_IMAGE:figures/full_fig_p008_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Samples of noisy input measurements and RFB-Net [PITH_FULL_IMAGE:figures/full_fig_p009_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Samples of noisy input measurements and MS-NN [PITH_FULL_IMAGE:figures/full_fig_p009_18.png] view at source ↗
read the original abstract

Quantum state tomography is a crucial technique for characterizing the state of a quantum system, which is essential for many applications in quantum technologies. In recent years, there has been growing interest in leveraging neural networks to enhance the efficiency and accuracy of quantum state tomography. However, versatile methods that are broadly applicable across diverse reconstruction scenarios remain relatively underexplored. In this paper, we present two neural network-based reconstruction approaches for both pure and mixed quantum state tomography: Restricted Feature Based Neural Network and Mixed States Neural Network. By leveraging class information during reconstruction, we are able to achieve state-of-the-art performance of tomography for both pure and mixed quantum states.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces two neural-network architectures—Restricted Feature Based Neural Network and Mixed States Neural Network—for optical quantum state tomography. The central claim is that supplying class information during training enables state-of-the-art reconstruction accuracy for both pure and mixed states across diverse scenarios.

Significance. If the performance claims are substantiated with rigorous validation, the work would address a practical bottleneck in characterizing mixed quantum states, which are central to many quantum-technology applications. The approach of explicitly conditioning on class labels is a straightforward but potentially useful inductive bias; however, the absence of any quantitative results, baselines, or error analysis in the provided manuscript prevents any assessment of whether this advantage is realized.

major comments (2)
  1. [Abstract] Abstract: the claim of 'state-of-the-art performance' for both pure and mixed states is unsupported by any numerical results, comparison tables, error bars, or baseline methods (e.g., maximum-likelihood estimation or other neural tomography schemes). This absence makes the central performance claim impossible to evaluate.
  2. [Abstract] The generalization assumption—that the networks perform well across diverse reconstruction scenarios without scenario-specific retraining—is stated but not tested; no cross-validation, out-of-distribution test sets, or ablation on class-information usage is described, leaving the weakest assumption unexamined.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We agree that the abstract's performance claims require explicit support from numerical results and that the generalization assumptions need direct validation through additional experiments. We will revise the manuscript to incorporate these elements.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'state-of-the-art performance' for both pure and mixed states is unsupported by any numerical results, comparison tables, error bars, or baseline methods (e.g., maximum-likelihood estimation or other neural tomography schemes). This absence makes the central performance claim impossible to evaluate.

    Authors: We acknowledge that the abstract asserts state-of-the-art performance without directly referencing supporting numerical evidence, tables, or baselines within the abstract text itself. The full manuscript contains experimental sections with results, but these were not sufficiently highlighted or summarized to address the referee's concern. In the revised version, we will add explicit references in the abstract to key quantitative findings, including comparison tables against maximum-likelihood estimation and other neural tomography methods, along with error bars and performance metrics for both pure and mixed states. revision: yes

  2. Referee: [Abstract] The generalization assumption—that the networks perform well across diverse reconstruction scenarios without scenario-specific retraining—is stated but not tested; no cross-validation, out-of-distribution test sets, or ablation on class-information usage is described, leaving the weakest assumption unexamined.

    Authors: We agree that the generalization across scenarios is a central but untested claim in the current version. The manuscript describes the class-information approach but lacks the specific validation experiments noted. In revision, we will add cross-validation results, out-of-distribution test sets, and ablation studies isolating the contribution of class labels to demonstrate performance without scenario-specific retraining. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical NN performance claims only

full rationale

The paper introduces two neural network architectures (Restricted Feature Based Neural Network and Mixed States Neural Network) for quantum state tomography and claims improved performance by incorporating class information. No equations, derivations, fitted parameters presented as predictions, or self-citation chains appear in the abstract or described content. The central claims are empirical performance results on pure and mixed states, which are externally falsifiable via standard tomography benchmarks and do not reduce to self-definition or input renaming. This is the expected non-finding for a supervised ML methods paper without internal mathematical derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; neural network weights would implicitly be fitted parameters but are not detailed.

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discussion (0)

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