qst-flow-quantum-tomography

name	qst-flow-quantum-tomography
description	QST-Flow framework for continuous-variable quantum state tomography using flow-based generative modeling. Models Husimi-Q functions with QST-QFlow and Wigner functions with QST-WFlow as difference of normalized flows. Use when working with non-Gaussian bosonic states, phase-space tomography, or quantum state reconstruction.
metadata	{"arxiv_id":"2607.21584","published":"2026-07-23","authors":"Owen Dugan, Rumen Dangovski, Peter Y. Lu, Di Luo","tags":["quantum","tomography","flow-based","continuous-variable","Wigner","Husimi-Q"]}
license	Complete terms in LICENSE.txt

QST-Flow: Flow-based Phase-space Tomography

Overview

QST-Flow is a quantum state tomography framework that uses flow-based generative modeling to represent experimentally accessible phase-space quasiprobability distributions. Instead of truncating density matrices or using fixed grids, QST-Flow represents quantum states with normalized, samplable neural densities.

Key Components

QST-QFlow

• Models the positive Husimi-Q function with a single normalizing flow
• Provides normalized probability model for coherent-state measurements
• Enables exact density evaluation and direct sampling

QST-WFlow

• Models sign-changing Wigner functions as a trainable difference of two normalized flows
• Explicitly captures negativity while preserving normalization
• Handles interference fringes and negative lobes that carry non-classical information

Methodology

1. Phase-space representation: Work directly in continuous phase space without grid discretization
2. Flow-based modeling: Use invertible transformations with tractable Jacobians
3. Normalization preservation: Ensure quasiprobability distributions remain properly normalized
4. Importance sampling: Learn from finite phase-space measurements without fixed grid constraints
5. Difference-of-flows construction: For Wigner functions, represent as Q₁(α) - Q₂(α) where both Q₁ and Q₂ are normalized flows

Applications

• Single-mode non-Gaussian state reconstruction (cat, binomial, GKP, number, Fock states)
• Extension to multimode states
• Robust reconstruction from noisy Wigner data
• Measurement-efficient tomography of nonclassical bosonic systems

Advantages over Prior Methods

• Avoids Fock-basis truncation limitations
• No fixed grid resolution constraints
• Exact density evaluation and direct sampling capabilities
• Improved reconstruction error compared to QST-CGAN and other ML tomography methods
• Scalable to higher-dimensional phase spaces

Implementation Considerations

• Requires normalizing flow architectures with invertible transformations
• Training uses importance-sampled likelihood estimates from experimental measurements
• For Wigner functions, ensure both component flows are properly normalized
• Validate reconstruction quality using quantum fidelity bounds

Activation Keywords

• qst-flow
• quantum tomography flow
• phase-space tomography
• continuous-variable tomography
• Wigner flow modeling
• Husimi-Q flow

References

• Original paper: arXiv:2607.21584
• Related: quantum-state-tomography, flow-based-generative-modeling, continuous-variable-quantum