# Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty

arXiv: https://arxiv.org/abs/2607.11273 · HTML: https://mlsanity.com/paper/2607.11273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform](https://mlsanity.com/paper/2406.01781/) (2024)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Attention-based Quantum Tomography](https://mlsanity.com/paper/2006.12469/) (2020)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [Tensor Train Quantum State Tomography using Compressed Sensing](https://mlsanity.com/paper/2506.23560/) (2025)
- [Demonstration of machine-learning-enhanced Bayesian quantum state estimation](https://mlsanity.com/paper/2212.08032/) (2022)
- [Scalable bayesian shadow tomography for quantum property estimation with set transformers](https://mlsanity.com/paper/2509.18674/) (2025)

## Abstract (arXiv)

Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A k=0 prior-only control shows that on concentrated families a prior estimate is already near-optimal, so ``high fidelity at few measurements'' can be family memorization rather than tomography; genuine measurement-efficiency needs a model that conditions on the measurements and demonstrably uses them. On a shared matrix-product-state (MPS) core parameterization we study two routes. Approach~A learns a generative prior over MPS cores with measurement-guided posterior inference (gold-standard-validated, but whose few-measurement accuracy the control shows is largely the prior). Approach~B, our main proposal, is a fixed-protocol amortized MPS estimator trained once with a gauge-invariant fidelity loss; we deliberately do not rest it on a permutation-invariant set encoder (a plain MLP matches it). The decisive lever is the measurement design: motivated by the fact that local reduced density matrices determine a chi-MPS, conditioning on an informative local Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one (≈!0.95, up to +0.59 over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives ≈!90%-coverage intervals -- including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity 0.90 at n=10, gain growing in n; 0.88 at bond dimension chi=4), the parameterization is polynomial (native contraction to 20 qubits), and we close the loop on IBM hardware (5 states at 0.97 from hardware-measured Paulis).