# Adaptive Quantum State Tomography with Neural Networks

arXiv: https://arxiv.org/abs/1812.06693 · HTML: https://mlsanity.com/paper/1812.06693/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2018.

## Built on by (most cited first, 15 of 15)

- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Learning Temporal Quantum Tomography](https://mlsanity.com/paper/2103.13973/) (2021)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Quantum State Tomography using Quantum Machine Learning](https://mlsanity.com/paper/2308.10327/) (2023)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Hamiltonian-Driven Shadow Tomography of Quantum States](https://mlsanity.com/paper/2102.10132/) (2021)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Adaptive Bayesian Single-Shot Quantum Sensing](https://mlsanity.com/paper/2507.16477/) (2025)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [Scalable bayesian shadow tomography for quantum property estimation with set transformers](https://mlsanity.com/paper/2509.18674/) (2025)
- [Batch Entanglement Detection in Parameterized Qubit States using Classical Bandit Algorithms](https://mlsanity.com/paper/2406.19738/) (2024)
- [Guess, SWAP, Repeat : Capturing Quantum Snapshots in Classical Memory](https://mlsanity.com/paper/2504.14459/) (2025)
- [Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction](https://mlsanity.com/paper/2605.22338/) (2026)

## Abstract (arXiv)

Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as in terms of the computational time to analyze those measurements. In this paper, we address the problem of analysis speed and flexibility, introducing textitNeural Adaptive Quantum State Tomography (NA-QST), a machine learning based algorithm for quantum state tomography that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. Our algorithm is inspired by particle swarm optimization and Bayesian particle-filter based adaptive methods, which we extend and enhance using neural networks. The resampling step, in which a bank of candidate solutions -- particles -- is refined, is in our case learned directly from data, removing the computational bottleneck of standard methods. We successfully replace the Bayesian calculation that requires computational time of O(poly(n)) with a learned heuristic whose time complexity empirically scales as O(log(n)) with the number of copies measured n, while retaining the same reconstruction accuracy. This corresponds to a factor of a million speedup for 107 copies measured. We demonstrate that our algorithm learns to work with basis, symmetric informationally complete (SIC), as well as other types of POVMs. We discuss the value of measurement adaptivity for each POVM type, demonstrating that its effect is significant only for basis POVMs. Our algorithm can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems. It can also adapt to a subset of possible states, a choice of the type of measurement, and other experimental details.