# Fast and robust quantum state tomography from few basis measurements

arXiv: https://arxiv.org/abs/2009.08216 · HTML: https://mlsanity.com/paper/2009.08216/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 10 of 10)

- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates](https://mlsanity.com/paper/2305.13409/) (2023)
- [Certifying almost all quantum states with few single-qubit measurements](https://mlsanity.com/paper/2404.07281/) (2024)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [Robust Low-rank Tensor Train Recovery](https://mlsanity.com/paper/2410.15224/) (2024)
- [Robust Iterative Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/2510.23237/) (2025)
- [Parametric Quantum State Tomography with HyperRBMs](https://mlsanity.com/paper/2601.20950/) (2026)
- [Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements](https://mlsanity.com/paper/2308.07175/) (2023)
- [Batch Entanglement Detection in Parameterized Qubit States using Classical Bandit Algorithms](https://mlsanity.com/paper/2406.19738/) (2024)

## Abstract (arXiv)

Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.