# Experimental learning of quantum states

arXiv: https://arxiv.org/abs/1712.00127 · HTML: https://mlsanity.com/paper/1712.00127/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 7 of 7)

- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [An Invitation to Distributed Quantum Neural Networks](https://mlsanity.com/paper/2211.07056/) (2022)
- [Deep learning of quantum entanglement from incomplete measurements](https://mlsanity.com/paper/2205.01462/) (2022)
- [On the Hardness of PAC-learning Stabilizer States with Noise](https://mlsanity.com/paper/2102.05174/) (2021)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [Concept learning of parameterized quantum models from limited measurements](https://mlsanity.com/paper/2408.05116/) (2024)

## Abstract (arXiv)

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to argue against the universal validity of quantum mechanics itself. However, from a computational learning theory perspective, it can be shown that, in a probabilistic setting, quantum states can be approximately learned using only a linear number of measurements. Here we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.