# A learning theory for quantum photonic processors and beyond

arXiv: https://arxiv.org/abs/2209.03075 · HTML: https://mlsanity.com/paper/2209.03075/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 64 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Private learning implies quantum stability](https://mlsanity.com/paper/2102.07171/) (2021)
- [The Learnability of Unknown Quantum Measurements](https://mlsanity.com/paper/1501.00559/) (2015)
- [Real-time calibration of coherent-state receivers: learning by trial and error](https://mlsanity.com/paper/2001.10283/) (2020)
- [Reinforcement-learning calibration of coherent-state receivers on variable-loss optical channels](https://mlsanity.com/paper/2203.09807/) (2022)

## Built on by (most cited first, 3 of 3)

- [Efficient learning of bosonic Gaussian unitaries](https://mlsanity.com/paper/2510.05531/) (2025)
- [Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes](https://mlsanity.com/paper/2308.12304/) (2023)
- [Quantum Attention by Overlap Interference: Predicting Classical and Many-Body Quantum Sequences](https://mlsanity.com/paper/2602.06699/) (2026)

## Abstract (arXiv)

We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes state-of-the-art photonic processors capable of showing quantum advantage. We define classes of functions that map classical variables, encoded into the CV circuit parameters, to outcome probabilities evaluated on those circuits. We then establish efficient learnability guarantees for such classes, by computing bounds on their pseudo-dimension or covering numbers, showing that CV quantum circuits can be learned with a sample complexity that scales polynomially with the circuit's size, i.e., the number of modes. Our results show that CV circuits can be trained efficiently using a number of training samples that, unlike their finite-dimensional counterpart, does not scale with the circuit depth.