# Quantum Similarity Testing with Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2211.01668 · HTML: https://mlsanity.com/paper/2211.01668/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 56 references that are in the map.
- First posted on arXiv 3 Nov 2022.

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

- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models](https://mlsanity.com/paper/2109.02490/) (2021)
- [Efficient Quantum State Sample Tomography with Basis-dependent Neural-networks](https://mlsanity.com/paper/2009.07601/) (2020)
- [Experimental quantum homodyne tomography via machine learning](https://mlsanity.com/paper/1907.06589/) (2019)

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

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Multimodal deep representation learning for quantum cross-platform verification](https://mlsanity.com/paper/2311.03713/) (2023)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Learning quantum properties from short-range correlations using multi-task networks](https://mlsanity.com/paper/2310.11807/) (2023)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models](https://mlsanity.com/paper/2311.01727/) (2023)
- [Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors](https://mlsanity.com/paper/2507.17470/) (2025)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [Optical Quantum Sensing for Agnostic Environments via Deep Learning](https://mlsanity.com/paper/2311.07203/) (2023)

## Abstract (arXiv)

The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained offline with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, or with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.