# Generalized quantum similarity learning

arXiv: https://arxiv.org/abs/2201.02310 · HTML: https://mlsanity.com/paper/2201.02310/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Quantum versus Classical Generative Modelling in Finance](https://mlsanity.com/paper/2008.00691/) (2020)
- [A Quantum-inspired Similarity Measure for the Analysis of Complete Weighted Graphs](https://mlsanity.com/paper/1904.13239/) (2019)
- [Quantum constraint learning for quantum approximate optimization algorithm](https://mlsanity.com/paper/2105.06770/) (2021)

## Built on by (most cited first, 2 of 2)

- [A quantum generative model for multi-dimensional time series using Hamiltonian learning](https://mlsanity.com/paper/2204.06150/) (2022)
- [SLIQ: Quantum Image Similarity Networks on Noisy Quantum Computers](https://mlsanity.com/paper/2309.15259/) (2023)

## Abstract (arXiv)

The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the underlying data and task. Moreover, conventional distance functions limit the space of similarity measures to be symmetric and do not directly allow comparing objects from different spaces. We propose using quantum networks (GQSim) for learning task-dependent (a)symmetric similarity between data that need not have the same dimensionality. We analyze the properties of such similarity function analytically (for a simple case) and numerically (for a complex case) and showthat these similarity measures can extract salient features of the data. We also demonstrate that the similarity measure derived using this technique is (ε,γ,τ)-good, resulting in theoretically guaranteed performance. Finally, we conclude by applying this technique for three relevant applications - Classification, Graph Completion, Generative modeling.