# Quantum Deep Sets and Sequences

arXiv: https://arxiv.org/abs/2504.02241 · HTML: https://mlsanity.com/paper/2504.02241/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Revisiting Point Cloud Shape Classification with a Simple and Effective Baseline](https://mlsanity.com/paper/2106.05304/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [On the expressivity of embedding quantum kernels](https://mlsanity.com/paper/2309.14419/) (2023)
- [Concentration of Data Encoding in Parameterized Quantum Circuits](https://mlsanity.com/paper/2206.08273/) (2022)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers](https://mlsanity.com/paper/2302.13555/) (2023)

## Built on by (most cited first, 1 of 1)

- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)

## Abstract (arXiv)

This paper introduces the quantum deep sets model, expanding the quantum machine learning tool-box by enabling the possibility of learning variadic functions using quantum systems. A couple of variants are presented for this model. The first one focuses on mapping sets to quantum systems through state vector averaging: each element of the set is mapped to a quantum state, and the quantum state of the set is the average of the corresponding quantum states of its elements. This approach allows the definition of a permutation-invariant variadic model. The second variant is useful for ordered sets, i.e., sequences, and relies on optimal coherification of tristochastic tensors that implement products of mixed states: each element of the set is mapped to a density matrix, and the quantum state of the set is the product of the corresponding density matrices of its elements. Such variant can be relevant in tasks such as natural language processing. The resulting quantum state in any of the variants is then processed to realise a function that solves a machine learning task such as classification, regression or density estimation. Through synthetic problem examples, the efficacy and versatility of quantum deep sets and sequences (QDSs) is demonstrated.