# Quantum pixel representations and compression for N-dimensional images

arXiv: https://arxiv.org/abs/2110.04405 · HTML: https://mlsanity.com/paper/2110.04405/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)

## Built on by (most cited first, 4 of 4)

- [Quantum Natural Language Processing](https://mlsanity.com/paper/2403.19758/) (2024)
- [Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attention](https://mlsanity.com/paper/2403.14753/) (2024)
- [Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins](https://mlsanity.com/paper/2309.13108/) (2023)
- [Vectorized Attention with Learnable Encoding for Quantum Transformer](https://mlsanity.com/paper/2508.18464/) (2025)

## Abstract (arXiv)

We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all considered quantum pixel representations. Our method only requires a linear number of gates in terms of the number of pixels and does not use ancilla qubits. Furthermore, the circuits only consist of Ry gates and CNOT gates making them practical in the NISQ era. Additionally, we propose a circuit and image compression algorithm that is shown to be highly effective, being able to reduce the necessary gates to prepare an FRQI state for example scientific images by up to 90% without sacrificing image quality. Our algorithms are made publicly available as part of QPIXL++, a Quantum Image Pixel Library.