# EnQode: Fast Amplitude Embedding for Quantum Machine Learning Using Classical Data

arXiv: https://arxiv.org/abs/2503.14473 · HTML: https://mlsanity.com/paper/2503.14473/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 18 Mar 2025.

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

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)
- [A divide-and-conquer algorithm for quantum state preparation](https://mlsanity.com/paper/2008.01511/) (2020)
- [MosaiQ: Quantum Generative Adversarial Networks for Image Generation on NISQ Computers](https://mlsanity.com/paper/2308.11096/) (2023)
- [SupermarQ: A Scalable Quantum Benchmark Suite](https://mlsanity.com/paper/2202.11045/) (2022)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [QUILT: Effective Multi-Class Classification on Quantum Computers Using an Ensemble of Diverse Quantum Classifiers](https://mlsanity.com/paper/2309.15056/) (2023)
- [NAPA: Intermediate-level Variational Native-pulse Ansatz for Variational Quantum Algorithms](https://mlsanity.com/paper/2208.01215/) (2022)
- [SLIQ: Quantum Image Similarity Networks on Noisy Quantum Computers](https://mlsanity.com/paper/2309.15259/) (2023)

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

- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)
- [Three Birds with One Stone: Improving Performance, Convergence, and System Throughput with Nest](https://mlsanity.com/paper/2510.09578/) (2025)

## Abstract (arXiv)

Amplitude embedding (AE) is essential in quantum machine learning (QML) for encoding classical data onto quantum circuits. However, conventional AE methods suffer from deep, variable-length circuits that introduce high output error due to extensive gate usage and variable error rates across samples, resulting in noise-driven inconsistencies that degrade model accuracy. We introduce EnQode, a fast AE technique based on symbolic representation that addresses these limitations by clustering dataset samples and solving for cluster mean states through a low-depth, machine-specific ansatz. Optimized to reduce physical gates and SWAP operations, EnQode ensures all samples face consistent, low noise levels by standardizing circuit depth and composition. With over 90% fidelity in data mapping, EnQode enables robust, high-performance QML on noisy intermediate-scale quantum (NISQ) devices. Our open-source solution provides a scalable and efficient alternative for integrating classical data with quantum models.