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

TL;DR

EnQode tackles the problem of high-depth, data-dependent amplitude embedding on NISQ devices by clustering data and representing each cluster with a fixed-depth, hardware-efficient ansatz. It employs a symbolic optimization framework for fast, gradient-based refinement and uses transfer learning to initialize new samples from cluster means, enabling real-time AE. The approach yields over $0.90$ fidelity in data mapping with dramatic reductions in circuit depth ($>28\times$) and gate counts (up to $12\times$), while maintaining consistent noise exposure across samples and reducing online/offline compilation times. This combination of clustering, symbolic optimization, and transfer learning provides a practical, scalable path for robust QML on noisy quantum hardware, and the authors supply open-source implementations for broader use.

Abstract

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.

Figures (9)

• Figure 1: EnQode provides short-depth and consistent circuits for amplitude embedding across different dataset samples.
• Figure 2: EnQode's ansatz design to reduce the circuit depth and the number of physical gates. $CY$ gates are indicated with $C$ for the control qubit and $Y$ for the target qubit.
• Figure 3: EnQode employs symbolic representation for fast optimization of its amplitude embedding circuit ansatz.
• Figure 4: EnQode divides a dataset into multiple clusters and trains a symbolic representation model for each cluster.
• Figure 5: An inference sample gets matched to one of the clusters, and its amplitude embedding circuit is quickly trained using the cluster's trained model to initialize the parameters.