# Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

arXiv: https://arxiv.org/abs/2602.16266 · HTML: https://mlsanity.com/paper/2602.16266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Tensor networks in machine learning](https://mlsanity.com/paper/2207.02851/) (2022)
- [Coarse-To-Fine Tensor Trains for Compact Visual Representations](https://mlsanity.com/paper/2406.04332/) (2024)
- [MNISQ: A Large-Scale Quantum Circuit Dataset for Machine Learning on/for Quantum Computers in the NISQ era](https://mlsanity.com/paper/2306.16627/) (2023)
- [Comparing Quantum Encoding Techniques](https://mlsanity.com/paper/2410.09121/) (2024)
- [Quantum Data Encoding and Variational Algorithms: A Framework for Hybrid Quantum Classical Machine Learning](https://mlsanity.com/paper/2502.11951/) (2025)

## Abstract (arXiv)

Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose TNQE, a circuit-efficient quantum data encoding framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as 0.04× the depth of amplitude encoding, while naturally scaling to high-resolution images (256 × 256) and demonstrating practical feasibility on real quantum hardware.