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

2026-02-18

AI Summary

This work addresses the bottleneck in quantum machine learning caused by the high circuit depth and resource demands of conventional quantum data encoding schemes. To overcome this limitation, the authors propose TNQE, a novel framework that represents classical data using structured unitary tensor networks. By incorporating block-wise unitary parameterization and unitarity-aware constraints, TNQE enables end-to-end trainable and highly efficient encoding. Coupled with a differentiable quantum circuit compilation strategy, the method substantially reduces both circuit depth and qubit overhead. Experimental results demonstrate that TNQE can process high-resolution 256×256 images using only 4% of the circuit depth required by amplitude encoding, while maintaining feasibility on real quantum hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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 $0.04\times$ the depth of amplitude encoding, while naturally scaling to high-resolution images ($256 \times 256$) and demonstrating practical feasibility on real quantum hardware.

Problem

• quantum data encoding
• circuit efficiency
• quantum machine learning
• scalability
• quantum resources

Innovation

• unitary tensor network
• quantum data encoding
• circuit-efficient
• trainable quantum circuits
• tensor-to-circuit compilation