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

TL;DR

This paper introduces TNQE, a novel framework for quantum data encoding that uses structured unitary tensor networks to create shallow, resource-efficient circuits suitable for high-resolution images and practical quantum hardware.

Contribution

TNQE is the first to combine tensor network decompositions with trainable, unitary cores for circuit-efficient quantum data encoding.

Findings

Achieves encoding circuits as shallow as 4% of amplitude encoding depth.

Scales effectively to high-resolution images like 256x256.

Demonstrates practical feasibility on real quantum hardware.

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.