用结构化张量网络实现高效量子数据编码，大幅降低电路深度。
Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding
- 基于结构化酉张量网络分解输入数据，分步编译为量子电路。
- 编码电路深度仅为振幅编码的4%，支持256×256图像处理。
- 可直接优化参数，适合实际量子硬件部署与高维数据应用。
将经典数据编码为量子态是量子机器学习的核心瓶颈：许多常用编码方式电路效率低，需深电路和大量量子资源，限制了在量子硬件上的可扩展性。本文提出TNQE，一种基于结构化酉张量网络（TN）表示的电路高效量子数据编码框架。首先将每个经典输入通过张量网络分解表示，再通过两种互补的核到电路策略将其编译为编码电路。为使编译过程可训练且保持量子操作的酉特性，引入酉感知约束，将张量核参数化为可学习的块酉矩阵，可直接优化并作为量子算子编码。该框架可显式控制电路深度和量子比特资源，实现浅层、资源高效的电路构造。在多个基准测试中，TNQE生成的编码电路深度仅为振幅编码的0.04倍，同时自然扩展至高分辨率图像（256×256），并在真实量子硬件上展示出实际可行性。
原文摘要 · Abstract (English)
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.
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