Though there has been substantial progress in developing quantum algorithms
to study classical datasets, the cost of simply loading classical data is an
obstacle to quantum advantage. When the amplitude encoding is used, loading an
arbitrary classical vector requires up to exponential circuit depths with
respect to the number of qubits. Here, we address this ``input problem'' with
two contributions. First, we introduce a circuit compilation method based on
tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layer Loader
Exploiting TNs) -- proceeds via careful construction of a specific TN topology
and can be tailored to arbitrary circuit depths. Second, we perform numerical
experiments on real-world classical data from four distinct areas: finance,
images, fluid mechanics, and proteins. To the best of our knowledge, this is
the broadest numerical analysis to date of loading classical data into a
quantum computer. Consistent with other recent work in this area, the required
circuit depths are often several orders of magnitude lower than the
exponentially-scaling general loading algorithm would require. Besides
introducing a more efficient loading algorithm, this work demonstrates that
many classical datasets are loadable in depths that are much shorter than
previously expected, which has positive implications for speeding up classical
workloads on quantum computers.

我们提出了一种基于张量网络理论的电路编译方法（AMLET），通过精确构建特定的张量网络拓扑，可解决将任意经典向量加载到量子计算机所需的指数级电路深度问题。并通过对金融、图像、流体力学和蛋白质等领域的实际经典数据进行数值实验，证明相比指数级扩展的通用加载算法，所需电路深度通常要低几个数量级，进而为在量子计算机上加速经典工作负载带来积极影响。

数据常有短路径加载：金融、图像、流体和蛋白质的量子电路张量网络

Data is often loadable in short depth: Quantum circuits from tensor  networks for finance, images, fluids, and proteins

In recent years, interest in expressing the success of neural networks to the
quantum computing has increased significantly. Tensor network theory has become
increasingly popular and widely used to simulate strongly entangled correlated
systems. Matrix product state (MPS) is the well-designed class of tensor
network states, which plays an important role in processing of quantum
information. In this paper, we have shown that matrix product state as
one-dimensional array of tensors can be used to classify classical and quantum
data. We have performed binary classification of classical machine learning
dataset Iris encoded in a quantum state. Further, we have investigated the
performance by considering different parameters on the ibmqx4 quantum computer
and proved that MPS circuits can be used to attain better accuracy. Further,
the learning ability of MPS quantum classifier is tested to classify
evapotranspiration ($ET_{o}$) for Patiala meteorological station located in
Northern Punjab (India), using three years of historical dataset (Agri).
Furthermore, we have used different performance metrics of classification to
measure its capability. Finally, the results are plotted and degree of
correspondence among values of each sample is shown.

本文探讨了将矩阵乘积状态作为一维张量数组用于分类经典和量子数据的能力，对传统机器学习数据集 Iris 进行了二元分类，并进一步通过考虑探讨不同参数来证明 MPS 电路可用于获得更好的准确性，实验了 MPS 量子分类器的学习能力，用于对北旁遮普邦（印度）Patiala 气象站的蒸发散进行分类，并使用不同的分类性能度量对其能力进行了测量，并展示了其各项值的一致性程度。