论文标题
处理和测量算子对量子模型表达能力的影响
The effect of the processing and measurement operators on the expressive power of quantum models
论文作者
论文摘要
量子机学习（QML）模型，它们的工作方式以及对它们可能有用的应用程序的兴趣越来越大。关于如何编码经典数据以及应使用哪些电路Ansätze和测量运算符来处理编码数据并测量ANSATZ的输出状态，有许多不同的建议。上述操作员的选择在QML模型的表达能力中起着决定性作用。在这项工作中，我们研究了电路结构的某些变化如何改变这种表现力。我们介绍了数值和分析工具，以探索这些运营商对QML模型的整体性能的影响。这些工具基于以前关于教师计划，部分傅立叶系列和平均操作员大小的工作。我们将分析集中在具有两个和三个量子位的简单QML模型上，并观察到增加参数化和纠缠门的数量会导致某些电路结构的更具表现力的模型。同样，进行测量的量子量会影响QML模型可以学习的功能的类型。这项工作概述了处理和测量运算符在简单量子电路的表达能力上的决定性作用。
There is an increasing interest in Quantum Machine Learning (QML) models, how they work and for which applications they could be useful. There have been many different proposals on how classical data can be encoded and what circuit ansätze and measurement operators should be used to process the encoded data and measure the output state of an ansatz. The choice of the aforementioned operators plays a determinant role in the expressive power of the QML model. In this work we investigate how certain changes in the circuit structure change this expressivity. We introduce both numerical and analytical tools to explore the effect that these operators have in the overall performance of the QML model. These tools are based on previous work on the teacher-student scheme, the partial Fourier series and the averaged operator size. We focus our analysis on simple QML models with two and three qubits and observe that increasing the number of parameterized and entangling gates leads to a more expressive model for certain circuit structures. Also, on which qubit the measurement is performed affects the type of functions that QML models could learn. This work sketches the determinant role that the processing and measurement operators have on the expressive power of simple quantum circuits.
