Panadero Iván, Ban Yue, Espinós Hilario, Puebla Ricardo, Casanova Jorge, Torrontegui Erik
Departamento de Física, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés, Spain.
Arquimea Research Center, Camino las Mantecas s/n, 38320, Santa Cruz de Tenerife, Spain.
Sci Rep. 2024 Dec 30;14(1):31669. doi: 10.1038/s41598-024-81436-5.
Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decomposition of the generated output and systematically benchmarked with the aid of a teacher-student scheme. While the maximal expressive power increases with the depth of the network and the number of qubits, it is fundamentally bounded by the data encoding mechanism. However, we show that the measurement of the network generated output drastically modifies the attainability of this bound. Global-entangling measurements on the network can saturate the maximal expressive bound leading to an enhancement of the approximation capabilities of the network compared to local readouts of the individual qubits in non-entangling networks. We attribute this enhancement to a larger survival set of Fourier harmonics when decomposing the output signal.
考虑一个由一系列嵌套量子比特旋转组成的通用深度神经网络，这些旋转通过可调整的数据重新上传来完成，我们分析了它的表现力。在回归任务中近似连续函数的这种能力通过对生成输出的部分傅里叶分解进行量化，并借助师生方案进行系统基准测试。虽然最大表达能力随着网络深度和量子比特数量的增加而提高，但它从根本上受到数据编码机制的限制。然而，我们表明，对网络生成输出的测量会极大地改变这个界限的可达性。与非纠缠网络中单个量子比特的局部读出相比，对网络进行全局纠缠测量可以使最大表达界限饱和，从而提高网络的近似能力。我们将这种增强归因于在分解输出信号时傅里叶谐波的更大生存集。
