A Simple Quantum Neural Net with a Periodic Activation Function
This work addresses the challenge of efficient quantum neural networks for machine learning, but it appears incremental as it builds on existing quantum computing concepts with a specific activation function.
The authors tackled the problem of designing a quantum neural network with reduced resource requirements, achieving a network that uses O(n log2 k) qubits and O(nk) quantum gates, and demonstrated its potential for exponential speedup over classical counterparts on iris and breast cancer datasets.
In this paper, we propose a simple neural net that requires only $O(nlog_2k)$ number of qubits and $O(nk)$ quantum gates: Here, $n$ is the number of input parameters, and $k$ is the number of weights applied to these parameters in the proposed neural net. We describe the network in terms of a quantum circuit, and then draw its equivalent classical neural net which involves $O(k^n)$ nodes in the hidden layer. Then, we show that the network uses a periodic activation function of cosine values of the linear combinations of the inputs and weights. The backpropagation is described through the gradient descent, and then iris and breast cancer datasets are used for the simulations. The numerical results indicate the network can be used in machine learning problems and it may provide exponential speedup over the same structured classical neural net.