In this paper, we propose a simple neural net that requires only O(nlog(2)k) 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.