Variational Quantum Neural Programming

Variational algorithms used for quantum simulations are naturally resistant to some errors and are therefore well suited for NISQ devices. Their application in quantum machine learning has yielded methods for data classification, compression and generation such as the quantum autoencoder. Using inspiration from neural programming in classical machine learning, we show how a quantum program can be learned through gradient descent. Quantum programs are usually defined operationally over a variable number of qubits while variational quantum algorithms are typically meant to operate on fixed-size quantum registers. We define a class of differentiable ansatz that can operate on an arbitrary number of qubits and be used to reproduce algorithms such as the quantum Fourier transform and phase estimation using only a set of examples on few qubits. We generalize this class of ansatz to explore the space of shallow algorithms.