Hierarchical Learning for Training Large-Scale Variational Quantum Circuits

Quantum Circuit Born Machines (QCBMs) are variational circuits whose goal is to encode a classical probability distribution in the measurement outcomes. With Hierarchical Learning (HL), we exploit the structure of the qubit mapping in this variational circuit to learn gates of a few qubits first before expanding to the whole system. Using adjoint simulation techniques on GPUs, we manage to load a 3 dimensional Gaussian distribution on 27 qubits to within 4% total variational distance (TVD). An additional benefit of this circuit structure is that it can reduce the number of gates required compared to other methods. To demonstrate the use, we benchmark the performance hierarchically learned circuits on IBM hardware with FireOpal optimization.