Training an analog quantum bosonic neural network through backpropagation

In the quest for a quantum neural network, quantum systems have been utilized either through parameterized quantum circuits or analog quantum reservoirs. The latter can be implemented on qubit ensembles or bosonic systems, which offer a larger Hilbert space for feature embedding. However, quantum reservoir computing (QRC) is limited by the fact that training occurs after measurement, thus requiring a large number of observables to be measured and ultimately reducing its expressivity. In this work, we propose a method for training complex drive and interaction parameters directly within an analog bosonic quantum system. Our results show that these parameters can be optimized via backpropagation, reducing the number of observables to measure compared to QRC. Furthermore, we demonstrate that a trained system can learn tasks of increasing complexity, with data encoding in entanglement drives proving to be the most efficient. We introduce a technique for encoding higher-dimensional data and show that using local variables in the loss function, rather than global ones, accelerates training convergence, likely due to the mitigation of barren plateaus.