Arbitrary state preparation in quantum harmonic oscillators using neural networks

Preparing quantum states is a fundamental task in various quantum algorithms. In particular, state preparation in quantum harmonic oscillators (HOs) is crucial for the manipulation of qudits and the implementation of high-dimensional algorithms. In this work, we develop a general methodology for quantum state preparation in an HO coupled to an auxiliary qubit, guaranteeing that any target state is physically preparable. Both the qubit and the HO are driven by two lasers with time-dependent phase modulation. The modulation times and phase values are generated by a neural network whose input is the desired target state. In contrast to conventional quantum control approaches, this framework eliminates the need for per-instance optimization of the control protocol. Instead, the control parameters required to prepare an arbitrary quantum state of the HO are obtained directly from a single forward pass through the neural network. Specifically, we present results for preparing arbitrary qubit, qutrit, and qudit (n=4) states in the HO, achieving average fidelities of 99.99%, 99.5%, and 98.9%, respectively, across random target states.