Steering the Fidelity in State Preparation on Noisy Bosonic Systems with Risk-Seeking Optimization

Riccardo Piantoni, Riccardo Pellini, Maurizio Ferrari Dacrema, Paolo Cremonesi

In order to execute quantum algorithms on bosonic quantum computers, it is necessary to encode their inputs into a desired target quantum state, with a process called state preparation. In real settings, state preparation methods operate in stochastic scenarios, where the prepared state is represented as a mixed state, that is a probabilistic ensemble of pure states. Therefore, existing state preparation methods optimize a variational ansatz by averaging over all possible sequences of photon loss events contained in the prepared ensemble, yielding an output state which approximates the desired target with a certain average fidelity. Such an approach, however, does not take into account directly the distribution of fidelities across states in the ensemble. In this work, we aim to maximize the fidelity of only a subset of pure states sampled from the prepared ensemble, at the cost of reducing the average fidelity overall. This trade-off is relevant when the goal is to obtain high-fidelity states with a certain probability, rather than maximizing the average fidelity of the prepared ensemble. We borrow and adapt objective functions from risk-sensitive optimization, a framework that…