Measurement-based preparation of stable coherent states of a Kerr parametric oscillator.

Kerr parametric oscillators (KPOs) have attracted increasing attention in terms of their application to quantum information processing and quantum simulations. The state preparation and measurement of KPOs are typical requirements when used as qubits. The methods previously proposed for state preparations of KPOs utilize modulation of external fields such as a pump and drive fields. We study the stochastic state preparation of stable coherent states of a KPO with homodyne detection, which does not require modulation of external fields, and thus can reduce experimental efforts and exclude unwanted effects of possible imperfection in control of external fields. We quantitatively show that the detection data, if averaged over an optimal averaging time to decrease the effect of measurement noise, has a strong correlation with the state of the KPO, and therefore can be used to estimate the state (stochastic state preparation). We examine the success probability of the state estimation taking into account the measurement noise and bit flips. Moreover, the proper range of the averaging time to realize a high success probability is obtained by developing a binomial-coherent-state model, which describes the stochastic dynamics of the KPO under homodyne detection.