Universal Control with Weak Kerr Cavities

Cavities with a weak Kerr nonlinearity can be used to prepare single photon states in the presence of a loss much larger than their nonlinearity. Two necessary ingredients are large displacements and two-photon driving [1]. Here, we prove that these systems can be used for universal control in arbitrary finite dimensions. Moreover, we show that the requirement of two-photon driving can be relaxed. We present two novel schemes, one based on Trotter-Suzuki decomposition, and another using gradient-based optimization to find control pulses for a desired gate. These schemes utilize large displacements while circumventing the need for considering large photon number states, thus taking advantage of the nonlinear effects while keeping the computation tractable.

[1] A. Lingenfelter, D. Roberts, and A. A. Clerk, Unconditional Fock State Generation Using Arbitrarily Weak Photonic Nonlinearities, arXiv:2103.12041 [quant-ph] (2021).