Bosonic Non-linearity with Trapped Ions

Mechanical oscillators represented by the bosonic motional modes of trapped ions are a promising candidate to realize continuous-variable quantum information processing. However, universal control of these modes require non-linear operations, such as cubic phase gates or exponential swap (E-SWAP) gates. Here, we report the implementation of the cubic phase gate evolution by applying a series of spin dependent displacement pulses to a single mode of motion [1]. We also discuss our experimental progress towards the demonstration of the E-SWAP operation for two motional modes of the trapped ions controlled by the ion internal state.

[1] K. Park and R. Filip, npj Quantum Inf. 10 25 (2024).