The realization of error-corrected logical qubits and operations between them is the key to performing useful quantum computation. The system of vibrational modes in ions is a good candidate for the realization of logical qubits. Using stimulated Raman transition to realize beam-splitter interactions between collective vibrational phonon modes and thereby realizing quantum entanglement between phonon modes are important steps to realize operations between logical qubits. Such entanglement manipulations for multiple modes and squeezed states can be used to generate continuous-variable cluster states. Furthermore, by preparing bosonic codes as vibrational states of ions and utilizing the beam-splitter interaction described above, it is possible to implement gate operations across multiple modes.

To generate states that can be used for error correction in vibrational modes, experiments were conducted to generate vibrational squeezed states using reservoir engineering (Figs. 2 and 3). Figure 2 shows the blue-side band Rabi oscillation results for the squeezing parameter r = 0.00, i.e., no squeezing at all (vibrational ground state), and shows the shape of a damped oscillation. On the other hand, Figure 3 shows the experimental results for the squeezing parameter r=0.86, which reflects the characteristics of blue-sideband Rabi oscillation for the squeezed state.

In this regard, improvement of the vibrational state coherence is considered necessary to obtain even higher fidelity. In addition, we have already realized a beam-splitter interaction between vibration modes, and it is considered necessary to improve the vibrational state coherence in the same way to improve the fidelity of the beam-splitter interaction. In this study, we evaluated the vibrational state coherence and obtained a value of 1.5 ms as the decay time of the vibrational state Ramsey interference. In the future, it will be necessary to improve this value by about one order of magnitude, and possible measures include improving the accuracy of AC voltage amplitude stabilization for trapping in the radial direction, using modes other than the center-of-mass mode, and using an axial vibration mode. We are currently preparing for these measures.