Scalable and Programmable Phononic Network Using Vibrational Modes of Trapped Ions

Trapped ion system is one of the leading physical platforms to realize a practical quantum computer and quantum simulator. Recently, the vibrational degrees of freedom of trapped ions have been extensively studied and are getting attentions for the application to quantum information processing with continuous variables [1]. In particular, phonons in multiple vibrational modes can be configured as bosonic networks that can perform boson sampling to reveal quantum advantage. Differently from photonic systems the phonon number states in the phononic systems can be deterministically prepared and detected and the total number of phonons is well conserved for all the collective modes except the center of mass mode. However, to our knowledge, there has been no experimental realization of a phononic network with more than two modes. Here we present the phononic network that consists of up to four modes with the capability of programming an arbitrary network as well as the deterministic preparation and detection. In the network, beam splitting operations between any pairs of modes are implemented through the coupling with ion-qubits [2]. As the benchmark of the performance of the phononic network, we demonstrated the algorithms of tomography for any multi-modes phononic states in a single measurement configuration [3]. Our experiment demonstrates a clear and novel pathway to scale up a phononic network for various quantum information processing beyond the limitations of classical and other quantum systems.

[1] W. Chen, J. Gan, J.-N. Zhang, D. Matuskevich, and K. Kim, Chin. Phys. B 30, 060311 (2021).

[2] W. Chen, et al., arXiv:2207.06115 (2022)

[3] L. Banchi, W. S. Kolthammer, and M. Kim, Phys. Rev. Lett. 121, 250402 (2018).