**Introduction**

The **Dynamical Casimir Effect (DCE) **consists in the generation of photons out of the vacuum of a quantum field by means of the non-adiabatic modulation of boundary conditions -e.g. a mirror oscillating at speeds comparable to the speed of light. Predicted in 1970, an experimental demonstration remained elusive until 2011, when it was implemented in a superconducting circuit architecture. In addition to its fundamental interest, it has been shown that the radiation generated in the DCE displays entanglement and other forms of quantum correlations, which poses the question of its utility as a resource for the heralded **quantum-technological revolution**. In this talk, we establish a **bridge between **multimode parametric amplification induced by the modulation of boundary conditions - for which **DCE **is a paradigmatic case- and quantum computing devices.

**Methods**

Bipartite and multipartite entanglement generation by means of multimode parametric amplification has been very recently experimentally demonstrated with superconducting-circuits technology. This paves the way to quantum computing applications. For instance, we consider **boson sampling (BS)**. BS has recently gained a great deal of attention, as it solves a tailor-made problem that is widely believed to be intractable in any classical device. We consider **Gaussian BS (GBS) **and in particular **scattershot BS**, a generalization of the original BS problem which possesses similar computational complexity. We show that GBS can be implemented in a superconducting circuit architecture by exploiting multimode parametric amplification.

**Results**

We propose a setup consisting of two superconducting resonators coupled through a superconducting quantum interferometric device **(SQUID)**. The resonators possess different lengths and thus different energy spectra and the SQUID plays the role of a shared tunable mirror-like boundary condition. The modulation of the external magnetic flux threading the SQUID implements an effective motion of the mirror which results in multimode parametric amplification. We show that suitable choices of the SQUID pumping are able to implement the operations of a GBS. In this way, we illustrate how the DCE can be exploited as a quantum simulator of GBS.

References

[1] C.W. Sandbo Chang, M. Simoen, J. Aumentado, C. S., P. Forn-Díaz, A. M. Vadiraj et al. arXiv: 1709.00083.

[2] B. Peropadre, J. Hu, C.S. Sci. Rep. **8**, 3751 (2018).

Quantum information processing and computing , Fundamental science for quantum technologies , Superconducting circuits