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Abstract In recent years, there has been considerable focus on exploring driven-dissipative quantum systems, as they exhibit distinctive dissipation-stabilized phases. Among themdissipative time crystalis a unique phase emerging as a shift from disorder or stationary states to periodic behaviors. However, understanding the resilience of these non-equilibrium phases against quantum fluctuations remains unclear. This study addresses this query within a canonical parametric quantum optical system, specifically, a multi-mode cavity with self- and cross-Kerr non-linearity. Using mean-field (MF) theory we obtain the phase diagram and delimit the parameter ranges that stabilize a non-stationary limit-cycle phase. Leveraging the Keldysh formalism, we study the unique spectral features of each phase. Further, we extend our analyses beyond the MF theory by explicitly accounting for higher-order correlations through cumulant expansions. Our findings unveil insights into the modifications of the open quantum systems phases, underscoring the significance of quantum correlations in non-equilibrium steady states. Importantly, our results conclusively demonstrate the resilience of the non-stationary phase against quantum fluctuations, rendering it a dissipation-induced genuine quantum synchronous phase. 

Blind quantum computing is a promising application of distributed quantum systems, in which a client can perform computations on a remote server without revealing any details of the applied circuit. Although the most promising realizations of quantum computers are based on various matter-qubit platforms, implementing blind quantum computing on matter qubits remains a challenge. Using silicon-vacancy (SiV) centers in nanophotonic diamond cavities with an efficient optical interface, we demonstrated a universal quantum gate set consisting of single- and two-qubit blind gates over a distributed two-node network. Using these ingredients, we performed a distributed algorithm with blind operations across our two-node network, proving a route to develop blind quantum computation with matter qubits in distributed, modular architectures.