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A symmetry of a state$|\psi ⟩$is a unitary operator of which$|\psi ⟩$is an eigenvector. When$|\psi ⟩$is an unknown state supplied by a black-box oracle, the state’s symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum–classical learning scheme to systematically probe for symmetries of$|\psi ⟩$with noa prioriassumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes.

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.

Chirality, or handedness, is a geometrical property denoting a lack of mirror symmetry. Chirality is ubiquitous in nature and is associated with the nonreciprocal interactions observed in complex systems ranging from biomolecules to topological materials. Here, we demonstrate that chiral arrangements of dipole-coupled atoms or molecules can facilitate the helicity-dependent superradiant emission of light. We show that the collective modes of these systems experience an emergent spin-orbit coupling that leads to chirality-dependent photon transport and nontrivial topological properties. These phenomena are fully described within the electric dipole approximation, resulting in very strong optical responses. Our results demonstrate an intimate connection between chirality, superradiance, and photon helicity and provide a comprehensive framework for studying electron transport dynamics in chiral molecules using cold atom quantum simulators.