Wei Yi

The Liouvillian skin effect describes the boundary affinity of Liouvillian eignemodes that originates from the intrinsic non-Hermiticity of the Liouvillian superoperators. Dynamically, it manifests as directional flow in the transient dynamics, and the accumulation of population near open boundaries at long times. Intriguingly, similar dynamic phenomena exist in the well-known process of optical pumping, where the system is driven into a desired state (or a dark-state subspace) through the interplay of dissipation and optical drive. In this work, we show that typical optical pumping processes can indeed be understood in terms of the Liouvillian skin effect. By studying the Liouvillian spectra under different boundary conditions, we reveal that the Liouvillian spectra of the driven-dissipative pumping process sensitively depend on the boundary conditions in the state space, a signature that lies at the origin of the Liouvillian skin effect. Such a connection provides insights and practical means for designing efficient optical-pumping schemes through engineering Liouvillian gaps under the open-boundary condition. Based on these understandings, we show that the efficiency of a typical side-band cooling scheme for trapped ions can be dramatically enhanced by introducing counterintuitive dissipative channels. Our results provide a useful perspective for optical pumping, with interesting implications for state preparation and cooling.

Non-Hermitian skin effect (NHSE) describes the exponential localization of all eigenstates toward boundaries in non-Hermitian systems, and has attracted intense research interest of late. Here we theoretically propose a scheme in which the NHSE significantly impacts the external motion of a single trapped ion through complex spin-motion dynamics. On the one hand, we show the competition between the NHSE and the coherent Bloch dynamics. On the other hand, since the NHSE manifests as a non-reciprocal flow in occupied phonon modes, we demonstrate that such dynamics can have potential applications in cooling and sensing. Our proposal can be readily implemented using existing experimental techniques, and offers a scalable (in terms of the available ions and phonon modes) simulation platform for relevant non-Hermitian physics.

Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical problems. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art experiments. Here we demonstrate highly successful classifications of real-life images using photonic qubits, combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization. Specifically, we focus on binary classification for hand-written zeroes and ones, whose features are cast into the tensor-network representation, further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states. We then demonstrate image classification with a high success rate exceeding 98%, through successive gate operations and projective measurements. Although we work with photons, our approach is amenable to other physical realizations such as nitrogen-vacancy centers, nuclear spins and trapped ions, and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation, thereby setting the stage for quantum-enhanced multi-class classification.