The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect (NHSE) attracts wide attention due to its novel physics and promising applications. Here, we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena, including the dynamical chiral phenomenon, the funneling phenomenon on the domain wall, and the anomalous reflection on the phase impurity. Furthermore, we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum (NISQ) devices. Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.
The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect (NHSE) attracts wide attention due to its novel physics and promising applications. Here, we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena, including the dynamical chiral phenomenon, the funneling phenomenon on the domain wall, and the anomalous reflection on the phase impurity. Furthermore, we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum (NISQ) devices. Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.
Abstract Non-Hermitian physics has attracted considerable attention in the recent years, in particular the non-Hermitian skin effect (NHSE) for its extreme sensitivity and non-locality. While the NHSE has been physically observed in various classical metamaterials and even ultracold atomic arrays, its highly-nontrivial implications in many-body dynamics have never been experimentally investigated. In this work, we report the first observation of the NHSE on a universal quantum processor, as well as its characteristic but elusive Fermi skin from many-fermion statistics. To implement NHSE dynamics on a quantum computer, the effective time-evolution circuit not only needs to be non-reciprocal and non-unitary, but must also be scaled up to a sufficient number of lattice qubits to achieve spatial non-locality. We show how such a non-unitary operation can be systematically realized by post-selecting multiple ancilla qubits, as demonstrated through two paradigmatic non-reciprocal models on a noisy IBM quantum processor, with clear signatures of asymmetric spatial propagation and many-body Fermi skin accumulation. To minimize errors from inevitable device noise, time evolution is performed using a trainable optimized quantum circuit produced with variational quantum algorithms. Our study represents a critical milestone in the quantum simulation of non-Hermitian lattice phenomena on present-day quantum computers, and can be readily generalized to more sophisticated many-body models with the remarkable programmability of quantum computers.
Abstract Quantum walks hold enormous potential applications in various areas such as quantum computing and quantum simulation. Discrete-time quantum walks on a ladder offer greater prospects compared to traditional quantum walks, especially in addressing physical problems in higher-dimension coupled systems. Here we give an experimental proposal of quantum walks on a two-leg ladder using linear optics, and further apply it to non-Hermitian systems by introducing loss-based non-unitary evolutions. Non-Hermitian systems under nonreciprocity-induced evolution present an exotic phenomenon, known as the non-Hermitian skin effect (NHSE). In a two-leg non-Hermitian system with the same preferred direction of NHSE, the direction has recently been found to reverse when interchain couplings are introduced. Based on quantum walks on a ladder, we also propose an experimentally feasible scheme to demonstrate the direction reversal of NHSE. Through the simulated results we show that particles on each chain accumulate to the preferred boundary driven by nonreciprocal hopping, while particles are transported in the opposite direction when interchain hopping is allowed, clearly demonstrating the existence of reversed NHSE. Our work further expands the application of the quantum walk platform and opens a door for the experimental investigation of reversed NHSE.
The interplay between topology and non-Hermiticity gives rise to exotic dynamic phenomena that challenge conventional wave-packet propagation and entanglement dynamics. While recent studies have established the non-Hermitian skin effect (NHSE) as a key mechanism for anomalous wave dynamics, a unified framework for characterizing and controlling entanglement evolution in non-Hermitian topological systems remains underdeveloped. Here, by combining theory and experiments, we demonstrate that entanglement entropy (EE) and transport currents serve as robust dynamic probes to distinguish various non-Hermitian topological regimes. Using a generalized non-Hermitian Su-Schrieffer-Heeger model implemented in an acoustic analog platform, we identify three dynamic phases, bulk-like, edge-like, and skin-like regimes, each exhibiting unique EE signatures and transport characteristics. In particular, skin-like dynamics exhibit periodic information shuttling with finite, oscillatory EE, while edge-like dynamics lead to complete EE suppression. We further map the dynamic phase diagram and show that EE scaling and temporal profiles directly reflect the competition between coherent delocalization and NHSE-driven localization. Our results establish a programmable approach to steering entanglement and transport via tailored non-Hermitian couplings, offering a pathway for engineering quantum information dynamics in synthetic phononic, photonic, and quantum simulators.
The non-Hermitian skin effect (NHSE), referring to the anomalous localization of eigenstates, has been widely discussed in single-particle systems. However, the interplay between the interacting NHSE and the quantum optical phenomena remains elusive. Here, We present the non-Hermitian quantum walks of strongly correlated photon pairs. Through studying the dynamic behavior of the photon pairs in the nonreciprocal Bose-Hubbard chain, we theoretically demonstrate the interplay between interactions and the NHSE. When launching two non-entangled photons, the photons exhibit the nonreciprocal bunching effect, which can be suppressed by the interactions. When launching two path-entangled photons, the interactions can not only suppress but reverse the nonreciprocal bunching. In stark contrast to the common wisdom that the NHSE suppresses the entanglement of the quantum many-body system, the entanglement of the photons here can be significantly enhanced. Our results reveal that many-body interactions and entanglement significantly restrain the non-Hermitian nonreciprocal quantum dynamics, offering insights into the interplay between many-body quantum entanglement and non-Hermitian physics. The non-Hermitian skin effect, which nonreciprocally accumulates particles at the boundary, generally suppresses entanglement by constraining global correlations. Here, the authors demonstrate that interactions can suppress nonreciprocal bunching, while entangled photons can reverse bunching direction, leading to enhanced entanglement.
Non-Hermitian Hamiltonians are widely used in describing open systems with gain and loss, among which a key phenomenon is the non-Hermitian skin effect. Here we report an experimental scheme to realize a two-dimensional (2D) discrete-time quantum walk with non-Hermitian skin effect in a single trapped ion. It is shown that the coin and 2D walker states can be labeled in the spin of the ion and the coherent-state lattice of the ion motion, respectively. We numerically observe a directional bulk flow, whose orientations are controlled by dissipative parameters, showing the emergence of the non-Hermitian skin effect. We then discuss an experimental implementation of our scheme in a laser-controlled trapped Ca+ ion. Our experimental proposal may be applicable to research of dissipative quantum walk systems and may be able to generalize to other platforms, such as superconducting circuits and atoms in cavity.
Non-Hermitian systems under nonreciprocity-induced evolution present an exotic phenomenon, known as the non-Hermitian skin effect. Yet, the control mechanisms and the generalized Brillouin zone in disordered systems have not been fully understood. Here, using Floquet quantum-walk models with disorder, we demonstrate effective control of the direction of the non-Hermitian skin effect in both one- and two-dimensional systems. Once the disorder strength exceeds a critical threshold, the direction of the skin effect is reversed. We develop a modified generalized Brillouin zone theory that correctly predicts skin effect reversal. Furthermore, we also investigate how the direction of the non-Hermitian skin effect depends on the disorder strength in each subsystem of the two-dimensional quantum walk. Our work paves the way for the design of quantum transport devices in quantum simulation platforms.