Yong-Jian Han

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann geometric phase offers a natural extension of pure-state paradigms and can exhibit a topological character. However, observation of this invariant is impeded by the incompatibility between Uhlmann parallel transport and Hamiltonian dynamics, as well as the difficulty of preparing topologically nontrivial mixed states. To address this challenge, we report an experimentally accessible protocol for directly measuring the mixed-state topological invariant. By engineering controlled nonunitary dynamics in a photonic quantum walk, we prepare topologically nontrivial mixed states from a trivial initial state. Then, by machine learning the full density matrix in momentum space, we directly extract the quantized geometric phase of the nontrivial mixed states. Furthermore, we observe that this transition of the quantized mixed-state topological invariant from a trivial to a nontrivial value is closely associated with the emergence of a topological kink structure. These results highlight a geometric phase framework that naturally extends to open quantum systems both in and out of thermal equilibrium.

Quantum memories for light are essential building blocks for quantum repeaters and quantum networks. Integrated operations of quantum memories could enable scalable application with low-power consumption. However, the photonic quantum storage lifetime in integrated devices has so far been limited to tens of microseconds, falling short of the requirements for practical applications. Here, we demonstrate quantum storage of photonic qubits for 1.021 milliseconds based on a laser-written optical waveguide fabricated in a ¹⁵¹ Eu ³⁺ :Y ₂ SiO ₅ crystal. Spin dephasing of ¹⁵¹ Eu ³⁺ is mitigated through dynamical decoupling applied via on-chip electric waveguides, and we obtain a storage efficiency of 12.0 ± 0.5% at 1.021 milliseconds, which is a demonstration of integrated quantum memories that outperforms the efficiency of a simple fiber delay line. Such long-lived waveguide-based quantum memory could support applications in quantum repeaters, and further combination with critical magnetic fields could enable potential application as transportable quantum memories.

Noise-enhanced applications in open quantum walk (QW) have recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (~97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network–based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Photonic quantum computation plays an important role and offers unique advantages. Two decades after the milestone work of Knill-Laflamme-Milburn, various architectures of photonic processors have been proposed, and quantum advantage over classical computers has also been demonstrated. It is now the opportune time to apply this technology to real-world applications. However, at current technology level, this aim is restricted by either programmability in bulk optics or loss in integrated optics for the existing architectures of processors, for which the resource cost is also a problem. Here we present a von-Neumann-like architecture based on temporal-mode encoding and looped structure on table, which is capable of multimode-universal programmability, resource-efficiency, phase-stability and software-scalability. In order to illustrate these merits, we execute two different programs with varying resource requirements on the same processor, to investigate quantum signature of chaos from two aspects: the signature behaviors exhibited in phase space (13 modes), and the Fermi golden rule which has not been experimentally studied in quantitative way before (26 modes). The maximal program contains an optical interferometer network with 1694 freely-adjustable phases. Considering current state-of-the-art, our architecture stands as the most promising candidate for real-world applications.

The quantum spin liquid (QSL) state of Kitaev-like materials, such as iridium oxides A ₂IrO₃ and α-RuCl₃, has been explored in depth. The half-filled Kitaev–Hubbard model with bond-dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard U. We suggest that a promising approach to finding QSL states is by finding iridium oxides that are near the Mott insulator transition.

The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.

Demonstrating quantum advantage on noisy quantum devices is one of the most important tasks of quantum computing research in the near future. Random quantum circuit sampling is proposed as the most promising approach to the task and has been implemented in experiments for achieving quantum advantage. A series of encouraging computational complexity results, based on some plausible assumptions, show that this task is impossible to complete efficiently by classical computers. However, in practical experiments on noisy quantum devices, the approximate average‐case hardness and the effects of the noise need to be further checked. The competition between the classical simulation algorithm (mainly based on tensor network algorithms) and noisy quantum devices is the explicit way to understand quantum advantage in practice. This review briefly overviews the computational complexity arguments for the hardness of classical simulation of random quantum circuits sampling, then focus on various methods of classical simulation of quantum circuits based on tensor network method.

Exceptional points (EPs), at which more than one eigenvalue and eigenvector coalesce, are unique spectral features of non-Hermiticity (NH) systems. They exist widely in open systems with complex energy spectra. We experimentally demonstrate the appearance of paired EPs in a periodical-driven degenerate optical cavity along the synthetic orbital angular momentum dimension with a tunable parameter. The complex-energy band structures and the key features of EPs, i.e., their bulk Fermi arcs, parity-time symmetry breaking transition, energy swapping, and half-integer band windings, are directly observed by detecting the wavefront angle–resolved transmission spectrum. Our results demonstrate the flexibility of using the photonic synthetic dimensions to implement NH systems beyond their geometric dimension and EP-based sensing.