Hamiltonian inverse engineering enables the design of protocols for specific quantum evolutions or target state preparation. Perfect state transfer (PST) and remote entanglement generation are notable examples, as they serve as key primitives in quantum information processing. However, Hamiltonians obtained through conventional methods often lack robustness against noise. Assisted by inverse engineering, we begin with a noise-resilient energy spectrum and construct a class of Hamiltonians, referred to as the dome model, that significantly improves the system's robustness against noise, as confirmed by numerical simulations. This model introduces a tunable parameter $m$ that modifies the energy-level spacing and gives rise to a well-structured Hamiltonian. It reduces to the conventional PST model at $m=0$ and simplifies to a SWAP model involving only two end qubits in the large-$m$ regime. To address the challenge of scalability, we propose a cascaded strategy that divides long-distance PST into multiple consecutive PST steps. Our work is particularly suited for demonstration on superconducting qubits with tunable couplers, which enable rapid and flexible Hamiltonian engineering, thereby advancing the experimental potential of robust and scalable quantum information processing.

Neural networks have been used as variational wave functions for quantum many-particle problems. It has been shown that the correct sign structure is crucial to obtain the high accurate ground state energies. In this work, we propose a hybrid wave function combining the convolutional neural network (CNN) and projected entangled pair states (PEPS), in which the sign structures are determined by the PEPS, and the amplitudes of the wave functions are provided by CNN. We benchmark the ansatz on the highly frustrated spin-1/2 $J_1$-$J_2$ model. We show that the achieved ground energies are competitive to state-of-the-art results.

Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The exiting researches on two-photon interference were mainly limited in one degree of freedom (DoF), hence it is still a challenge to realize the quantum interference in multiple DoFs. Here we demonstrate the HOM interference between two hyper-entangled photons in two DoFs of polarization and orbital angular momentum (OAM) for all the sixteen hyper-entangled Bell states. We observe hyper-entangled two-photon interference with bunching effect for ten symmetric states (nine Boson-Boson states, one Fermion-Fermion state) and anti-bunching effect for six anti-symmetric states (three Boson-Fermion states, three Fermion-Boson states). More interestingly, expanding the Hilbert space by introducing an extra DoF for two photons enables to transfer the unmeasurable external phase in the initial DoF to a measurable internal phase in the expanded two DoFs. We directly measured the symmetric exchange phases being $0.012 \pm 0.002$, $0.025 \pm 0.002$ and $0.027 \pm 0.002$ in radian for the three Boson states in OAM and the anti-symmetric exchange phase being $0.991 \pi \pm 0.002$ in radian for the other Fermion state, as theoretical predictions. Our work may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DoFs.

Calibration of the polarization basis between the transmitter and receiver is an important task in quantum key distribution (QKD). An effective polarization-basis tracking scheme will decrease the quantum bit error rate (QBER) and improve the efficiency of a polarization encoding QKD system. In this paper, we proposed a polarization-basis tracking scheme using only unveiled sifted key bits while performing error correction by legitimate users, rather than introducing additional reference light or interrupting the transmission of quantum signals. A polarization-encoding fiber BB84 QKD prototype was developed to examine the validity of this scheme. An average QBER of 2.32% and a standard derivation of 0.87% have been obtained during 24 hours of continuous operation.

Localization of wave functions in the disordered models can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is a smooth function of eigenenergy in the same phase, thus its non-smoothness can serve as strong evidence to determine the phase transition from the extended phase to the localized phase. However, logically, there is no fundamental reason that prohibits this Lyapunov exponent from being non-smooth in the localized phase. In this work, we show that if the localization centers are inhomogeneous in the whole chain and if the system possesses (at least) two different localization modes, the Lyapunov exponent can become non-smooth in the localized phase at the boundaries between the different localization modes. We demonstrate these results using several slowly varying models and show that the singularities of density of states are essential to these non-smoothness, according to the Thouless formula. These results can be generalized to higher-dimensional models, suggesting the possible delicate structures in the localized phase, which can revise our understanding of localization hence greatly advance our comprehension of Anderson localization.

Symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anti-commutators. This method is originated from the Lyapunov representation and would be very useful for cases that the anti-commutators among the state and its partial derivative exhibits periodic properties. As an application, we discuss a class of states, whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation problems.

A typical imaging scenario requires three basic ingredients: 1. a light source that emits light, which in turn interacts and scatters off the object of interest; 2. detection of the light being scattered from the object and 3. a detector with spatial resolution. These indispensable ingredients in typical imaging scenarios may limit their applicability in the imaging of biological or other sensitive specimens due to unavailable photon-starved detection capabilities and inevitable damage induced by interaction. Here, we propose and experimentally realize a quantum imaging protocol that alleviates all three requirements. By embedding a single-photon Michelson interferometer into a nonlinear interferometer based on induced coherence and harnessing single-pixel imaging technique, we demonstrate interaction-free, single-pixel quantum imaging of a structured object with undetected photons. Thereby, we push the capability of quantum imaging to the extreme point in which no interaction is required between object and photons and the detection requirement is greatly reduced. Our work paves the path for applications in characterizing delicate samples with single-pixel imaging at silicon-detectable wavelengths.

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our work reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.

The transmon, a fabrication-friendly superconducting qubit, remains a leading candidate for scalable quantum computing. Recent advances in tunable couplers have accelerated progress toward high-performance quantum processors. However, extending coherent interactions beyond millimeter scales to enhance quantum connectivity presents a critical challenge. Here, we introduce a hybrid-mode coupler exploiting resonator-transmon hybridization to simultaneously engineer the two lowest-frequency mode, enabling high-contrast coupling between centimeter-scale transmons. For a 1-cm coupler, our framework predicts flux-tunable $XX$ and $ZZ$ coupling strengths reaching 23 MHz and 100 MHz, with modulation contrasts exceeding $10^2$ and $10^4$, respectively, demonstrating quantitative agreement with an effective two-channel model. This work provides an efficient pathway to mitigate the inherent connectivity constraints imposed by short-range interactions, enabling transmon-based architectures compatible with hardware-efficient quantum tasks.

Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate ground state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity can also be applied to other models.

Exploring two-dimensional (2D) magnetic semiconductors with room temperature magnetic ordering and electrically controllable spin polarization is a highly desirable but challenging task for nanospintronics. Here, through first principles calculations, we propose to realize such a material by exfoliating the recently synthesized organometallic layered crystal Li$_{0.7}$[Cr(pyz)$_2$]Cl$_{0.7}$0.25$\cdot$(THF) (pyz = pyrazine, THF = tetrahydrofuran) [Science 370, 587 (2020)]. The feasibility of exfoliation is confirmed by the rather low exfoliation energy of 0.27 J/m$^2$, even smaller than that of graphite. In exfoliated Cr(pyz)$_2$ monolayer, each pyrazine ring grabs one electron from the Cr atom to become a radical anion, then a strong $d$-$p$ direct exchange magnetic interaction emerges between Cr cations and pyrazine radicals, resulting in room temperature ferrimagnetism with a Curie temperature of 342 K. Moreover, Cr(pyz)$_2$ monolayer is revealed to be an intrinsic bipolar magnetic semiconductor where electrical doping can induce half-metallic conduction with controllable spin-polarization direction.

Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the physics of quantum amplification is not fully explored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic quantum phenomena such as time crystals. Here we investigate the magnetic-field signal amplification by periodically driven $^{129}$Xe spins and observe signal amplification at frequencies of transitions between Floquet spin states. This "Floquet amplification" allows to simultaneously enhance and measure multiple magnetic fields with at least one order of magnitude improvement, offering the capability of femtotesla-level measurements. Our findings extend the physics of quantum amplification to Floquet systems and can be generalized to a wide variety of existing amplifiers, enabling a previously unexplored class of "Floquet amplifiers".

Quantum sensing utilizes quantum systems as sensors to capture weak signal, and provides new opportunities in nowadays science and technology. The strongest adversary in quantum sensing is decoherence due to the coupling between the sensor and the environment. The dissipation will destroy the quantum coherence and reduce the performance of quantum sensing. Here we show that quantum sensing can be realized by engineering the steady-state of the quantum sensor under dissipation. We demonstrate this protocol with a magnetometer based on ensemble Nitrogen-Vacancy centers in diamond, while neither high-quality initialization/readout of the sensor nor sophisticated dynamical decoupling sequences is required. Thus our method provides a concise and decoherence-resistant fashion of quantum sensing. The frequency resolution and precision of our magnetometer are far beyond the coherence time of the sensor. Furthermore, we show that the dissipation can be engineered to improve the performance of our quantum sensing. By increasing the laser pumping, magnetic signal in a broad audio-frequency band from DC up to 140 kHz can be tackled by our method. Besides the potential application in magnetic sensing and imaging within microscopic scale, our results may provide new insight for improvement of a variety of high-precision spectroscopies based on other quantum sensors.

Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength $W$ increases, the systems undergo a transition from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder $W_{c,1}$. Further increase of $W$, another transition from the marginal metal to an insulator occurs at $W_{c,2}$. Through highly accurate numerical procedures based on the recursive Green's function method and the exact diagonalization, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The intrinsic conductances follow an unorthodox single-parameter scaling law: They collapse onto two branches of curves corresponding to diffusive metal phase and insulating phase with correlation lengths diverging exponentially as $\xi\propto\exp[\alpha/\sqrt{|W-W_c|}]$ near transition points. Finite-size analysis of inverse participation ratios reveals that the states within the critical regime $[W_{c,1},W_{c,2}]$ are fractals of a universal fractal dimension $D=1.90\pm0.02$ while those in metallic (insulating) regime spread over the whole system (localize) with $D=2$ ($D=0$). A phase diagram in the parameter space illuminates the occurrence and evolution of diffusive metals, marginal metals, and the Anderson insulators.

We report the experimental measurement of the winding number in an unitary chiral quantum walk. Fundamentally, the spin-orbit coupling in discrete time quantum walks is implemented via birefringent crystal collinearly cut based on time-multiplexing scheme. Our protocol is compact and avoids extra loss, making it suitable for realizing genuine single-photon quantum walks at a large-scale. By adopting heralded single-photon as the walker and with a high time resolution technology in single-photon detection, we carry out a 50-step Hadamard discrete-time quantum walk with high fidelity up to 0.948$\pm$0.007. Particularly, we can reconstruct the complete wave-function of the walker that starts the walk in a single lattice site through local tomography of each site. Through a Fourier transform, the wave-function in quasi-momentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasi-momentum space and directly read out the winding numbers in different topological phases (trivial and non-trivial) in the presence of chiral symmetry. By introducing nonequivalent time-frames, we show that the whole topological phases in periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.

We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of two-dimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in momentum space. Such a dynamical topological invariant reflects the vorticity of dynamical vortices responsible for the DQPTs, and thus serves as a dynamical topological order parameter in two dimensions. We demonstrate that when the contour crosses topologically protected fixed points in the quench dynamics, an intimate connection can be established between the dynamical topological order parameter in two dimensions and those in one dimension. We further define a reduced rate function of the Loschmidt echo on the contour, which features non-analyticities at critical times and is sufficient to characterize DQPTs in two dimensions. We illustrate our results using the Haldane honeycomb model and the quantum anomalous Hall model as concrete examples, both of which have been experimentally realized using cold atoms.

Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the spin-qubits in solids with the accuracy required by fault-tolerant quantum computation under ambient conditions remains elusive. Here, we quantitatively characterize the source of noise during quantum gate operation and demonstrate strategies to suppress the effect of these. A universal set of logic gates in a nitrogen-vacancy centre in diamond are reported with an average single-qubit gate fidelity of 0.999952 and two-qubit gate fidelity of 0.992. These high control fidelities have been achieved at room temperature in naturally abundant 13C diamond via composite pulses and an optimized control method.

The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE algorithm for simulating extended systems. However, the numerical study of an one-dimensional (1D) infinite hydrogen chain using existing VQE algorithms shows a remarkable deviation of the ground state energy with respect to the exact full configuration interaction (FCI) result. Here, we present two schemes to improve the accuracy of quantum simulations for extended systems. The first one is a modified VQE algorithm, which introduces an unitary transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The second one is a Post-VQE approach combining VQE with the quantum subspace expansion approach (VQE/QSE). Numerical benchmark calculations demonstrate that both of two schemes provide an accurate enough description of the potential energy curve of the 1D hydrogen chain. In addition, excited states computed with the VQE/QSE approach also agree very well with FCI results.

K-means clustering, as a classic unsupervised machine learning algorithm, is the key step to select the interpolation sampling points in interpolative separable density fitting (ISDF) decomposition. Real-valued K-means clustering for accelerating the ISDF decomposition has been demonstrated for large-scale hybrid functional enabled \textit{ab initio} molecular dynamics (hybrid AIMD) simulations within plane-wave basis sets where the Kohn-Sham orbitals are real-valued. However, it is unclear whether such K-means clustering works for complex-valued Kohn-Sham orbitals. Here, we apply the K-means clustering into hybrid AIMD simulations for complex-valued Kohn-Sham orbitals and use an improved weight function defined as the sum of the square modulus of complex-valued Kohn-Sham orbitals in K-means clustering. Numerical results demonstrate that this improved weight function in K-means clustering algorithm yields smoother and more delocalized interpolation sampling points, resulting in smoother energy potential, smaller energy drift and longer time steps for hybrid AIMD simulations compared to the previous weight function used in the real-valued K-means algorithm. In particular, we find that this improved algorithm can obtain more accurate oxygen-oxygen radial distribution functions in liquid water molecules and more accurate power spectrum in crystal silicon dioxide compared to the previous K-means algorithm. Finally, we describe a massively parallel implementation of this ISDF decomposition to accelerate large-scale complex-valued hybrid AIMD simulations containing thousands of atoms (2,744 atoms), which can scale up to 5,504 CPU cores on modern supercomputers.

Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e. the eigenvectors of the density matrix with largest eigenvalues. However, due to the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with the minimal resource for ancillary qubits, in which only one frequency scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4$\times$4 density matrix, with the efficiency of 86.0% and fidelity of 0.90. This work shows the speed-up ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.