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Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the hard-to-control environments and cannot last for too long times. An alternative approach is to use quantum simulation with the closed system, whereas how to simulate non-Hermitian Hamiltonian dynamics remains a great challenge. To tackle this problem, we propose a protocol which combines a dilation method with the variational quantum algorithm. The dilation method is used to transform a non-Hermitian Hamiltonian into a Hermitian one through an exquisite quantum circuit, while the variational quantum algorithm is for efficiently approximating the complex entangled gates in this circuit. As a demonstration, we apply our protocol to simulate the dynamics of an Ising chain with nonlocal non-Hermitian perturbations, which is an important model to study quantum phase transition at nonzero temperatures. The numerical simulation results are highly consistent with the theoretical predictions, revealing the effectiveness of our protocol. The presented protocol paves the way for practically simulating small-scale non-Hermitian dynamics., Comment: 9 pages, 5 figures

Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises for improving the metrology performance. Our scheme can automatically alter the parameter encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. Through comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments., Comment: 9 pages, 5 figures

Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires rather complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC--the Fibonacci anyon system--lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can realize the Fibonacci anyon system, and construct the topologically protected logical spaces with the Fibonacci anyons. Via braiding the Fibonacci anyons, we can implement universal quantum gates on the logical space. Our proposal is platform-independent. As a demonstration, we implement a topological Hadamard gate on a logical qubit through a sequence of $15$ braiding operations of three Fibonacci anyons with merely $2$ nuclear spin qubits. The gate fidelity reaches 97.18% by randomized benchmarking. We further prove by experiment that the logical space and Hadamard gate are topologically protected: local disturbances due to thermal fluctuations result in a global phase only. Our work is a proof of principle of TQC and paves the way towards fault-tolerant quantum computation., Comment: 8 pages, 4 figures

Entanglement is a key property in the development of quantum technologies and in the study of quantum many-body simulations. However, entanglement measurement typically requires quantum full-state tomography (FST). Here we present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians. Instead of FST, it can learn comprehensive entanglement quantities from single-qubit or two-qubit Pauli measurements, such as R\'enyi entropy, partially-transposed (PT) moments, and coherence. It is also exciting that our neural network is able to learn the future entanglement dynamics using only single-qubit traces from the previous time. In addition, we perform experiments using a nuclear spin quantum processor and train an adoptive neural network to study entanglement in the ground and dynamical states of a one-dimensional spin chain. Quantum phase transitions (QPT) are revealed by measuring static entanglement in ground states, and the entanglement dynamics beyond measurement time is accurately estimated in dynamical states. These precise results validate our neural network. Our work will have a wide range of applications in quantum many-body systems, from quantum phase transitions to intriguing non-equilibrium phenomena such as quantum thermalization., Comment: 5 pages, 4 figures. All comments are welcome

In open quantum systems, the precision of metrology inevitably suffers from the noise. {In Markovian open quantum dynamics, the precision can not be improved by using entangled probes although the measurement time is effectively shortened.} However, it was predicted over one decade ago that in a non-Markovian one, the error can be significantly reduced by the quantum Zeno effect (QZE) [Chin, Huelga, and Plenio, Phys. Rev. Lett. \textbf{109}, 233601 (2012)]. In this work, we apply a recently-developed quantum simulation approach to experimentally verify that entangled probes can improve the precision of metrology by the QZE. Up to $n=7$ qubits, we demonstrate that the precision has been improved by a factor of $n^{1/4}$, which is consistent with the theoretical prediction. Our quantum simulation approach may provide an intriguing platform for experimental verification of various quantum metrology schemes., Comment: 6 pages, 4 figures

Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH) model using the nuclear magnetic resonance processor. Unlike the usual experiments using auxiliary qubits, we develop a stochastic average approach based on the stochastic Schr\"odinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifies implementation of quantum gates. We demonstrate the stability of dynamical topology against weak noise, and observe two types of dynamical topological transitions driven by strong noise. Moreover, a region that the emergent topology is always robust regardless of the noise strength is observed. Our work shows a feasible quantum simulation approach for dissipative quantum dynamics with stochastic Schr\"odinger equation and opens a route to investigate non-Hermitian dynamical topological physics.

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ans\"atze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks., Comment: 9 pages, 7 figures

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem. In this work, we extend and apply the recently proposed robust control technique of inverse geometric optimization to time-dependent noises by working it in the filter-function formalism. The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density. This then effectively reduces the noise susceptibility of the controlled system evolution. We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models, and thus will find practical applications for current physical platforms., Comment: 5+7 pages, 3+4 figures

We performed a first-principles study of the tunneling anisotropic magneto-resistance (TAMR) in Ag(Ir,Pt)$/$MgO$/$Fe junctions. Enhanced TAMR with ideal and skewed fourfold angular dependence is found in-plane and out-of-plane TAMR of the system, respectively, which shows simple barrier thickness dependency with number around 10\% in some junctions. The complex angular dependency of the interfacial resonant states due to the spin-orbit coupling should be responsible to the complex and enhanced TAMR found in these junctions., Comment: 6 pages, 8 figures

The recent research of topological photonics has not only proposed and realized novel topological phenomena such as one-way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with high-performance indexes which are immune to fabrication errors such as defects or disorders. Photonic crystals, which are periodic optical structures with the advantages of good light field confinement and multiple adjusting degrees of freedom, provide a powerful platform to control the flow of light. With the topology defined in the reciprocal space, photonic crystals have been widely used to reveal different topological phases of light and demonstrate topological photonic functionalities. In this review, we present the physics of topological photonic crystals with different dimensions, models and topological phases. The design methods of topological photonic crystals are introduced. Furthermore, we review the applications of topological photonic crystals in passive and active photonics. These researches pave the way of applying topological photonic crystals in practical photonic devices.

Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers are expected. However, a crystal can be either topologically trivial or nontrivial, depending on its detailed configuration, and one needs to carefully design the structure and calculate its topological invariant before the actual applications. Here, we theoretically study and experimentally demonstrate the second Chern crystal in a four-dimensional space by introducing two extra synthetic translation dimensions. Due to the inherently nontrivial topology of the synthetic translation space, this abstract four-dimensional crystal is guaranteed to be topologically nontrivial regardless of the detailed configuration. The dimensional hierarchy of gapless boundary modes can be deduced by dimension reduction. Remarkably, one-dimensional gapless dislocation modes are observed and their robustness is confirmed in our experiments. This ubiquitous phenomenon in synthetic translation space provides perspectives on the findings of topologically nontrivial crystals and inspires the designs of classical wave devices., Comment: 10 pages, 4 figures