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The quantum repeater protocol is a promising approach for implementing long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve an efficient entanglement connection between different repeater segments, with polynomial scaling. Here, we report an experiment that realizes the efficient connection of two quantum repeater segments via on-demand entanglement swapping through the use of two atomic quantum memories with storage times of tens of milliseconds. With the memory enhancement, acceleration in the scaling is demonstrated in the rate for a successful entanglement connection. Experimental realization of the entanglement connection of two quantum repeater segments with an efficient memory-enhanced scaling demonstrates a key advantage of the quantum repeater protocol, creating a cornerstone for the development of future large-scale quantum networks. Two quantum repeater segments are connected via on-demand entanglement swapping by using two atomic quantum memories. The efficiency improves from a quadratic scaling to a linear one with the preparation efficiency of the atom–photon entanglement.

Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report the first experimental demonstration of a QPT in the QRM using a single trapped ion. We measure the average spin-up state population of the ion and the average phonon number in its spatial oscillation mode as two order parameters and observe the clear evidences of the phase transition via slow quench of the coupling between the ion and its spatial motion. An experimental probe of the phase transitions in a fundamental quantum optics model without imposing the thermodynamic limit opens up a new window for the controlled study of QPTs and quantum critical phenomena., Comment: 15 pages, 9 figures

Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent state photons from a microwave cavity containing a superconducting qubit. We show that, with a coherent control of the qubit state, a full control over the coherent state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit state dependent reflection photon field. We further quantify quantum coherence in the prepared cat states based on the resource theory, revealing a good experimental control on the coherent state superpositions. The photon number statistic and the squeezing properties are also analyzed. Remarkably, fourth-order squeezing is observed in the experimental states. Those results open up new possibilities of applying generalized cat states for the purpose of quantum information processing., 16 pages, 15 figures

A photonic transistor that can switch or amplify an optical signal with a single gate photon requires strong non-linear interaction at the single-photon level. Circuit quantum electrodynamics provides great flexibility to generate such an interaction, and thus could serve as an effective platform to realize a high-performance single-photon transistor. Here we demonstrate such a photonic transistor in the microwave regime. Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on the qubit state through one cavity, and further shifts the resonance frequency of the other cavity. In this way, we realize a gain of the transistor up to 53.4 dB, with an extinction ratio better than 20 dB. Our device outperforms previous devices in the optical regime by several orders in terms of optical gain, which indicates a great potential for application in the field of microwave quantum photonics and quantum information processing.

For scalable quantum communication and networks, a key step is to realize a quantum repeater node that can efficiently connect different segments of atom-photon entanglement using quantum memories. We report a compact and hardware-efficient realization of a quantum repeater node using a single atomic ensemble for multicell quantum memories. Millisecond lifetime is achieved for individual memory cells after suppressing the magnetic-field-induced inhomogeneous broadening and the atomic-motion-induced spin-wave dephasing. Based on these long-lived multicell memory cells, we achieve heralded asynchronous entanglement generation in two quantum repeater segments one after another and then an on-demand entanglement connection of these two repeater segments. As another application of the multicell atomic quantum memory, we further demonstrate storage and on-demand retrieval of heralded atomic spin-wave qubits by implementing a random access quantum memory with individual addressing capacity. This work provides a promising constituent for efficient realization of quantum repeaters for large-scale quantum networks., 8 pages, 6 figures

Non-Hermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulk-boundary correspondence. Here, we implement the non-Hermitian Su-Schrieffer-Heeger (SSH) Hamiltonian, which is a prototypical model for studying non-Hermitian topological phases, with a solid-state quantum simulator consisting of an electron spin and a $^{13}$C nuclear spin in a nitrogen-vacancy (NV) center in a diamond. By employing a dilation method, we realize the desired non-unitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. Our result paves the way for further exploiting and understanding the intriguing properties of non-Hermitian topological phases with solid-state spins or other quantum simulation platforms., 10 pages, 6 figures

A quantum memory that can store quantum states faithfully and retrieve them on demand has wide applications in quantum information science. An efficient quantum memory in the microwave regime working alongside quantum processors based on superconducting quantum circuits may serve as an important architecture for quantum computers. Here we realize on-demand storage and retrieval of weak coherent microwave photon pulses at the single-photon level. We implement a superconducting multi-resonator quantum memory which is composed of a set of frequency-tunable coplanar transmission line (CPW) resonators. By dynamically tuning the resonant frequencies of the resonators, we achieve tunable memory bandwidth from 10 MHz to 55 MHz, with an overall storage efficiency up to 12 % with well preserved phase coherence. We further demonstrate on-demand storage and retrieval of a time-bin flying qubit. This result opens up a prospect to integrate our chip-based quantum memory with the state-of-the-art superconducting quantum circuit technology for quantum information processing.

Adversarial machine learning is an emerging field that focuses on studying vulnerabilities of machine learning approaches in adversarial settings and developing techniques accordingly to make learning robust to adversarial manipulations. It plays a vital role in various machine learning applications and has attracted tremendous attention across different communities recently. In this paper, we explore different adversarial scenarios in the context of quantum machine learning. We find that, similar to traditional classifiers based on classical neural networks, quantum learning systems are likewise vulnerable to crafted adversarial examples, independent of whether the input data is classical or quantum. In particular, we find that a quantum classifier that achieves nearly the state-of-the-art accuracy can be conclusively deceived by adversarial examples obtained via adding imperceptible perturbations to the original legitimate samples. This is explicitly demonstrated with quantum adversarial learning in different scenarios, including classifying real-life images (e.g., handwritten digit images in the dataset MNIST), learning phases of matter (such as, ferromagnetic/paramagnetic orders and symmetry protected topological phases), and classifying quantum data. Furthermore, we show that based on the information of the adversarial examples at hand, practical defense strategies can be designed to fight against a number of different attacks. Our results uncover the notable vulnerability of quantum machine learning systems to adversarial perturbations, which not only reveals a novel perspective in bridging machine learning and quantum physics in theory but also provides valuable guidance for practical applications of quantum classifiers based on both near-term and future quantum technologies., 22 pages, 16 figures, 5 tables

We study disorder effects in a two-dimensional system with chiral symmetry and find that disorder can induce a quadrupole topological insulating phase (a higher-order topological phase with quadrupole moments) from a topologically trivial phase. Their topological properties manifest in a topological invariant defined based on effective boundary Hamiltonians, the quadrupole moment, and zero-energy corner modes. We find gapped and gapless topological phases and a Griffiths regime. In the gapless topological phase, all the states are localized, while in the Griffiths regime, the states at zero energy become multifractal. We further apply the self-consistent Born approximation to show that the induced topological phase arises from disorder renormalized masses. We finally introduce a practical experimental scheme with topoelectrical circuits where the predicted topological phenomena can be observed by impedance measurements. Our work opens the door to studying higher-order topological Anderson insulators and their localization properties., 14 pages, 11 figures

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints., Comment: 32 pages, 17 figures

Building blocks of quantum computers have been demonstrated in small to intermediate-scale systems. As one of the leading platforms, the trapped ion system has attracted wide attention. A significant challenge in this system is to combine fast high-fidelity gates with scalability and convenience in ion trap fabrication. Here we propose an architecture for large-scale quantum computing with a two-dimensional array of atomic ions trapped at such large distance which is convenient for ion-trap fabrication but usually believed to be unsuitable for quantum computing as the conventional gates would be too slow. Using gate operations far outside of the Lamb–Dicke region, we show that fast and robust entangling gates can be realized in any large ion arrays. The gate operations are intrinsically parallel and robust to thermal noise, which, together with their high speed and scalability of the proposed architecture, makes this approach an attractive one for large-scale quantum computing.

Multiplexed quantum memories and high-dimensional entanglement can improve the performance of quantum repeaters by promoting the entanglement generation rate and the quantum communication channel capacity. Here, we experimentally generate a high-dimensional entangled state between a photon and a collective spin wave excitation stored in the multiplexed atomic quantum memory. We verify the entanglement dimension by the quantum witness and the entanglement of formation. Then we use the high-dimensional entangled state to test the violation of the Bell-type inequality. Our work provides an effective method to generate multidimensional entanglement between the flying photonic pulses and the atomic quantum interface., 9 pages, 6 figures, comments are welcome

Entanglement is a fascinating feature of quantum mechanics and a key ingredient in most quantum information processing tasks. Yet the generation of entanglement is usually hampered by undesired dissipation owing to the inevitable coupling of a system with its environment. Here, we report an experiment on how to entangle two $^{13}$C nuclear spins via engineered dissipation in a nitrogen-vacancy system. We utilize the electron spin as an ancilla, and combine unitary processes together with optical pumping of the ancilla to implement the engineered dissipation and deterministically produce an entangled state of the two nuclear spins, independent of their initial states. Our experiment demonstrates the power of engineered dissipation as a tool for generation of multi-qubit entanglement in solid-state systems., Comment: 9 pages, 11 figures

We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static $ZZ$ coupling strength. We quantitatively calculate the dynamic $ZZ$ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic $ZZ$ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic $ZZ$ coupling and high-order oscillation error degrades the parametric gate performance. This approach, which has not yet been previously explored, provides a guiding principle to improve gate fidelity of a parametric iswap gate by suppression of the unwanted qubit interactions. This controllable interaction, together with the parametric modulation technique, is desirable for crosstalk-free multiqubit quantum circuits and quantum simulation applications.

We propose and demonstrate experimentally a scheme to create entangled history states of the Greenberger-Horne-Zeilinger (GHZ) type. In our experiment, the polarization states of a single photon at three different times are prepared as a GHZ entangled history state. We define a GHZ functional which attains a maximum value $1$ on the ideal GHZ entangled history state and is bounded above by $1/16$ for any three-time history state lacking tripartite entanglement. We have measured the GHZ functional on a state we have prepared experimentally, yielding a value of $0.656\pm 0.005$, clearly demonstrating the contribution of entangled histories., 15 pages, 2 figures v. 2: 16 pages, 2 figures. Fundamental improvements to introduction, added references

The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum many-body states and the neural network representation (\textit{arXiv:1606.02318}). An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to popularity of the deep learning methods. Here, we give a rigorous proof that a deep neural network can efficiently represent most physical states, including those generated by any polynomial size quantum circuits or ground states of many body Hamiltonians with polynomial-size gaps, while a shallow network through a restricted Boltzmann machine cannot efficiently represent those states unless the polynomial hierarchy in computational complexity theory collapses., 12 pages, 7 figures

To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key element for quantum repeaters, we demonstrate that entanglement with flying optical qubits can be stored into any neighboring memory cells and read out after a programmable time with high fidelity. Experimental realization of a multiplexed quantum memory with many individually accessible memory cells and programmable control of its addressing and readout makes an important step for its application in quantum information technology., Comment: 8 pages, 4 figures

Controllable interaction between superconducting qubits is desirable for large-scale quantum computation and simulation. Here, based on a theoretical proposal by Yan et al. [Phys. Rev. Appl. 10, 054061 (2018)] we experimentally demonstrate a simply-designed and flux-controlled tunable coupler with a continuous tunability by adjusting the coupler frequency, which can completely turn off adjacent superconducting qubit coupling. Utilizing the tunable interaction between two qubits via the coupler, we implement a different type of controlled-phase (CZ) gate with 'dynamically decoupled regime', which allows the qubit-qubit coupling to be only 'on' at the usual operating point while dynamically 'off' during the tuning process of one qubit frequency into and out of the operating point. This scheme not only efficiently suppresses the leakage out of the computational subspace, but also allows for the acquired two-qubit phase being geometric at the operating point. We achieve an average CZ gate fidelity of 98.3(0.6), which is dominantly limited by qubit decoherence. The demonstrated tunable coupler provides a desirable tool to suppress adjacent qubit coupling and is suitable for large scale quantum computation and simulation., 4 pages and 4 figures

Dynamical quantum phase transitions are closely related to equilibrium quantum phase transitions for ground states. Here, we report an experimental observation of a dynamical quantum phase transition in a spinor condensate with correspondence in an excited state phase diagram, instead of the ground state one. We observe that the quench dynamics exhibits a non-analytical change with respect to a parameter in the final Hamiltonian in the absence of a corresponding phase transition for the ground state there. We make a connection between this singular point and a phase transition point for the highest energy level in a subspace with zero spin magnetization of a Hamiltonian. We further show the existence of dynamical phase transitions for finite magnetization corresponding to the phase transition of the highest energy level in the subspace with the same magnetization. Our results open a door for using dynamical phase transitions as a tool to probe physics at higher energy eigenlevels of many-body Hamiltonians., Comment: 7 pages; 6 figures

We study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast to the traditional Weyl semimetals, topological amorphous metals break translational symmetry, and thus cannot be characterized by the first Chern number defined based on the momentum space band structures. Instead, their topological properties will manifest in the Bott index and the Hall conductivity as well as the surface states. By studying the energy band and quantum transport properties, we find that topological amorphous metals exhibit a diffusive metal behavior. We further introduce a practical experimental proposal with electric circuits where the predicted phenomena can be observed using state-of-the-art technologies. Our results open a door for exploring topological gapless phenomena in amorphous systems., Comment: 12 pages, 10 figures, including SMs, Editors' suggestion

We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks---a class of deep feed-forward artificial neural networks with widespread applications in machine learning---can be trained to successfully identify different topological phases protected by chiral symmetry from experimental raw data generated with a solid-state quantum simulator. Our results explicitly showcase the exceptional power of machine learning in the experimental detection of topological phases, which paves a way to study rich topological phenomena with the machine learning toolbox., Main text: 5 pages with 3 figures; supplemental materials: 8 pages with 4 figures and 2 tables; accepted at Physical Review Letters

Representation by neural networks, in particular by restricted Boltzmann machines (RBM), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of quantum states can be efficiently represented with the RBM. Here, we show that the RBM can efficiently represent a wide class of many-body entangled states with rich exotic topological orders. This includes: (1) ground states of double semion and twisted quantum double models with intrinsic topological orders; (2) states of the AKLT model and 2D CZX model with symmetry protected topological order; (3) states of Haah code model with fracton topological order; (4) generalized stabilizer states and hypergraph states that are important for quantum information protocols. One twisted quantum double model state considered here harbors non-abelian anyon excitations. Our result shows that it is possible to study a variety of quantum models with exotic topological orders and rich physics using the RBM computational toolbox., 10 pages, 5 figures

We elucidate the relation between out-of-time-order correlators (OTOCs) and quantum phase transitions via analytically studying the OTOC dynamics in a degenerate spectrum. Our method points to key ingredients to dynamically detect quantum phases via out-of-time-order correlators for a wide range of quantum phase transitions and explains the existing numerical results in the literature. We apply our method to a critical model, XXZ model that numerically confirms our predictions., Comment: Presentation improved

The marriage of machine learning and quantum physics may give birth to a new research frontier that could transform both., Comment: The following article appeared in Physics Today, March 2019, page 48

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D $Z_2$ topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic nonintegrable models: topological order induced prescrambling, paralleling the notion of prethermalization of two-time correlators, that defines a time-scale for the restricted scrambling of topologically-protected quantum information., Comment: Journal publication version: presentation improved, typos fixed, 18 pages with 9+12 figures

Random access memory is an indispensable device for classical information technology. Analog to this, for quantum information technology, it is desirable to have a random access quantum memory with many memory cells and programmable access to each cell. We report an experiment that realizes a random access quantum memory of 105 qubits carried by 210 memory cells in a macroscopic atomic ensemble. We demonstrate storage of optical qubits into these memory cells and their read-out at programmable times by arbitrary orders with fidelities exceeding any classical bound. Experimental realization of a random access quantum memory with many memory cells and programmable control of its write-in and read-out makes an important step for its application in quantum communication, networking, and computation., Comment: 12 pages, 5 figures

Author(s): Monroe, C; Campbell, WC; Duan, LM; Gong, ZX; Gorshkov, AV; Hess, PW; Islam, R; Kim, K; Linke, NM; Pagano, G; Richerme, P; Senko, C; Yao, NY | Abstract: Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated to produce long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields in a prototypical example of a quantum simulator. Here the theoretical mapping of atomic ions to interacting spin systems, the preparation of complex equilibrium states, and the study of dynamical processes in these many-body interacting quantum systems are reviewed, and the use of this platform for optimization and other tasks is discussed. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on the behavior of interacting quantum systems that cannot be modeled with conventional computers.

Heat generated as a result of the breakdown of an adiabatic process is one of the central concepts of thermodynamics. In isolated systems, the heat can be defined as an energy increase due to transitions between distinct energy levels. Across a second-order quantum phase transition (QPT), the heat is predicted theoretically to exhibit a power-law scaling, but it is a significant challenge for an experimental observation. In addition, it remains elusive whether a power-law scaling of heat can exist for a first-order QPT. Here we experimentally observe a power-law scaling of heat in a spinor condensate when a system is linearly driven from a polar phase to an antiferromagnetic (AFM) phase across a first-order QPT. We experimentally evaluate the heat generated during two non-equilibrium processes by probing the atom number on a hyperfine energy level. The experimentally measured scaling exponents agree well with our numerical simulation results. Our work therefore opens a new avenue to experimentally and theoretically exploring the properties of heat in non-equilibrium dynamics.

Quantum entanglement, the essential resource for quantum information processing, has rich dynamics under different environments. Probing different entanglement dynamics typically requires exquisite control of complicated system-environment coupling in real experimental systems. Here, by a simple control of the effective solid-state spin bath in a diamond sample, we observe rich entanglement dynamics, including the conventional asymptotic decay as well as the entanglement sudden death, a term coined for the phenomenon of complete disappearance of entanglement after a short finite time interval. Furthermore, we observe counter-intuitive entanglement rebirth after its sudden death in the same diamond sample by tuning an experimental parameter, demonstrating that we can conveniently control the non-Markovianity of the system-environment coupling through a natural experimental knob. Further tuning of this experimental knob can make the entanglement dynamics completely coherent under the same environmental coupling. Probing of entanglement dynamics, apart from its fundamental interest, may find applications in quantum information processing through control of the environmental coupling.

We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of > 99.9% for logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis on the error subsets from the importance sampling method used to approximate the logical error rates in this paper to gain insight into which error sources are particularly detrimental to error correction.

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a SWAP operation between the transmon and NV ensemble is feasible and a quantum non-demolition measurement on the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, on this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in cavity can be thus stored into NV spins more efficiently through this virtual coupling., 24 pages, 5 figures

Unconventional fermions with high degeneracies in three dimensions beyond Weyl and Dirac fermions have sparked tremendous interest in condensed matter physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D) unconventional fermion system with a pair of gapped spin-1 fermions. We find that the original unlimited number of zero energy Landau levels (LLs) in the gapless case develop into a series of bands, leading to a novel QHE phenomenon that the Hall conductance first decreases (or increases) to zero and then revives as an infinite ladder of fine staircase when the Fermi surface is moved toward zero energy, and it suddenly reverses with its sign being flipped due to a Van Hove singularity when the Fermi surface is moved across zero. We further investigate the peculiar QHEs in a dice model with a pair of spin-1 fermions, which agree well with the results of the continuous model., 7 pages, 5 figures, references updated, typos corrected and manuscript thoroughly revised

A twofold delayed-choice experiment was performed, where the behavior of a quantum system was a posteriori chosen twice., Wave-particle complementarity lies at the heart of quantum mechanics. To illustrate this mysterious feature, Wheeler proposed the delayed-choice experiment, where a quantum system manifests the wave- or particle-like attribute, depending on the experimental arrangement, which is made after the system has entered the interferometer. In recent quantum delayed-choice experiments, these two complementary behaviors were simultaneously observed with a quantum interferometer in a superposition of being closed and open. We suggest and implement a conceptually different quantum delayed-choice experiment by introducing a which-path detector (WPD) that can simultaneously record and neglect the system’s path information, but where the interferometer itself is classical. Our experiment is realized with a superconducting circuit, where a cavity acts as the WPD for an interfering qubit. Using this setup, we implement the first twofold delayed-choice experiment, which demonstrates that the system’s behavior depends not only on the measuring device’s configuration that can be chosen even after the system has been detected but also on whether we a posteriori erase or mark the which-path information, the latter of which cannot be revealed by previous quantum delayed-choice experiments. Our results represent the first demonstration of both counterintuitive features with the same experimental setup, significantly extending the concept of quantum delayed-choice experiment.

We propose and experimentally demonstrate a new method to generate arbitrary Fock-state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode without the need of fine-frequency tuning. Here the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation, and is more robust to noise and accumulation of experimental errors compared to previous ones. Using the method, we experimentally generate high-fidelity phase eigenstates under various Hilbert-space dimensions and squeezed states, which are useful for quantum walk and high-precision measurements., Comment: 3 figures and 2 tables in the main, 5 figures and 1 table in the supplement

Duan-Lukin-Cirac-Zoller (DLCZ) quantum repeater protocol, which was proposed to realize long distance quantum communication, requires usage of quantum memories. Atomic ensembles interacting with optical beams based on off-resonant Raman scattering serve as convenient on-demand quantum memories. Here, a complete free space, three-dimensional theory of the associated read and write process for this quantum memory is worked out with the aim of understanding intrinsic retrieval efficiency. We develop a formalism to calculate the transverse mode structure for the signal and the idler photons and use the formalism to study the intrinsic retrieval efficiency under various configurations. The effects of atomic density fluctuations and atomic motion are incorporated by numerically simulating this system for a range of realistic experimental parameters. We obtain results that describe the variation in the intrinsic retrieval efficiency as a function of the memory storage time for skewed beam configuration at a finite temperature, which provides valuable information for optimization of the retrieval efficiency in experiments., Comment: 16 pages, 12 figures

Resolution of the century-long paradox on Maxwell's demon reveals a deep connection between information theory and thermodynamics. Although initially introduced as a thought experiment, Maxwell's demon can now be implemented in several physical systems, leading to intriguing test of information-thermodynamic relations. Here, we report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates. A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell's demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including fascinating topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians., Comment: including supplementary materials

The manipulation of spins in a solid-state system — nitrogen–vacancy defects in diamond — allows the experimental realization of a universal set of geometric quantum gates using holonomies, that is, non-Abelian generalizations of the Berry phase, and offers a scalable platform with the potential for room-temperature quantum computing. One obstacle to the development of practical quantum computers is the perceived need for substantial error-correction schemes. Such schemes, however, would slow down the computation process and negate some of the potential advantages of quantum technology. An alternative approach would be to use inherently fault-tolerant quantum computing principles that are robust to noise, such as that due to protection from geometric rules. Some all-geometric quantum computation experiments have been reported but the challenge is to find a platform that is scalable. Luming Duan and colleagues now report the experimental realization of a universal set of geometric quantum gates with spins residing in diamond defect centres. Although the experiments are based on two qubits in one diamond centre, the work offers a promising direction to all-geometric, robust quantum computation in the solid state and at room temperature. Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an ‘all-geometric’ approach to quantum computation1,2, the quantum gates are implemented using Berry phases3 and their non-Abelian extensions, holonomies4, from geometric transformation of quantum states in the Hilbert space5. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features1,2,6,7. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance8,9; however, such systems are known to be non-scalable for the purposes of quantum computing10. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions11, superconducting quantum bits12 and quantum dots13, and a recent experiment has realized geometric single-bit gates in a superconducting system14. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen–vacancy centres. These diamond defects provide a scalable experimental platform15,16,17 with the potential for room-temperature quantum computing16,17,18,19, which has attracted strong interest in recent years20. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system15,16,17,18,19,20.

Three-dimensional topological Weyl semimetals can generally support a zero-dimensional Weyl point characterized by a quantized Chern number or a one-dimensional Weyl nodal ring (or line) characterized by a quantized Berry phase in the momentum space. Here, in a dissipative system with particle gain and loss, we discover a new type of topological ring, dubbed Weyl exceptional ring consisting of exceptional points at which two eigenstates coalesce. Such a Weyl exceptional ring is characterized by both a quantized Chern number and a quantized Berry phase, which are defined via the Riemann surface. We propose an experimental scheme to realize and measure the Weyl exceptional ring in a dissipative cold atomic gas trapped in an optical lattice., Comment: 6 pages, 3 figures

We experimentally demonstrate a robust dynamical decoupling protocol with bounded controls using long soft pulses, eliminating a challenging requirement of strong control pulses in conventional implementations. This protocol is accomplished by designing the decoupling propagators to go through a Eulerian cycle of the coupler group [Phys. Rev. Lett. 90, 037901(2003)]. We demonstrate that this Eulerian decoupling scheme increases the coherence time by two orders of magnitude in our experiment under either dephasing or a universal noise environment., Comment: 7 pages, 4 figures

We observe evidence of first-order superfluid-to-Mott-insulator quantum phase transitions in a lattice-confined antiferromagnetic spinor Bose-Einstein condensate. The observed signatures include the hysteresis effect, significant heatings across the phase transitions, and changes in spin populations due to the formation of spin singlets in the Mott-insulator phase. The nature of the phase transitions is found to strongly depend on the ratio of the quadratic Zeeman energy to the spin-dependent interaction. Our observations are qualitatively understood by the mean field theory and suggest tuning the quadratic Zeeman energy is a new approach to realize superfluid-to-Mott-insulator phase transitions.

With the recent development of optomechanics, the vibration in solids, involving collective motion of trillions of atoms, gradually enters into the realm of quantum control. Here, building on the recent remarkable progress in optical control of motional states of diamonds, we report an experimental demonstration of quantum teleportation from light beams to vibrational states of a macroscopic diamond under ambient conditions. Through quantum process tomography, we demonstrate average teleportation fidelity (90.6±1.0)%, clearly exceeding the classical limit of 2/3. The experiment pushes the target of quantum teleportation to the biggest object so far, with interesting implications for optomechanical quantum control and quantum information science., Quantum teleportation has found important applications in quantum technologies, but pushing it to macroscopic objects is challenging because of the fragility of quantum states. Here, the authors demonstrate teleportation of states from light beams to the vibrational states of a macroscopic diamond sample.

The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts [Y. Song et al., Nano Lett. 16, 6245 (2016)], we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a potential exhibits a transition from one group of Landau levels to the other group, which can be understood analytically through perturbation theory. Our results provide insight to the transport property of TLG QDs, with possible applications to study of spin qubits and valleytronics in TLG QDs., Comment: 9+3 pages, 7+3 figures; added a reference

We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small., Comment: Phys. Rev. Lett.(2017, in press), "one-instance" is replaced by "single-instance-hardness", references added, "Simulation with variation Distance Errors" in Supplemental Material is rewritten in a clearer way

The router is a key element for a network. We describe a scheme to realize genuine quantum routing of single-photon pulses based on cascading of conditional quantum gates in a Mach-Zehnder interferometer and report a proof-of-principle experiment for its demonstration using linear optics quantum gates. The polarization of the control photon routes in a coherent way the path of the signal photon while preserving the qubit state of the signal photon represented by its polarization. We demonstrate quantum nature of this router by showing entanglement generated between the initially unentangled control and signal photons and confirm that the qubit state of the signal photon is well preserved by the router through quantum process tomography.

We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate effects: renormalization of the equilibrium positions, coupling to the transverse motional modes, and amplitude modulation in the addressing beam. We demonstrate that all of these effects can be taken into account and high-fidelity gates are possible in the presence of micromotion. This proposal opens the prospect to realize large-scale fault-tolerant quantum computation within a single Paul trap., Comment: 10 pages, 5 figures, including Supplemental Material

Protected by the chiral symmetry, three dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here we show that the magneto-electric polarization can identify the integer-valued invariant if we gap the system without coating a quantum Hall layer on the surface. The quantized response is demonstrated to be robust against weak perturbations. We also study the topological properties by adiabatically coupling two nontrivial phases, and find that gapless states appear and are localized at the boundary region. Finally, an experimental scheme is proposed to realize the Hamiltonian and measure the quantized response with ultracold atoms in optical lattices., 8 pages, 6 figures, 2 Appendices

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential speedup in both the number of training vectors $M$ and the feature space dimension $N$. We generalize the previous quantum algorithm for solving systems of linear equations [Phys. Rev. Lett. 103, 150502 (2009)] to efficiently implement a Hermitian chain product of $k$ trace-normalized $N \times N$ Hermitian positive-semidefinite matrices with time complexity of $O(\log (N))$. Using this result, we perform linear as well as nonlinear Fisher discriminant analysis for dimensionality reduction over $M$ vectors, each in an $N$-dimensional feature space, in time $O(p \text{polylog} (MN)/\epsilon ^{3})$, where $\epsilon $ denotes the tolerance error, and $p$ is the number of principal projection directions desired. We also present a quantum discriminant analysis algorithm for data classification with time complexity $O(\log (MN)/\epsilon^{3})$., Comment: 11 pages, published version

We propose a scheme to implement arbitrary-speed quantum entangling gates on two trapped ions immersed in a large linear crystal of ions, with minimal control of laser beams. For gate speeds slower than the oscillation frequencies in the trap, a single appropriately-detuned laser pulse is sufficient for high-fidelity gates. For gate speeds comparable to or faster than the local ion oscillation frequency, we discover a five-pulse protocol that exploits only the local phonon modes. This points to a method for efficiently scaling the ion trap quantum computer without shuttling ions., Comment: 4 pages

It was shown recently that entanglement of identical particles has a feature called dualism [Phys. Rev. Lett. 110, 140404 (2013)], which is fundamentally connected with quantum indistinguishability. Here we report an experiment that observes the entanglement duality for the first time with two identical photons, which manifest polarization entanglement when labeled by different paths or path entanglement when labeled by polarization states. By adjusting the mismatch in frequency or arrival time of the entangled photons, we tune the photon indistinguishability from quantum to classical limit and observe that the entanglement duality disappears under emergence of classical distinguishability, confirming it as a characteristic feature of quantum indistinguishable particles., 9 pages, 4 figures