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Cross-resonance (CR) gates have emerged as a promising scheme for fault-tolerant quantum computation with fixed-frequency qubits. We experimentally implement an entangling CR gate by using a microwave-only control in a tunable coupling superconducting circuit, where the tunable coupler provides extra degrees of freedom to verify optimal conditions for constructing a CR gate. By developing a three-qubit Hamiltonian tomography protocol, we systematically investigate the dependency of gate fidelities on spurious qubit interactions and present the first experimental approach to the evaluation of the perturbation impact arising from spectator qubits. Our results reveal that the spectator qubits lead to reductions in CR gate fidelity dependent on $ZZ$ interactions and particular frequency detunings between spectator and gate qubits. The target spectator demonstrates a more serious impact than the control spectator under a standard echo pulse scheme, whereas the degradation of gate fidelity is observed up to 22.5% as both the spectators are present with a modest ZZ coupling to the computational qubits. Our experiments uncover an optimal CR operation regime, and the method we develop here can readily be applied to improving other kinds of two-qubit gates in large-scale quantum circuits.

An ion trap is one of the most promising candidates for quantum computing. Current schemes mainly focus on a linear chain of up to about 100 ions in a Paul trap. To further scale up the qubit number, one possible direction is to use 2D or 3D ion crystals (Wigner crystals). In these systems, ions are generally subjected to large micromotion due to the strong fast-oscillating electric field, which can significantly influence the performance of entangling gates. In this paper, we develop an efficient numerical method to design high-fidelity entangling gates in a general 3D ion crystal. We present numerical algorithms to solve the equilibrium configuration of the ions and their collective normal modes. We then give a mathematical description of the micromotion and use it to generalize the gate scheme for linear ion chains into a general 3D crystal. The involved time integral of highly oscillatory functions is expanded into a fast-converging series for accurate and efficient evaluation and optimization. As a numerical example, we show a high-fidelity entangling gate design between two ions in a 100-ion crystal, with a theoretical fidelity above 99.9%.

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 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

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

Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2$$\end{document}0+N∕2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications., Reaching a quantum advantage in metrology usually requires hard-to-prepare two-mode entangled states such as NOON states. Here, instead, the authors demonstrate single-mode phase estimation using Fock states superpositions in a superconducting qubit-oscillator system.

We experimentally realize a universal set of single-bit and two-bit geometric quantum gates by adiabatically controlling solid-state spins in a diamond defect. Compared with the nonadiabatic approach, the adiabatic scheme for geometric quantum computation offers a unique advantage of inherent robustness to parameter variations, which is explicitly demonstrated in our experiment by showing that the single-bit gates remain unchanged when the driving field amplitude varies by a factor of 2 or the detuning fluctuates in a range comparable to the inverse of the gate time. The reported adiabatic control technique and its convenient implementation offer a paradigm for achieving quantum computation through robust geometric quantum gates, which is important for quantum information systems with parameter-fluctuation noise such as those from the inhomogeneous coupling or the spectral diffusion.

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.

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 develop a deterministic method to generate and verify arbitrarily high NOON states of quantized vibrations (phonons), through the coupling to the internal state. We experimentally create the entangled states up to $N=9$ phonons in two vibrational modes of a single trapped ${^{171}\mathrm{Yb}}^{+}$ ion. We observe an increasing phase sensitivity of the generated NOON state as the number of phonons $N$ increases and obtain the fidelity from the contrast of the phase interference and the population of the phonon states through the two-mode projective measurement, which are significantly above the classical bound. We also measure the quantum Fisher information of the generated state and observe Heisenberg scaling in the lower bounds of phase sensitivity as $N$ increases. Our scheme is generic and applicable to other photonic or phononic systems such as circuit QED systems or nanomechanical oscillators, which have Jaynes-Cummings-type of interactions.

Using a single atom in a cavity to control a propagating optical pulse can deterministically create a Schrodinger-cat state — an intriguing quantum superposition of classically distinct states. The result is a new opportunity for quantum state engineering with potential applications in quantum networks and computation.

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

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.

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

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.

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

Quantum computation and communication exploit the quantum properties of superposition and entanglement in order to perform tasks that may be impossible using classical means. In this Colloquium recent experimental and theoretical progress in the generation of entangled quantum networks based on the use of optical photons as carriers of information between fixed trapped atomic ion quantum memories are reviewed. Taken together, these quantum platforms offer a promising vision for the realization of a large-scale quantum network that could impact the future of communication and computation.

In the version of this Letter originally published, in Fig. 2c legend, the entry ‘LO phase noise’ should not have been included. This has now been corrected in the online versions.

Quantum information science involves the storage, manipulation and communication of information encoded in quantum systems, where the phenomena of superposition and entanglement can provide enhancements over what is possible classically. Large-scale quantum information processors require stable and addressable quantum memories, usually in the form of fixed quantum bits (qubits), and a means of transferring and entangling the quantum information between memories that may be separated by macroscopic or even geographic distances. Atomic systems are excellent quantum memories, because appropriate internal electronic states can coherently store qubits over very long timescales. Photons, on the other hand, are the natural platform for the distribution of quantum information between remote qubits, given their ability to traverse large distances with little perturbation. Recently, there has been considerable progress in coupling small samples of atomic gases through photonic channels, including the entanglement between light and atoms and the observation of entanglement signatures between remotely located atomic ensembles. In contrast to atomic ensembles, single-atom quantum memories allow the implementation of conditional quantum gates through photonic channels, a key requirement for quantum computing. Along these lines, individual atoms have been coupled to photons in cavities, and trapped atoms have been linked to emitted photons in free space. Here we demonstrate the entanglement of two fixed single-atom quantum memories separated by one metre. Two remotely located trapped atomic ions each emit a single photon, and the interference and detection of these photons signals the entanglement of the atomic qubits. We characterize the entangled pair by directly measuring qubit correlations with near-perfect detection efficiency. Although this entanglement method is probabilistic, it is still in principle useful for subsequent quantum operations and scalable quantum information applications.

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science.

We propose an experimental scheme to observe non-abelian statistics with cold atoms in a two dimensional optical lattice. We show that the Majorana-Schockley modes associated with line defects obey non-abelian statistics and can be created, braided, and fused, all through adiabatic shift of the local chemical potentials. The detection of the topological qubit is transformed to local measurement of the atom number on a single lattice site. We demonstrate the robustness of the braiding operation by incorporating noise and experiential imperfections in numerical simulations, and show that the requirement fits well with the current experimental technology.

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 review theoretical proposals for implementation of quantum computing and quantum communication with quantum optical methods.

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

Two or three dimensional Paul traps can confine a large number of ions forming a Wigner crystal, which would provide an ideal architecture for scalable quantum computation except for the micromotion, an issue that is widely believed to be the killer for high fidelity quantum gates. Surprisingly, here we show that the micromotion is not an obstacle at all for design of high fidelity quantum gates, even though the magnitude of the micromotion is significantly beyond the requirement of the Lamb-Dicke condition. Through exact solution of the quantum Mathieu equations, we demonstrate the principle of the gate design under micromotion using two ions in a quadrupole Paul trap as an example. The proposed micromotion quantum gates can be extended to the many ion case, paving a new way for scalable trapped ion quantum computation., Comment: 7 pages, 3 figures

Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly measure the characteristic topological invariants (order) based on the time-of-flight imaging of cold atoms. The method is generally applicable to detection of topological band insulators in one, two, or three dimensions characterized by integer topological invariants. Using detection of the Chern number for the 2D anomalous quantum Hall states and the Chern-Simons term for the 3D chiral topological insulators as examples, we show that the proposed detection method is practical, robust to typical experimental imperfections such as limited imaging resolution, inhomogeneous trapping potential, and disorder in the system., Comment: 10 pages, 5 figures, including Supplemental Material, version accepted by PRA as a Rapid Communication

We propose and analyze a scheme for generating entangled atomic beams out of a Bose-Einstein condensate using spin-exchanging collisions. In particular, we show how to create both atomic squeezed states and entangled states of pairs of atoms., Comment: 4 pages, 2 figures

In quantum error correction schemes, it is usually assumed that the qubits are decohered independently. Starting from a practical decoherence model of the quantum register consisting of many qubits, we derive the explicit conditions for independent decoherence.

Cooperative effects in general dissipation of qubits are investigated. The qubits are decohered collectively. There exist coherence-preserving states, for which decoherence is much reduced. A scheme is proposed for reducing collective decoherence by encoding general input states of the qubits into the corresponding coherence-preserving states.

A scheme is proposed for protecting quantum states from both independent decoherence and cooperative decoherence. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into the corresponding coherence-preserving states of the qubit-pairs. In this scheme, the amplitude damping (loss of energy) is prevented as well as the phase damping (dephasing) by a strategy called the free-Hamiltonian-elimination We further extend the scheme to include quantum gate operations and show that loss and decoherence during the gate operations can also be prevented., Comment: 12 pages, Latex, some correction in the reference and introduction. Jour-ref: Phys. Rev. Lett. 79, 1953, 1997

Quantum noise of optical solitons is analysed based on the exact solutions of the quantum nonlinear Schrodinger equation (QNSE) and the construction of the quantum soliton states. The noise limits are obtained for the local photon number and for the local quadrature phase amplitude. They are larger than the vacuum fluctuation. So in the fundamental soliton states the variance of the local photon number and the local quadrature phase amplitude cannot be squeezed. The soliton states with the minimum noise are quasi-coherent states, in which the quantum dispersion effects are negligible.

We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [\textit{Phys. Rev. Lett. 102, 120401 (2009)}]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon coincidence measurements.

We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder., Comment: 15 pages, 10 figures

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the $^{171}\mathrm{Yb}^{+}$ ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.

The practical construction of scalable quantum computer hardware capable of executing non-trivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault-tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Yu and Oh, Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantity the entanglement depth of many-body systems and is easy to implement as it requires to measure only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits., Comment: 4 pages

We propose a phase-sensitive detection scheme to identify the unconventional $p_{x}\pm ip_{y}$ symmetry of the condensate wavefunctions of bosons, which have already been proposed and realized in high bands in optical lattices. Using the impulsive Raman operation combining with time-of-flight imaging, the off-diagonal correlation functions in momentum space give rise to the relative phase information between different components of condensate wavefunctions. This scheme is robust against the interaction and interband effects, and provides smoking gun evidence for unconventional Bose-Einstein condensations with nontrivial condensation symmetries., 4.5 pages, 6 figures

A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the use of quantum logic gates on a standard controllable quantum system to efficiently simulate the behavior of a model Hamiltonian. Recent experiments using trapped ions and neutral atoms have realized quantum simulation of Ising model in presence of external magnetic fields, and showed almost arbitrary control in generating non-trivial Ising coupling patterns. Here we use laser-cooled trapped 171-Yb+ ions to simulate the emergence of magnetism in a system of interacting spins by implementing a fully-connected non-uniform ferromagnetic Ising model in a transverse magnetic field. To link this quantum simulation to condensed matter physics, we measure scalable correlation functions and order parameters appropriate for the description of larger systems, such as various moments of the magnetization. By increasing the Ising coupling strengths compared with the external field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up from N = 2 to 9 trapped ion spins. This points toward the onset of a quantum phase transition that should become infinitely sharp as the system approaches the macroscopic scale. We compare the measured ground state order to theory, which may become intractable for non-uniform Ising couplings as the number of spins grows beyond 20- 30 and even NP complete for a fully-connected frustrated Ising model, making this experiment an important benchmark for large-scale quantum simulation., Comment: 7 pages, 4 figures

A single atom in an optical cavity is shown to interact strongly with an incoming photon and to switch the photon's state. This finding opens up a path towards optical quantum computation and quantum networks. See Letters p.237 & p.241 The development of a quantum gate between a flying optical photonic qubit (polarization) and a single trapped atomic qubit (spin) has been a long-standing goal in quantum information science. Such gates are required both for quantum computation to be scaled to a large number of qubits and for quantum communication to be scaled to long distances. Now two groups, working independently, report the successful implementation of such gates. Gerhard Rempe and colleagues demonstrate a quantum gate between a laser-trapped atomic qubit and a single photon, where the polarization of the photon is flipped depending exactly on the spin state of the atom. Mikhail Lukin and co-workers describe a similar achievement — a quantum gate effect between a single atom trapped near a photonic crystal and a single photon.

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace., 4 pages; Add detailed discussion of feasibility of the scheme;add refs

A network is termed 'frustrated' when competing interactions between nodes prevent each bond from being satisfied. Frustration in quantum networks can lead to massively entangled ground states. The authors study this process by performing a quantum simulation of a frustrated spin system using three trapped atomic ions, whose interactions are precisely controlled using optical forces. A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. Frustration in quantum networks can lead to massively entangled ground states, as occurs in exotic materials such as quantum spin liquids and spin glasses. Here, a quantum simulation of a frustrated spin system is described, in which there are three trapped atomic ions whose interactions are controlled using optical forces. A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social1 and neural2 networks to protein folding3 and magnetism4,5. Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses6,7,8,9. Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions10,11,12, whose interactions are precisely controlled using optical forces13. We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.

We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed., Comment: 4 pages, 2 figures. V2: Modified discussion of disorder, added references - final version as published in Phys. Rev. Lett

Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. We report teleportation of quantum information between atomic quantum memories separated by about 1 meter. A quantum bit stored in a single trapped ytterbium ion (Yb+) is teleported to a second Yb+ atom with an average fidelity of 90% over a replete set of states. The teleportation protocol is based on the heralded entanglement of the atoms through interference and detection of photons emitted from each atom and guided through optical fibers. This scheme may be used for scalable quantum computation and quantum communication., Comment: 5 pages, 4 figures