Exploring large-scale entanglement in quantum simulation

Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science1. Here we perform experimental investigations of entanglement on the basis of the entanglement Hamiltonian (EH)2 as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a one-dimensional XXZ Heisenberg chain on a 51-ion programmable quantum simulator3 and perform sample-efficient 'learning' of the EH for subsystems of up to 20 lattice sites4. Our experiments provide compelling evidence for a local structure of the EH. To our knowledge, this observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann5,6, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially varying temperature profile as a signature of entanglement2. Our results also show the transition from area- to volume-law scaling7 of von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.

Quantum-enhanced sensing on optical transitions through finite-range interactions

The control over quantum states in atomic systems has led to the most precise optical atomic clocks so far1-3. Their sensitivity is bounded at present by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can-nevertheless-be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real-world sensors is extremely challenging. Here we illustrate a pathway for harnessing large-scale entanglement in an optical transition using 1D chains of up to 51 ions with interactions that decay as a power-law function of the ion separation. We show that our sensor can emulate many features of the one-axis-twisting (OAT) model, an iconic, fully connected model known to generate scalable squeezing4 and Greenberger-Horne-Zeilinger-like states5-8. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, that is, spin-wave excitations (SWE), at finite momenta, the generation of spin squeezing comparable with OAT (a Wineland parameter9,10 of -3.9 ± 0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of multi-headed cat states in the Q-distribution. We demonstrate the metrological utility of the states in a Ramsey-type interferometer, in which we reduce the measurement uncertainty by -3.2 ± 0.5 dB below the standard quantum limit for N = 51 ions.

Observing emergent hydrodynamics in a long-range quantum magnet

Identifying universal properties of nonequilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. We experimentally probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. By measuring space-time-resolved correlation functions in an infinite temperature state, we observed a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by Lévy flights. We extracted the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of nonequilibrium states of quantum matter.

Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions

In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.

Cross-Platform Verification of Intermediate Scale Quantum Devices

We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[ρ_{1}ρ_{2}] and the purities Tr[ρ_{1,2}^{2}], and thus a fidelity of two, possibly mixed, quantum states ρ_{1} and ρ_{2} prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof of principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.

Probing Rényi entanglement entropy via randomized measurements

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

Environment-Assisted Quantum Transport in a 10-qubit Network

The way in which energy is transported through an interacting system governs fundamental properties in nature such as thermal and electric conductivity or phase changes. Remarkably, environmental noise can enhance the transport, an effect known as environment-assisted quantum transport (ENAQT). In this Letter, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions, and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We find that in the regime where ENAQT is most effective, the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by non-Markovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport efficiency. Our approach represents a controlled and scalable way to investigate quantum transport in many-body networks under static disorder and dynamic noise.

Revealing Quantum Statistics with a Pair of Distant Atoms

Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics differ in the exchange phase, either 0 or π, which the wave function acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wave function. We discuss possible implementations with a pair of trapped atoms or ions.

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

Measurement of Dipole Matrix Elements with a Single Trapped Ion

We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e., the 4(2)S(1/2)↔4(2)P(1/2) transition of (40)Ca(+), for which we find the value 2.8928(43) ea(0). Moreover, the method allows us to deduce the lifetime of the 4(2)P(1/2) state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a long-standing discrepancy between calculated values and experimental results.

Spectroscopy of Interacting Quasiparticles in Trapped Ions

The static and dynamic properties of many-body quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely controlled and otherwise inaccessible way. We present a spectroscopic technique to study artificial quantum matter and use it for characterizing quasiparticles in a many-body system of trapped atomic ions. Our approach is to excite combinations of the system's fundamental quasiparticle eigenmodes, given by delocalized spin waves. By observing the dynamical response to superpositions of such eigenmodes, we extract the system dispersion relation, magnetic order, and even detect signatures of quasiparticle interactions. Our technique is not limited to trapped ions, and it is suitable for verifying quantum simulators by tuning them into regimes where the collective excitations have a simple form.

Experimental violation of multipartite Bell inequalities with trapped ions

We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First, we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second, we analyze Greenberger-Horne-Zeilinger states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

Measurement-based quantum computation with trapped ions

Measurement-based quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurement-based quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurement-based quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.

Experimental generation of quantum discord via noisy processes

Quantum systems in mixed states can be unentangled and yet still nonclassically correlated. These correlations can be quantified by the quantum discord and might provide a resource for quantum information processing tasks. By precisely controlling the interaction of two ionic qubits with their environment, we investigate the capability of noise to generate discord. Firstly, we show that noise acting on only one quantum system can generate discord between two. States generated in this way are restricted in terms of the rank of their correlation matrix. Secondly, we show that classically correlated noise processes are capable of generating a much broader range of discordant states with correlation matrices of any rank. Our results show that noise processes prevalent in many physical systems can automatically generate nonclassical correlations and highlight fundamental differences between discord and entanglement.

Quantum simulation of quantum field theories in trapped ions

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.

Quantum simulation of the Klein paradox with trapped ions

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.

Realization of a quantum walk with one and two trapped ions

We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ions. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin tossing operations. To analyze the ion's motional state after each step we apply a technique that directly maps the probability density distribution onto the ion's internal state. The measured probability distributions and the position's second moment clearly show the nonclassical character of the quantum walk. To further highlight the difference between the classical (random) and the quantum walk, we demonstrate the reversibility of the latter. Finally, we extend the quantum walk by using two ions, giving the walker the additional possibility to stay instead of taking a step.

Realization of universal ion-trap quantum computation with decoherence-free qubits

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.

Absolute frequency measurement of the 40Ca+ 4s(2)S_(1/2)-3d(2)D_(5/2) clock transition

We report on the first absolute transition frequency measurement at the 10;{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40Ca+ 4s ;{2}S_{1/2}-3d ;{2}D_{5/2} electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency nu_{Ca;{+}}=411 042 129 776 393.2(1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Landé g factor of the 3d;{2}D_{5/2} level to be g_{5/2}=1.200 334 0(3).

Process tomography of ion trap quantum gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

‘Designer atoms’ for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' (ref. 10) protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements--a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, 'Greenberger-Horne-Zeilinger' entangled states with up to six ions have been created and analysed in Boulder.

Control and Measurement of Three-Qubit Entangled States

We report the deterministic creation of maximally entangled three-qubit states-specifically the Greenberger-Horne-Zeilinger (GHZ) state and the W state-with a trapped-ion quantum computer. We read out one of the qubits selectively and show how GHZ and W states are affected by this local measurement. Additionally, we demonstrate conditional operations controlled by the results from reading out one qubit. Tripartite entanglement is deterministically transformed into bipartite entanglement by local operations only. These operations are the measurement of one qubit of a GHZ state in a rotated basis and, conditioned on this measurement result, the application of single-qubit rotations.

Bell states of atoms with ultralong lifetimes and their tomographic state analysis

Arbitrary atomic Bell states with two trapped ions are generated in a deterministic and preprogrammed way. The resulting entanglement is quantitatively analyzed using various measures of entanglement. For this, we reconstruct the density matrix using single qubit rotations and subsequent measurements with near-unity detection efficiency. This procedure represents the basic building block for future process tomography of quantum computations. As a first application, the temporal decay of entanglement is investigated in detail. We observe ultralong lifetimes for the Bell states Psi(+/-), close to the fundamental limit set by the spontaneous emission from the metastable upper qubit level and longer than all reported values by 3 orders of magnitude.

Deterministic quantum teleportation with atoms

Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

Realization of the Cirac-Zoller controlled-NOT quantum gate

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac-Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac-Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.

Experimental demonstration of ground state laser cooling with electromagnetically induced transparency

Ground state laser cooling of a single trapped Ca(+)on is achieved with a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency. Using the Zeeman structure of the S(1/2) to P(1/2) dipole transition we achieve up to 90% ground state probability. The new method is robust, easy to implement, and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.

Current Status of the VU MFEL Compton X-Ray Program

The Vanderbilt University medical FEL (free electron laser) Compton x-ray program is close to being operational. The FEL modifications necessary for this new capability are near completion. The transport and detection systems for electron and IR beams have been designed, delivered, and tested. We initially expect to produce 108 x-ray photons per second in the 15- to 20-keV region.

Near-monochromatic X-ray beams produced by the free electron laser and Compton backscatter

The intense photon output of a free electron laser may be made to collide with its own high energy electron beam to create nearly monochromatic x-rays using Compton backscatter techniques. These x-rays can be used for imaging and non-imaging diagnostic and therapeutic experiments. The initial configuration of the Vanderbilt Medical Free Electron Laser (Sierra Laser Systems, Sunnyvale, CA) produces intense x-rays up to 17.9 keV, although higher energies are easily attainable through the use of frequency doubling methods, alteration of the energy of the electron beam and coupling to conventional laser inputs.

Inexpensive, air-driven ventricular assist or replacement device for use in MR research

A simple, inexpensive, non-magnetizable, pulsatile air-driven pump has been devised for use in magnetic resonance environments. The pump has a variable stroke volume and stroke rate, is easily cleaned and sterilized, requires relatively small priming volumes and causes no observable hemolysis when blood is used as the perfusate. This device is usable for phantoms, isolated organs or in situ preparations.

Doisynolic-type acids--uterotropically potent estrogens which compete poorly with estradiol for cytosolic estradiol receptors

Doisynolic acids, a class of seco-steroid acids some of which exhibit greater uterotropic estrogenicity than estradiol-17 beta, are D-ring cleavage products of steroidal estrogens formed by fusion with KOH above 200 degrees C. We have found that electron-transfer reactions between estrone or estradiol and CCl4 or CBrCl3 in KOH-t-BuOH at 25 degrees C rapidly provide 16,16-dichloro- or -dibromodoisynolic acid, respectively, the former approaching estradiol in uterotropic potency. Simple esters from these highly hindered tertiary carboxylic acids, easily prepared via phase-transfer-catalyzed alkylations, also rival estradiol in uterotropic activity. Unlike natural steroidal estrogens or their commonly used artificial equivalents (DES, hexoestrol, ethynylestradiol, etc.) whose uterotropic activity is accompanied by substantial binding affinity for cytosolic estradiol receptors, these highly uterotropic doisynolic-type acids and esters exhibit binding affinities for this receptor of only about 1% that of estradiol-17 beta as determined by the usual competitive binding-inhibition studies with [3H]estradiol. Other highly uterotropic carboxylic acids may exhibit similar characteristics. These unusual results leave open the possibilities that uterotropic seco-steroid and related carboxylic acids undergo some unknown metabolic activation, are exceptionally persistent estrogens, bind to a cytosolic receptor site other than the conventional (type I) estradiol site, or bind directly to type I or type II nuclear receptor sites. At dosages of 1000 times those required for a uterotropic effect, the doisynolic-type acids (24 doses over an 8-week period) were neither toxic nor carcinogenic.

Fiber-optic pressure transducer for use near MR magnetic fields

Measurement of physiologic pressures in the vicinity of magnetic fields has been difficult because present pressure transducers contain conductive elements. A fiber-optic pressure transducer was developed that contains no conductive parts and is useful for making continuous pressure measurements within magnetic resonance magnetic fields.