Near-field microwave quantum logic gates in scalable surface-electrode ion traps
We demonstrate the experimental realization of a two-qubit Mølmer-Sørensen gate on a magnetic field-insensitive hyperfine transition in 9Be+ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be 98.2±1.2% and is limited by technical imperfections, as confirmed by a comprehensive numerical error analysis. We discuss steps which allow us to reach even higher fidelities through advanced modulation techniques and by eliminating the technical imperfections.
The microwave conductor design employed can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer. To realize such structures, we present a surface-electrode ion trap fabrication process that lets us realize metal-dielectric structures with an in principle arbitrary number of lower interconnect layers connected to the top layer using vias. The process features thick electroplated gold electrodes, large aspect ratios and high surface quality without any cumulative non-planarity errors due to the use of chemical-mechanical polishing (CMP).
Sep 2, 2019
Elements of quantum information science using trapped Yb+ ions
Using a programmable quantum computer (QC) based on magnetic gradient induced coupling (MAGIC), we carried out a proof-of-principle experimental demonstration of the deliberation process in the framework of reinforcement learning. This experiment at the boundary between quantum information science and machine learning shows that decision making for reinforcement learning is sped up quadratically on a QC as compared to a classical agent.
Then we will report on experimental progress in realizing (fast) 2-qubit radio frequency RF quantum gates that are robust against variations in the secular trap frequency, motional excitation (varied by RF sideband cooling), and Rabi frequency. In future traps such gates will increase speed and fidelity of multi-qubit RF gates. Further enhancement of gate fidelity is achieved by precisely tracking the ions qubit resonances.
RF-driven atomic ions and MAGIC, as used in these experiments, are a promising approach for realizing scalable quantum computing using interconnected modules containing quantum processors. Transport of trapped ions is a prerequisite for this and other scalable strategies for quantum computing with trapped ions. We have shown, by shuttling a single 171Yb+ ion 22 x 106 times and quantifying the coherence of its hyperfine qubit, that the quantum information stored in this qubit is preserved with a fidelity of 99.9994(+6 -7)% during transport of the ion over a distance of 250 µm.
Already precise clocks based on single trapped ions can be further improved by using multiple ions allowing for shorter averaging times or advanced read-out schemes. Within the opticlock consortium, we contribute to a novel type of a portable multi-ion frequency standard.
Sep 2, 2019
Trapped ion quantum simulators: from topological models to applications in real life problems.
In the first part of my talk I will present some relatively recent theoretical results on the quantum simulation of topological models with trapped ions [P. Nevado et al. Phys. Rev. Lett. 119, 210401 (2017)]. I will show that Floquet engineering can be used to transform the usual trapped ion Ising model into a topological spin chain with edge-state solutions that are localzed at the ends of the chain. Since trapped ion Ising interactions can be long-range, the resulting topological model can be used to investigate the interplay between interaction range and topological properties.
In the second part I will present some on-going work on the applications of quantum computers and quantum simulators in the solution of optimization problems. In particular, some optimizacion problems of relevance in finance can be mapped into classical Ising models and solved dynamically by means of methods such as quantum annealing or the Quantum Optimizacion Approximate Algorithm, for example. I will discuss advantages and disadvantages of trapped ions for this short-term applications, as well as the particular challenges faced when dealing with practical problems.
Sep 2, 2019
Dynamic and spectral techniques in ion crystals control
In this talk I will review recent experiments in our group in which dynamic control and spectral engineering were used to improve on the coherent quantum control of ion-crystals. In a first experiment I will show how we used spectral engineering of the Molmer-Sorensen interaction to engineer two-ion robust entanglement gates. In the second experiment we used Dynamic control to null the inhomogeneous electric quadrupole shift in a multi-ion crystal.
Sep 3, 2019
New directions in laser-free entangling gates
Laser-free multi-ion entangling operations promise reduced experimental complexity and elimination of photon scattering errors, by coupling ion spin and motion with radiofrequency or microwave magnetic fields and gradients instead of laser beams. Two-qubit gates based on static  or oscillating  magnetic field gradients have been demonstrated in several groups, with fidelities now approaching those of the best laser-based gates. Our group is working on two new types of laser-free entangling gates. The first type of gate uses a strong magnetic field gradient oscillating near the motional frequency of the ions, combined with a pair of microwave magnetic fields symmetrically detuned about the qubit frequency. This gate scheme provides several advantages, including the ability to perform dynamical decoupling without additional control fields and the ability to perform either ZZ gates or XX gates simply by changing the microwave detuning . I will describe our experimental characterization of this gate, including fidelity, robustness to errors, and prospects for individual addressing using the gate fields. The second type of gate is an amplified version of a traditional microwave gradient XX gate , employing continuous squeezing of a shared motional mode of two ions during the gate operation to increase the gate speed . This allows us to perform multi-loop gates, with their improved robustness to errors, in the same or less time than an un-amplified single-loop gate, and with higher fidelity. The technique is sensitive to the phase relationship between the squeezing interaction and the sidebands used to perform the gate, and is thus particularly well-suited to laser-free gates, where this phase can be easily controlled.
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Sep 3, 2019
Entangling trapped ions via Rydberg interaction
Department of Physics, Stockholm University, S-10691, Stockholm, Sweden
Trapped Rydberg ions combine the key strengths of Rydberg atoms and trapped ion quantum processors in one technology. From Rydberg atoms they inherit the strong dipolar interaction, with trapped ions they share the full quantum information toolbox . This technology promises to speed up trapped ion entanglement operations and make them available in large ion crystals.
Rydberg ions have a weakly bound valance electron in a large orbital far away from the ionic core. As a result, they experience large transition dipole moments and are highly polarisable. We observe the classical and quantum effects experienced by trapped Rydberg ions due to their large polarizability. Effects include the observation of a modified trapping potential compared to ground state ions and the emergence of strong state-dependent forces . These effects are the basis of a recent proposal for fast entanglement gates .
Furthermore, we will report the first coherent Rydberg excitation of trapped ions . Finally, we show our recent realisation of a sub-microsecond entanglement gate between trapped ions via Rydberg interaction. These are important steps towards realizing a fast quantum processor or quantum simulator with trapped Rydberg ions.
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Sep 3, 2019
Photon Recoil Spectroscopy of Ions in the Unresolved Sideband Limit:
Applications to Cold Molecular Ion Research
Department of Physics and Astronomy, Aarhus University, Denmark
Quantum logic spectroscopy, or more generally photon recoil spectroscopy (PRS), has in the recent past been applied in ultra-precise spectroscopy of atomic ions, and the technique holds as well great promises for ultra-high-resolution molecular ion spectroscopy in the near future. In addition, PRS might be interesting for a range of other investigations of molecular ions in the gas phase. Specific implementations might be applied to internal state preparation of molecules for, e.g., state-to-state reaction experiments, while others might be used in performing single photon absorption studies of single complex molecular ions under well-controlled conditions. In the latter case, the technique can even be applied in situations where the absorption lead to complete internal energy conversion. In the talk I will present some of the prospect of using PRS in the sideband unresolved limit with respect to cold molecular ion research.
Sep 3, 2019
Quantum non-demolition detection of molecular rotational states
Ziv Meir, Mudit Sinhal, Kaveh Najafian, Gregor Hegi and Stefan Willitsch
University of Basel, Department of chemical physics
The development of methods for coherent manipulation of single isolated molecular ions [1,2] using quantum logic  techniques has made rapid progress in recent years with exciting applications in the fields of precision spectroscopy, fundamental-physics-theories tests, atomic clocks and quantum-controlled chemistry.
In this talk, I will describe our recent advances for achieving quantum control over a single N2+ molecular ion, in particular, the unambiguous detection of the rotation and vibration state of the molecular ion using quantum-non demolition state detection and its application for electronic spectroscopy and measurement of transition dipole moments and lifetimes of electronic states.
In our experiment , we overlap a molecular beam with a radio-frequency ion trap. We ionize single nitrogen molecules into a specific rotational-vibrational state and subsequently trap them in the ion trap. We use a co-trapped atomic ion (Ca+) for sympathetic cooling to the ground-state and for molecular-state detection. We use state-selective coherent motional excitation [4,5,6], which entangles the molecular-ion state with the motion of the atomic ion, as our quantum non-demolition state detection.
We are developing a narrow quantum-cascade laser to perform precision spectroscopy on a narrow dipole-forbidden vibrational transition at 65 THz  and to utilize projective state preparation of the molecular ion into a specific Zeeman state. We use N2+ as a prototype molecule particularly suited to precision measurements because it features narrow electric-dipole forbidden vibrational transitions in the electronic ground state. Nevertheless, our methods can be extended to a general class of diatomic and polyatomic molecules.
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Sep 3, 2019
Norbert M. Linke
Quantum-classical hybrid algorithms with trapped ions
Quantum-classical hybrid systems offer a path towards the application of near-term quantum computers to different optimization tasks. They are attractive since part of the effort is outsourced to a classical machine resulting in shallower and narrower quantum circuits, which can be executed with lower error rates. Several applications are currently being investigated in this context, such as the Variational Quantum Eigensolver (VQE) for eigenvalue approximation problems, or the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization.
We have realized several experimental demonstrations relating to the hybrid approach, such as finding the ground state binding energy of the deuteron nucleus with VQE , the training of shallow circuits for generative modeling using a Bayesian optimization routine, tackling the Max-Cut problem using QAOA , and the preparation of quantum critical states with a QAOA-inspired scheme .
Our experimental system combines different classical optimizers with a programmable trapped-ion quantum computer comprised of a chain of 171Yb+ ions. The latter features individual Raman beam addressing and individual readout, and can be configured to run any sequence of single- and two-qubit gates .
Recent results, limitations of the above methods, and ideas for boosting these concepts for scaling up the quantum-classical hybrid architecture will be discussed.
 O. Shehab et al., arXiv:1904.04338 (2019);  D. Zhu et al., arXiv:1812.08862 (2018);  O. Shehab et al., arXiv:1906.00476 (2019);  D. Zhu et al., arXiv:1906.02699 (2019);  S. Debnath et al., Nature 563:63 (2016)
Sep 4, 2019
Ion-Nodes for Quantum Networks
Prof Matthias Keller
ITCM-Group, University of Sussex
The complementary benefits of trapped ions and photons as carriers of quantum information make it appealing to combine them in a joint system. Ions provide low decoherence rates, long storage times and high readout efficiency, while photons are ideal candidates for the transmission of quantum states over long distances. To interface the quantum states of ions and photons efficiently, we use calcium ions coupled to an optical high-finesse cavity via a Raman transition.
To achieve strong ion-cavity coupling we employ fibre tip cavities integrated into the electrodes of an endcap style ion trap. With a cavity length of 380 mm the resulting ion-cavity coupling strength is 17 MHz with a cavity line width of 8 MHz. We trap single calcium ions with a life time of several hours and have optimised the ion-cavity overlap to observe the interaction of the cavity with the ion.
While fibre cavities are ideal tools for ion-photon interfaces the limited coupling between the cavity mode and the fibre mode poses severe limitations on their usability in efficient quantum interfaces. We have developed a system to integrate mode matching optics into a fibre system and have demonstrated a mode matching between cavity and fibre on the order of 90%.
Crucial for quantum networks is the indistinguishability of the photons that are generated by the ion-cavity system. We have investigated two scheme to generate single photons and compared their single photon efficiency and the indistinguishability of the photons using HOM interference.
Sep 4, 2019
Overcoming resolution limits with quantum sensing
In this talk I will present a formulation a general criterion for superresolution in quantum problems. Inspired by this, we develop new spectral resolution methods with quantum sensing. In particular, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by making the projection noise vanish as well.
Sep 4, 2019
Buffer gas cooling of a trapped ion to the quantum regime
In recent years, a novel field of physics and chemistry has developed in which trapped ions and ultracold atomic gases are made to interact with each other. These systems find applications in studying quantum chemistry and collisions , and a number of quantum applications are envisioned such as ultracold buffergas cooling of the trapped ion quantum computer and quantum simulation of fermion-phonon coupling . Up until now, however, the ultracold temperatures required for these applications have not been reached, because the electric traps used to hold the ions cause heating during atom-ion collisions . In our experiment, we overlap a cloud of ultracold 6Li atoms in a dipole trap with a 171Yb+ ion in a Paul trap. The large mass ratio of this combination allows us to suppress trap-induced heating. For the very first time, we buffer gas-cooled a single Yb+ ion to temperatures close to the quantum (or s-wave) limit for 6Li-Yb+ collisions. We find significant deviations from classical predictions for the temperature dependence of the spin exchange rates in these collisions. Our results open up the possibility to study trapped atom-ion mixtures in the quantum regime for the first time. Finally, I will present a novel way to control interactions between atoms and ions, that employs Rydberg-coupling of the atoms to tune their polarizability [4,5].
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Sep 4, 2019
Driven-dissipative dynamics with trapped ions and qubit-arrays
In the first part of the talk I will present a framework based on action-angle phase-space coordinates, that advances the understanding of trapped ion dynamics far from thermal equilibrium. Using this approach we quantify the loading and trapping efficiency of surface-electrode traps, and identify when the pseudopotential approximation breaks due to chaotic motion . Treating also stochastic dynamics in Paul traps, we find regimes of anharmonic motion in which laser cooling turns into effective heating that can kick the ion of the trap , or capture it in long-lived stochastic limit cycles of large-amplitude . Close to the effective trap minimum, "excess micromotion" is another important factor interfering with the cooling; our theory shows how all these mechanisms can be counteracted, and we derive a relation allowing to deduce just from the observable photon scattering rate both the required detuning for optimal cooling and the final mean phonon number .
In the second part, I will present a recent study on the dynamics of interacting spins driven by external fields and subject to dissipation, a fundamental model of nonequilibrium quantum dynamics . Experiments with trapped ions can naturally realize the model and possibly answer open questions on the lower critical dimension for bistability and the existence of a dissipative phase transition, beyond the system sizes accessible to state-of-the-art numerics.
 Phase space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions, V. Roberdel, D. Leibfried, D. Ullmo, and H. Landa, Phys. Rev. A 97, 053419 (2018)
 Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps, A. Maitra, D. Leibfried, D. Ullmo, and H. Landa, Phys. Rev. A 99, 043421 (2019)
 Can a periodically driven particle resist laser cooling and noise? A. Maitra, D. Leibfried, D. Ullmo, and H. Landa, arXiv:1810.01856
 Tuning nonthermal distributions to thermal ones in time-dependent Paul traps, H. Landa, Phys. Rev. A 100, 013413 (2019)
 Multistability of Driven-Dissipative Quantum Spins, H. Landa, M. Schiró, G. Misguich, arXiv:1905.10349
Sep 4, 2019
COST WP3 session
COST WP3 session
Sep 5, 2019
Coherence time, Scalable global gate and error mitigation with ion-qubits
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
The performance of a physical quantum device for quantum computation can be evaluated by the following three criteria; the coherence time of a qubit, the fidelity of a logical gate, and number of qubits involved in coherent operations.
We have demonstrated the coherence time of a single 171Yb+ ion-qubit over 600 s with sympathetic cooling by a 138Ba+ ion and optimized dynamical decoupling-pulses in an ambient magnetic field condition . Recently, we experimentally investigate the limiting factors and enhance the coherence time to more than twice. We find that ambient magnetic-field noise and phase noise of the local oscillator are main sources for decoherence. To suppress field fluctuation, we enclose our vacuum system with a two-layer m-metal magnetic-shielding and use a permanent magnets to produce stable field. For the reference of the local oscillator, we use a crystal oscillator, which has one order of magnitude smaller Allan deviation than our previous Rb clock at 1 s. With such improvements, we observe the enhancement for the coherence time of clock state of 171Yb+ ion.
We also have developed a five-qubit programmable system and realized a scalable global quantum gate. A quantum algorithm can be decomposed into a sequence consisting of single qubit and 2-qubit entangling gates. To optimize the decomposition and achieve more efficient construction of the quantum circuit, we can replace multiple 2-qubit gates with a single global entangling gate. Here, we propose and implement a scalable scheme to realize the global entangling gates on multiple 171Yb+ ion qubits by coupling to multiple motional modes through external fields. Such global gates require simultaneously decoupling of multiple motional modes and balancing of the coupling strengths for all the qubit-pairs at the gate time. To demonstrate the usefulness of the global gates, we prepare the Greenberger-Horne-Zeilinger (GHZ) states in a single global-gate operation, and successfully show the genuine multi-partite entanglements up to four qubits with the state fidelities over 93.4 % .
For the improvements of logic gate fidelities, we apply a scheme of quantum error mitigation based on probabilistic error cancellation , which requires no additional qubit resources different from the scheme of quantum error correction. We benchmark the performance of the protocol of the probabilistic error cancellation in our trapped-ion system. We clearly observe that effective gate fidelities exceed physical fidelities. The error rates are effectively reduced from 10-3 to 10-5 and from 10-2 to 10-3 for single- and two-qubit gates, respectively . We believe our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device.
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 Shuaining Zhang, et al., arXiv:1905.10135
Sep 5, 2019
Quantum networking tools with
single ions and single photons
Jürgen Eschner, Quantum Photonics, Saarland University, Germany
We develop interfaces between stationary and propagating quantum bits, using single trapped ions and single photons. We demonstrate high-fidelity photon-to-ion and ion-to-photon qubit conversion, ion-photon entanglement, teleportation, as well as quantum frequency conversion of ion-generated photonic qubits to the telecom range. Such tools are required, for example, in quantum repeater protocols for reliable intermediate storage of quantum information.
Specifically, we implemented a programmable ion-photon interface, employing controlled quantum interaction between a single trapped 40Ca+ ion and single photons [1,2]. Using the same basic protocol, the interface serves as an ion-to-photon or photon-to-ion qubit converter, or as a source of entangled ion-photon states.
The interface lends itself particularly to integrating Ca+ ions with entangled photon pairs from a resonant, narrowband spontaneous parametric down-conversion (SPDC) source [3,4]. We demonstrate high-fidelity transfer of entanglement from an SPDC photon pair to atom-photon pairs, as well as atom-to-photon quantum bit teleportation . We also extend our quantum network toolbox into the telecom regime by quantum frequency conversion of ion-entangled photons .
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Sep 5, 2019
Developing a modular microwave trapped ion quantum computer
Winfried K. Hensinger1
1 Sussex Centre for Quantum Technologies, Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
Trapped ions are arguably the most mature technology capable of constructing practical large scale quantum computers. We are now moving away from fundamental physics studies towards tackling the required engineering tasks in order build such machines.
By inventing a new method where voltages applied to a quantum computer microchip are used to implement entanglement operations, we have managed to remove one of the biggest barriers traditionally faced to build a large-scale quantum computer using trapped ions, namely having to precisely align billions of lasers to execute quantum gate operations. This new approach, quantum computing with global radiation fields, is based on the use of well-developed microwave technology .
In order to be able to build large scale device, a quantum computer needs to be modular. One approach features modules that are connected via photonic interconnect, however, only very small connection speeds between modules demonstrated have been demonstrated so far. We have invented an alternative method where modules are connected via electric fields, allowing ions to be transported from one module to another giving rise to much faster connection speeds .
Incorporating these two inventions, we recently unveiled the first industrial blueprint on how to build a large-scale quantum computer which I will discuss in this talk . I will show progress in constructing a quantum computer prototype at the University of Sussex featuring this technology and I will discuss a new method we have demonstrated recently in order to make quantum gates with trapped ions more resilient to sources of decoherence such as motional heating, stray magnetic fields and noise in electrical components .
Trapped-ion quantum logic with global radiation fields, S. Weidt, J. Randall, S. C. Webster, K. Lake, A. E. Webb, I. Cohen, T. Navickas, B. Lekitsch, A. Retzker, and W. K. Hensinger, Phys. Rev. Lett. 117, 220501 (2016)
Blueprint for a microwave trapped ion quantum computer, B. Lekitsch, S. Weidt, A.G. Fowler, K. Mølmer, S.J. Devitt, Ch. Wunderlich, and W.K. Hensinger, Science Advances 3, e1601540 (2017)
Resilient entangling gates for trapped ions, A. E. Webb, S. C. Webster, S. Collingbourne, D. Bretaud, A. M. Lawrence, S. Weidt, F. Mintert and W. K. Hensinger, Phys. Rev. Lett. 121, 180501 (2018