Trapped atomic ions have been successfully used for demonstrating basic elements of universal quantum information processing (QIP) [1]. Nevertheless, scaling up of these methods and techniques to achieve large scale universal QIP, or more specialized quantum simulations [2][3][4][5] remains challenging. The use of easily controllable and stable microwave sources instead of complex laser systems [6,7] on the other hand promises to remove obstacles to scalability. Important remaining drawbacks in this approach are the use of magnetic field sensitive states, which shorten coherence times considerably, and the requirement to create large stable magnetic field gradients. Here, we present theoretically a novel approach based on dressing magnetic field sensitive states with microwave fields which addresses both issues and permits fast quantum logic. We experimentally demonstrate basic building blocks of this scheme to show that these dressed states are long-lived and coherence times are increased by more than two orders of magnitude compared to bare magnetic field sensitive states. This changes decisively the prospect of microwave-driven ion trap QIP and offers a new route to extend coherence times for all systems that suffer from magnetic noise such as neutral atoms, NV-centres, quantum dots, or circuit-QED systems. arXiv:1105.1146v1 [quant-ph] 5 May 20112 Introduction -Using laser light for coherent manipulation of qubits gives rise to fundamental issues, notably, unavoidable spontaneous emission which destroys quantum coherence [8,9]. The difficulty in cooling a collection of ions to their motional ground state and the time needed for such a process in the presence of spurious heating of Coulomb crystals limits the fidelity of quantum logic operations in laser-based quantum gates, and thus hampers scalability. This limitation is only partially removed by the use of 'hot' gates [10,11]. Technical challenges in accurately controlling the frequency and intensity of laser light as well as delivering a large number of laser beams of high intensity to trapped ions are further obstacles for scalability.These issues associated with the use of laser light for scalable QIP have lead to the development of novel concepts for performing conditional quantum dynamics with trapped ions that rely on radio frequency (rf) or microwave (mw) radiation instead of laser light [6,7,[12][13][14][15]. Rf or mw radiation can be employed for quantum gates through the use of magnetic gradient induced coupling (MAGIC) between spin states of ions [16], thus averting technical and fundamental issues of scalability that were described above. Furthermore, the sensitivity to motional excitation of ions is reduced in such schemes. A drawback of MAGIC is the necessity to use magnetic field sensitive states for conditional quantum dynamics, thus making qubits susceptible to ambient field noise and shortening their coherence time. This issue is shared with some optical ion trap schemes for QIP that usually rely on magnetic field sensitive states for cond...

The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science, the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g. the quantum transverse Ising model or a neural network), the Bose–Hubbard Hamiltonian, the Frenkel–Kontorova model, and quantum fields and relativistic effects.

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rfoptical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.PACS numbers: 37.10. Vz, 37.10.Ty, 32.60.+i Quantum simulations addressing a specific scientific problem and universal quantum computation are expected to yield new insight into as of yet unsolved physical problems that withstand efficient treatment on a classical computer (e.g., [1]). Already a small number of qubits (i.e., a few tens) used for quantum simulations could solve problems even beyond the realm of quantum information science. Creating and investigating entanglement in large physical systems is a related important experimental challenge with implications for our understanding of the transition between the elusive quantum regime and the classical world [2].Laser cooled atomic ions confined in an electrodynamic cage have successfully been used for quantum information processing (QIP) [3] and advantages and difficulties associated with this system have been and still are subject to detailed investigations. The electromagnetic radiation used to coherently drive ionic resonances that serve as qubits needs to be stable against variations in frequency, phase, and amplitude over the course of a quantum computation or simulation. Experimentally this is particularly challenging when laser light is used for realizing quantum gates. When employing laser light additional issues need to be dealt with to allow for accurate qubit manipulation such as the intensity profile of the laser beam, its pointing stability, and diffraction effects. Furthermore, the motional state of the ion chain strongly affects the gate fidelity which requires ground state cooling and low heating rates during the gate operation [4]. Also, spontaneous scattering of laser light off excited electronic states may pose a limit for the coherence time of a quantum many-body state. The probability for scattering can be reduced by increasing the detuning from excited states (when two laser light fields are used that drive a Raman transition between hyperfine or Zeeman states) which, however, leads to an increasing demand for laser power [5].For generating Raman laser beams with a desired frequency difference, first a radio-frequency (rf) or microwave signal at this difference frequency has to be generated that is then "imprinted" on the laser light and send to the ions. Using rf or microwave radiation directly for coherent driving of qubit transitions is impeded in usual ion trap schemes, since, (i) individual addressing of qubits by focusing radiation on just one ion is difficult due to the long wavelength of rf radiation, and (ii) the required coupling between qubit stat...

We report on the experimental investigation of an individual pseudomolecule using trapped ions with adjustable magnetically induced J-type coupling between spin states. Resonances of individual spins are well separated and are addressed with high fidelity. Quantum gates are carried out using microwave radiation in the presence of thermal excitation of the pseudomolecule's vibrations. Demonstrating controlled-NOT gates between non-nearest neighbors serves as a proof-of-principle of a quantum bus employing a spin chain. Combining advantageous features of nuclear magnetic resonance experiments and trapped ions, respectively, opens up a new avenue toward scalable quantum information processing.

Coherent operations constitutive for the implementation of single and multi-qubit quantum gates with trapped ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated for the first time with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses.In order to experimentally implement a device capable of performing fault-tolerant universal quantum computation (QC), quantum gate operations involving one or multiple qubits have to be carried out with demandingly high accuracy (see, for instance, [1,2]). According to recent theoretical investigations, the experimentally required accuracy of quantum gates for fault-tolerant universal quantum computation no longer seems daunting or even prohibitive [2]. But still, the desired error probability per gate (EPG) should be as small as possible in order to keep the experimental overhead necessary for quantum computation within a feasible limit. Thus a low error probability is prerequisite for scalable fault-tolerant QC.Any quantum algorithm can be decomposed into a sequence of unitary operations applied to individual qubits (single-qubit gate) and conditional quantum dynamics with at least two qubits [3]. Multi-qubit gates (involving two or more qubits) are synthesized by applying a sequence of elementary unitary operations on a collection of qubits. Each of these elementary operations is often similar, or identical, to what is needed for singlequbit gates, and therefore each operation has to be implemented with an error probability well below the tolerable EPG characterizing the full gate operation.If electrodynamically trapped ions are used as qubits, then a unitary operation amounts to letting ions interact with electromagnetic radiation with prescribed frequency, phase, amplitude, and duration of interaction in order to implement quantum gates. Recently, impressive experimental progress was demonstrated in entangling up to eight ions, and performing 2-qubit quantum gates [4,5,6]. Architectures allowing for scalable QC with trapped ions have been proposed (e.g., [7]), and building blocks necessary for achieving this ambitious goal are currently being investigated using various types of ions.The error budget, for instance, of the geometrical phase gate demonstrated in [6] is dominated by the frequency and amplitude uncertainty of the laser light field. These errors are also responsible for a part of the EPG of the controlled-NOT gate reported in [5]. If an "ion spin molecule", that is, trapped ions coupled via a long range spin-spin interaction, is to be used for quantum information processing, then the exact transition frequency of a particular ionic qubit depends on the internal state of other ions [8]. Therefore, here too, it is important to have quantum gates at hand that are insensitive to the detuning of the radiation driving the qubit tran...

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1 + 1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting smallscale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.

A promising scheme for building scalable quantum simulators and computers is the synthesis of a scalable system using interconnected subsystems. A prerequisite for this approach is the ability to faithfully transfer quantum information between subsystems. With trapped atomic ions, this can be realized by transporting ions with quantum information encoded into their internal states. Here, we measure with high precision the fidelity of quantum information encoded into hyperfine states of a 171 Yb + ion during ion transport in a microstructured Paul trap. Ramsey spectroscopy of the ion's internal state is interleaved with up to 4000 transport operations over a distance of 280 µm each taking 12.8 µs. We obtain a state fidelity of 99.9994 +6 −7 % per ion transport.PACS numbers: 03.67. Lx,37.10.Ty Ion traps have been a workhorse in demonstrating many proof-of-principle experiments in quantum information processing using small ion samples [1]. A major challenge to transform this ansatz into a powerful quantum computing machine that can handle problems beyond the capabilities of classical super computers remains its scalability [2][3][4][5]. Error correction schemes allow us to fight the ever sooner death of fragile quantum information stored in larger and larger quantum systems, but their economic implementation requires computational building blocks to be executed with sufficient fidelity [6,7]. Essential computational steps have been demonstrated with fidelities beyond a threshold of 99.99% that is often considered as allowing for economic error correction [8], and, thus for fault-tolerant scalable quantum information processing (QIP). These building blocks include single qubit rotation [9,10], individual addressing of interacting ions [11], and internal state detection [12]. In addition, high fidelity twoqubit quantum gates [10,[13][14][15][16] and coherent three-qubit conditional quantum gates [17,18] have been implemented.Straightforward scaling up to an arbitrary size of a single ion trap quantum register, at present, appears unlikely to be successful because the growing size of a single register usually introduces additional constraints imposed by the confining potential and by the Coulomb interaction of ion strings [19]. Even though, for instance, transverse modes and anharmonic trapping [20] may be employed for conditional quantum logic, a general claim might be that, at some point it is useful to divide a single ion register into subsystems and to exchange quantum information between these subsystems [2][3][4][5]. One might do that by transferring quantum information from ions to photons (and vice versa) and by then exchanging photons between subsystems [4,21].Alternatively, when exchanging quantum information between spatially separated individual registers within an ion trap-based quantum information processor, the transport of ions carrying this information is an attractive approach [2,3,5]. Methods to transport ions in segmented Paul traps have been developed and demonstrated [22][23][24][25], and opti...

We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states