We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity gates are achievable even in large arrays with hundreds of ions. To demonstrate the usefulness of this proposal, we investigate the application of these gates to the digital simulation of a 40-mode Fermi-Hubbard model. This also demonstrates why shorter chains of gates required to connect arbitrary pairs of ions makes this geometry well suited for large-scale computation.
We propose a configuration of a magnetic microtrap which can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order suppress these excitations…
We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped-ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than c…
Most attempts to produce a scalable quantum information processing platform based on ion traps have focused on the shuttling of ions in segmented traps. We show that an architecture based on an array of microtraps with fast gates will outperform architectures based on ion shuttling. This system requires higher power lasers, but does not require the manipulation of potentials or shuttling of ions. This improves optical access, reduces the complexity of the trap, and reduces the number of conductive surfaces close to the ions. The use of fast gates also removes limitations on gate time. The perf…
The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical …
An experimental demonstration of a novel all-optical technique for loading ion traps, that has particular application to microtrap architectures, is presented. The technique is based on photo-ionisation of an atomic beam created by pulsed laser ablation of a calcium target, and provides improved temporal control compared to traditional trap loading methods. Ion loading rates as high as 125 ions per second have so far been observed. Also described are observations of trap loading where Rydberg state atoms are photo-ionised by the ion Doppler cooling laser.
We propose a new design for a quantum information processor where qubits are encoded into Hyperfine states of ions held in a linear array of individually tailored microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single and multi-qubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the mic…
We present an efficient approach to optimising pulse sequences for implementing fast entangling two-qubit gates on trapped ion quantum information processors. We employ a two-phase procedure for optimising gate fidelity, which we demonstrate for multi-ion systems in linear Paul trap and microtrap architectures. The first phase involves a global optimisation over a computationally inexpensive cost function constructed under strong approximations of the gate dynamics. The second phase involves local optimisations that utilise a more precise ODE description of the gate dynamics, which captures th…
We review our experiments on quantum information processing with neutral atoms in optical lattices and magnetic microtraps. Atoms in an optical lattice in the Mott insulator regime serve as a large qubit register. A spin-dependent lattice is used to split and delocalize the atomic wave functions in a controlled and coherent way over a defined number of lattice sites. This is used to experimentally demonstrate a massively parallel quantum gate array, which allows the creation of a highly entangled many-body cluster state through coherent collisions between atoms on neighbouring lattice sites. I…
Arrays of trapped atoms are the ideal starting point for developing registers comprising large numbers of physical qubits for storing and processing quantum information. One very promising approach involves neutral atom traps produced on microfabricated devices known as atom chips, as almost arbitrary trap configurations can be realised in a robust and compact package. Until now, however, atom chip experiments have focused on small systems incorporating single or only a few individual traps. Here we report experiments on a two-dimensional array of trapped ultracold atom clouds prepared using a…
We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation; and to excite a condensate from the ground to the first excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use, namely gradient ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational p…
We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.
We examine the performance of a quantum phase gate implemented with cold neutral atoms in microtraps, when anharmonic traps are employed and the effects of finite temperature are also taken into account. Both the anharmonicity and the temperature are found to pose limitations to the performance of the quantum gate. We present a quantitative analysis of the problem and show that the phase gate has a high quality performance for the experimental values that are presently or in the near future achievable in the laboratory.
It is proposed to modify the Cirac-Zoller proposal of quantum computer with cold ions in a global oscillator trap potential by adding a periodic potential with an incommensurate average ratio of number of ions to number of periods being order of unity. With the increase of the periodic potential amplitude the system enters in the Aubry pinned phase characterized by quasi-frozen positions of ions and a gap of their first phonon excitations becomes independent of number of ions. This gives hopes that this quantum computer will be really scalable. It is argued that the usual single- and two-qubit…
Entangling multiple qubits is one of the central tasks for quantum information processings. Here, we propose an approach to entangle a number of cold ions (individually trapped in a string of microtraps) by a moved cavity. The cavity is pushed to include the ions one by one with an uniform velocity, and thus the information stored in former ions could be transferred to the latter ones by such a moving cavity bus. Since the positions of the trapped ions are precisely located, the strengths and durations of the ion-cavity interactions can be exactly controlled. As a consequence, by properly sett…
Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap in different storage and processing zones. The individual position control of many ions - each of them carrying qubit information in its long-lived electronic levels - by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent …
We propose a practical scheme for implementing two-dimension quantum dense coding (QDC) between three parties through manipulating three ions confined in microtraps addressed by microwaves and assisted by a magnetic field gradient. The ions in our scheme are not required to be strictly cooled to the vibrational ground state because single-qubit and multi-qubit operations are made via Ising terms, in which the vibrational modes of the ions remain unchanged throughout the scheme, rendering our scheme robust to the heating of the ions. We also present the detailed steps and parameters for impleme…
By means of the Ising terms generated by Coulomb interaction between ions and the magnetic field gradient, we carry out teleportation with insurance with trapped ions. We show the feasibility and the favorable feature of our scheme by comparing with the recently achieved teleportation experiments with trapped ions.
The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.
We propose a novel scheme to implement a quantum controlled phase gate for trapped ions in thermal motion with one standing wave laser pulse. Instead of applying the rotating wave approximation this scheme makes use of the counter-rotating terms of operators. We also demonstrate that the same scheme can be used to generate maximally entangled states of $N$ trapped ions by a single laser pulse.
We describe the optimal realization of entangling quantum gates for trapped ions mediated by a dissipative bus mode. With suitably shaped control pulses one can substantially decrease ion-phonon entanglement while maintaining the mediated interaction.
We propose a scheme to implement quantum phase gate for two $Λ$ ions trapped in optical cavity. It is shown that quantum phase gate can be implemented by applying a laser addressing to a single ions in strongly detuned optical cavity. We further demonstrate that geometric quantum phase gate can be implemented by introducing a auxiliary ground state.
A "continuous measurement" Quantum Zeno Effect (QZE) in the context of trapped ions is predicted. We describe the physical system and study its exact time evolution showing the appearance of Zeno Phenomena. New indicators for the occurrence of QZE in oscillatory systems are proposed and carefully discussed.
We propose and demonstrate a scalable scheme for the simultaneous determination of internal and motional states in trapped ions with single-site resolution. The scheme is applied to the study of polaritonic excitations in the Jaynes- Cummings Hubbard model with trapped ions, in which the internal and motional states of the ions are strongly correlated. We observe quantum phase transitions of polaritonic excitations in two ions by directly evaluating their variances per ion site. Our work establishes an essential technological method for large-scale quantum simulations of polaritonic systems.
There has been much interest in developing methods for transferring quantum information. We discuss a way to transfer quantum information between two trapped ions through a wire. The motion of a trapped ion induces oscillating charges in the trap electrodes. By sending this current to the electrodes of a nearby second trap, the motions of ions in the two traps are coupled. We investigate the electrostatics of a set-up where two separately trapped ions are coupled through an electrically floating wire. We also discuss experimental issues, including possible sources of decoherence.
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.
We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A $σ_x σ_x$-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of Yb ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely-spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.
We propose to use a large cloud of cold trapped ions as a medium for quantum optics and quantum information experiments. Contrary to most recent realizations of qubit manipulation based on a small number of trapped and cooled ions, we study the case of traps containing a macroscopic number of ions. We consider in particular the implementation of a quantum memory for quantum information stored in continuous variables and study the impact of the relevant physical parameters on the expected performances of the system.
A k-quantum nonlinear Jaynes-Cummings model for two trapped ions interacting with laser beams resonant to k-th red side-band of center-of-mass mode, far from Lamb-Dicke regime, has been obtained. The exact analytic solution showed the existence of quantum collapses and revivals of the occupation of two atoms.
We propose a method for generating maximally entangled states of N two-level trapped ions. The method is deterministic and independent of the number of ions in the trap. It involves a controlled-NOT acting simultaneously on all the ions through a dispersive interaction. We explore the potential application of our scheme for high precision frequency standards.
We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser whilst also being driven by a blue-detuned laser which results in self-oscillation. Working in a non-classical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom wit…
Invariant-based inverse engineering is an elegant approach to quantum control with corresponding experimental implementations that perform tasks with applications in quantum information processing such as shuttling trapped ions. We build on recent work to generalise invariant-based inverse engineering to control two coupled harmonic oscillators in any number of spatial dimensions. This may be used to perform experimentally relevant tasks such as separation of trapped ions, which is demonstrated numerically, achieving transfer fidelities of over 96% as well as low motional number excitations.
The mode-mode entanglement between trapped ions and cavity fields is investigated in the dispersive regime. We show how a simple initial preparation of Gaussian coherent states and a postselection may be used to generate motional non-local mesoscopic states (NLMS) involving ions in different traps. We also present a study of the entanglement induced by dynamical Stark-shifts considering a cluster of N-trapped ions. In this case, all entanglement is due to the dependence of the Stark-shifts on the ions' state of motion manifested as a cross-Kerr interaction between each ion and the field.
We propose a scheme to perform a fundamental two-qubit gate between two trapped ions using ideas from atom interferometry. As opposed to the scheme considered by J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995), it does not require laser cooling to the motional ground state.
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 rf-optical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.
Essentially all known quantum gates rely on a weak-coupling approximation resulting in linear dynamics. With the explicit example of trapped ions, we show how high-fidelity quantum gates can be achieved outside such an approximation, and we derive readily implementable driving fields to realize gates with extremely high fidelities for ions well outside the Lamb-Dicke regime with motional temperatures achievable by only Doppler cooling.
We show how to create quantum gates of arbitrary speed between trapped ions, using a laser walking wave, with complete insensitivity to drift of the optical phase, and requiring cooling only to the Lamb-Dicke regime. We present pulse sequences that satisfy the requirements and are easy to produce in the laboratory.
We study two trapped ions coupled to the axial phonon modes of a one-dimensional Coulomb crystal. This system is formally equivalent to the "two spin-boson" model. We propose a scheme to dynamically generate a maximally entangled state of two ions within a decoherence-free subspace. Here the phononic environment of the trapped ions, whatever its temperature and number of modes, serves as the entangling bus. The efficient production of the pure singlet state can be exploited to perform short-ranged quantum communication which is essential in building up a large-scale quantum computer.
We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.
We propose a method to manipulate the normal modes in a chain of trapped ions using only two lasers. Linear chains of trapped ions have proven experimentally to be highly controllable quantum systems with a variety of refined techniques for preparation, evolution, and readout, however, typically for quantum information processing applications people have been interested in using the internal levels of the ions as the computational basis. We analyse the case where the motional degrees of freedom of the ions is the quantum system of interest, and where the internal levels are leveraged to facili…
Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -- analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a $N$-qubit molecule with adjustable coupling constants.
We study theoretically the collective E$\otimes$e Jahn-Teller-Dicke distortion in a system of trapped ions. We focus in the limit of infinite range interactions in which an ensemble of effective spins interacts with two collective vibrational modes with U(1) symmetric couplings. Our model is exactly solvable in the thermodynamical limit and it is amenable to be solved by exact numerical diagonalization for a moderate number of ions. We show that trapped ions are ideally suited to study the emergence of spontaneous symmetry breaking of a continuous symmetry and magnetic structural phase transit…
We analyze nonlinear coupling between individual vibrational quanta for trapped ions. The nonlinear Coulomb interaction causes a Kerr-type Hamiltonian, for which we derive an analytical expression for the coupling constant. In contrast to a previously published formula [1], our result is in close agreement with experimental data.
We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.
Based on the exact conditional quantum dynamics for a two-ion system, we propose an efficient {\it single-step} scheme for coherently manipulating quantum information of two trapped cold ions by using a pair of synchronous laser pulses. Neither the auxiliary atomic level nor the Lamb-Dicke approximation are needed.
We collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits.
We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. Häffner \emph{et. al} [Nature \textbf{438}, 643-646 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.
We propose a potential scheme to generate entangled photons by manipulating trapped ions embedded in two-mode microcavities, respectively, assisted by a magnetic field gradient. By means of the spin-spin coupling due to the magnetic field gradient and the Coulomb repulsion between the ions, we show how to efficiently generate entangled photons by detecting the internal states of the trapped ions. We emphasize that our scheme is advantageous to create complete sets of entangled multi-photon states. The requirement and the experimental feasibility of our proposal are discussed in detail.
We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.
We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use the ions interaction to effectively infer the temperature of the individual ions, by optimising the interaction time evolution and by measuring only over one of the ions. We also investigate the effect of a non-thermal reservoir over the inference approach. The non-classicality of one of the ions vibrational modes, introduced due to a squeezed thermal reservoi…
We propose a scalable procedure to generate entangled superpositions of motional coherent states and electronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies of decoherence.
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 tra…
The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped $^{85}$Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number f…
We show how NOON states may be generated in ion traps. We use the individual interaction of light with each of two vibrational modes of the ion to entangle them. This allows us to generate NOON states with N=8.
We explore and develop the mathematics of the two multi-level ions. In particular, we describe some new features of quantum entanglement in two three-level trapped ions confined in a one-dimensional harmonic potential, allowing the instantaneous position of the center-of-mass motion of the ions to be explicitly time-dependent. By solving the exact dynamics of the system, we show how survivability of the quantum entanglement is determined by a specific choice of the initial state settings.
We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.
