In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the UK and Innsbruck University respectively. The secular frequencies for Strontium-88 and Calcium-40 ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control when no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.
We report on the construction and characterization of an apparatus for quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the $S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions' external and internal states. Oscillating magnetic fields …
We demonstrate a miniature, fiber-coupled optical tweezer to trap a single atom. The same fiber is used to trap a single atom and to read out its fluorescence. To obtain a low background level, the tweezer light is chopped, and we measure the influence of the chopping frequency on the atom's lifetime. We use the single atom as a single-photon source at 780 nm and measure the second-order correlation function of the emitted photons. Because of its miniature, robust, fiber-pigtailed design, this tweezer can be implemented in a broad range of experiments where single atoms are used as a resource.
We present a model for the scaling laws of the electric field noise spectral density as a function of the distance, $d$, above a conducting surface. Our analytical approach models the patch potentials by introducing a correlation length, $ζ$, of the electric potential on the surface. The predicted scaling laws are in excellent agreement with two different classes of experiments (cold trapped ions and cantilevers), that span at least four orders of magnitude of $d$. According to this model, heating rate in miniature ion traps could be greatly reduced by proper material engineering.
We investigate a surface-mounted electrode geometry for miniature linear radio frequency Paul ion traps. The electrodes reside in a single plane on a substrate, and the pseudopotential minimum of the trap is located above the substrate at a distance on order of the electrodes' lateral extent or separation. This architecture provides the possibility to apply standard microfabrication principles to the construction of multiplexed ion traps, which may be of particular importance in light of recent proposals for large-scale quantum computation based on individual trapped ions.
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac-component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctu…
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.
The electromagnetic manipulation of isolated atoms has led to many advances in physics, from laser cooling and Bose-Einstein condensation of cold gases to the precise quantum control of individual atomic ion. Work on miniaturizing electromagnetic traps to the micrometer scale promises even higher levels of control and reliability. Compared with 'chip traps' for confining neutral atoms, ion traps with similar dimensions and power dissipation offer much higher confinement forces and allow unparalleled control at the single-atom level. Moreover, ion microtraps are of great interest in the develop…
We present an ion trap with an integrated fiber cavity, designed for strong coupling at the level of single ions and photons. The cavity is aligned to the axis of a miniature linear Paul trap, enabling simultaneous coupling of multiple ions to the cavity field. We simulate how charges on the fiber mirrors affect the trap potential, and we test these predictions with an ion trapped in the cavity. Furthermore, we measure micromotion and heating rates in the setup.
The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes…
Silicon offers an attractive material platform for hardware realization of quantum computing. In this study, a microscopic stochastic simulation method is developed to model the effect of random interface charge traps in silicon metal-oxide-semiconductor (MOS) quantum gates. The statistical results show that by using a fast two-qubit gate in isotopically purified silicon, the two-qubit silicon-based quantum gates have the fidelity >98% with a probability of 75% for the state-of-the-art MOS interface quality. By using a composite gate pulse, the fidelity can be further improved to >99.5% with t…
We propose a scheme to implement high-fidelity conditional phase gates on pair of trapped ions immersed in a two-dimensional Coulomb crystal, using interaction mediated by all axial modes without side-band addressing. We show through numerical calculations that only local modes can be excited to achieve entangling gates through shaping the laser beams, so that the complexity of the quantum gate does not increase with the size of the system. These results suggest a promising approach for realization of large scale fault-tolerant quantum computation in two dimensional traps architecture.
Two or three dimensional Paul traps can confine a large number of ions forming a Wigner crystal, which would provide an ideal architecture for scalable quantum computation except for the micromotion, an issue that is widely believed to be the killer for high fidelity quantum gates. Surprisingly, here we show that the micromotion is not an obstacle at all for design of high fidelity quantum gates, even though the magnitude of the micromotion is significantly beyond the requirement of the Lamb-Dicke condition. Through exact solution of the quantum Mathieu equations, we demonstrate the principle …
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technica…
Qubit state detection is an important part of a quantum computation. As number of qubits in a quantum register increases, it is necessary to maintain high fidelity detection to accurately measure the multi-qubit state. Here we present experimental demonstration of high-fidelity detection of a multi-qubit trapped ion register with average single qubit detection error of 4.2(1.5) ppm and a 4-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a novel single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and lo…
We report reliable transport of 9Be+ ions through a 2-D trap array that includes a separate loading/reservoir zone and an "X-junction". During transport the ion's kinetic energy in its local well increases by only a few motional quanta and internal-state coherences are preserved. We also examine two sources of energy gain during transport: a particular radio-frequency (RF) noise heating mechanism and digital sampling noise. Such studies are important to achieve scaling in a trapped-ion quantum information processor.
We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field.
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 171Yb+ ion during ion transport in a microstructured Paul trap. Ramsey spectroscopy of the ion's internal s…
We discuss a simple architecture for a quantum Toffoli gate implemented using three trapped ions. The gate, which in principle can be implemented with a single laser-induced operation, is effective under rather general conditions and is strikingly robust (within any experimentally realistic range of values) against dephasing, heating and random fluctuations of the Hamiltonian parameters. We provide a full characterization of the unitary and noise-affected gate using three-qubit quantum process tomography.
We demonstrate single-shot qubit readout with fidelity sufficient for fault-tolerant quantum computation, for two types of qubit stored in single trapped calcium ions. For an optical qubit stored in the (4S_1/2, 3D_5/2) levels of 40Ca+ we achieve 99.991(1)% average readout fidelity in one million trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145us average detection time. For a hyperfine qubit stored in the long-lived 4S_1/2 (F=3, F=4) sub-levels of 43Ca+ we propose and implement a simple and robust optical pumping scheme …
We demonstrate high fidelity single-qubit gate operation in a trapped single neutral atom. The atom is trapped in the recently invented magic-intensity optical dipole trap (MI-ODT) with more stable magnetic field. The MI-ODT efficiently mitigates the detrimental effects of light shifts thus sufficiently improves the performance of single qubit-gates. The gates are driven with microwave, and the fidelity of gate operation is characterized by using the randomized benchmarking method. We obtain an average error per Clifford gate of $3.0(7)\times10^{-5}$ which is much below the error threshold ($1…
In this work, we introduce machine learning methods to implement readout of a single qubit on $^{171}\mathrm{Yb^{+}}$ trapped-ion system. Different machine learning methods including convolutional neural networks and fully-connected neural networks are compared with traditional methods in the tests. The results show that machine learning methods have higher fidelity, more robust readout results in relatively short time. To obtain a 99% readout fidelity, neural networks only take half of the detection time needed by traditional threshold or maximum likelihood methods. Furthermore, we implement …
We present a method that combines continuous and pulsed microwave radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $π$ pulses. This leads to high-fidelity entangling gates which are resilient against magnetic field fluctuations, changes on the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensiti…
Entanglement between a stationary quantum system and a flying qubit is an essential ingredient of a quantum-repeater network. It has been demonstrated for trapped ions, trapped atoms, color centers in diamond, or quantum dots. These systems have transition wavelengths in the blue, red or near-infrared spectral regions, whereas long-range fiber-communication requires wavelengths in the low-loss, low-dispersion telecom regime. A proven tool to interconnect flying qubits at visible/NIR wavelengths to the telecom bands is quantum frequency conversion. Here we use an efficient polarization-preservi…
To achieve high-fidelity operations on a large-scale quantum computer, the parameters of the physical system must be efficiently characterized with high accuracy. For trapped ions, the entanglement between qubits are mediated by the motional modes of the ion chain, and thus characterizing the motional-mode parameters becomes essential. In this paper, we develop and explore physical models that accurately predict both magnitude and sign of the Lamb-Dicke parameters when the modes are probed {\it in parallel}. We further devise an advanced characterization protocol that shortens the characteriza…
A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses, which reduces dramatically the addressing error in a lattice of closely spaced atoms or ions, and at the same time significantly enhances the robustness of qubit manipulations. To this end, we design novel high-fidelity composite pulses for the most important single-qubit operations. In principle, this method allows one to beat the diffraction limit, for only atoms situat…
We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above the approximately 99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed/fidelity trade-off for the two-qubit gate, for gate times between 3.8$μ$s and 520$μ$s, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.
The realization of high fidelity quantum gates in a multi-qubit system, with a typical target set at 99.9%, is a critical requirement for the implementation of fault-tolerant quantum computation. To reach this level of fidelity, one needs to carefully analyze the noises and imperfections in the experimental system and optimize the gate operations to mitigate their effects. Here, we consider one of the leading experimental systems for the fault-tolerant quantum computation, ions in an anharmonic linear Paul trap, and optimize entangling quantum gates using segmented laser pulses with the assist…
We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with $\hatσ^z$-dependent forces for trapped ion quantum computing. The force is exerted by two laser beams in a Raman configuration. Qubit-state dependency is achieved by a small frequency detuning from the virtually-excited state. Ion species with excited states of long radiative lifetimes are used to reduce the chance of a spontaneous photon emission to less than 10$^{-8}$ per gate-run. This eliminates the main source of gate infidelity of previous implementations. With this scheme it seems possible …
We have demonstrated transport of Be+ ions through a 2D Paul-trap array that incorporates an X-junction, while maintaining the ions near the motional ground-state of the confining potential well. We expand on the first report of the experiment [1], including a detailed discussion of how the transport potentials were calculated. Two main mechanisms that caused motional excitation during transport are explained, along with the methods used to mitigate such excitation. We reduced the motional excitation below the results in Ref. [1] by a factor of approximately 50. The effect of a mu-metal shield…
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for Hadamard gate when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.
We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) \times 10^{-3}$. We analyze the expected errors in the MS gate and find that pop…
We demonstrate high fidelity entangling quantum gates within a chain of five trapped ion qubits by optimally shaping optical fields that couple to multiple collective modes of motion. We individually address qubits with segmented optical pulses to construct multipartite entangled states in a programmable way. This approach enables both high fidelity and fast quantum gates that can be scaled to larger qubit registers for quantum computation and simulation.
Fast and efficient detection of the qubit state in trapped ion quantum information processing is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a $^{171}$Yb$^+$ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1 and 99.8\,$\upmu$s, corresponding to state detection fidelities of 99%, 99.85(1…
A quantum communication system is proposed that uses polarization-entangled photons and trapped-atom quantum memories. This system is capable of long-distance, high-fidelity teleportation, and long-duration quantum storage.
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
Trapped-ion qubits are a leading technology for practical quantum computing. In this work, we present an architectural analysis of a linear-tape architecture for trapped ions. In order to realize our study, we develop and evaluate mapping and scheduling algorithms for this architecture. In particular, we introduce TILT, a linear "Turing-machine-like" architecture with a multilaser control "head", where a linear chain of ions moves back and forth under the laser head. We find that TILT can substantially reduce communication as compared with comparable-sized Quantum Charge Coupled Device (QCCD) …
Integrated technologies greatly enhance the prospects for practical quantum information processing and sensing devices based on trapped ions. High-speed and high-fidelity ion state readout is critical for any such application. Integrated detectors offer significant advantages for system portability and can also greatly facilitate parallel operations if a separate detector can be incorporated at each ion-trapping location. Here we demonstrate ion quantum state detection at room temperature utilizing single-photon avalanche diodes (SPADs) integrated directly into the substrate of silicon ion tra…
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We find the fidelity for Hadamard gate and compute the purity of the final state when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate that in contradiction to the case of the systematic control errors the stochastic ones lead to decoherence of the final state. In the small errors limit we derive a simple formulae connecting the gate fidelity and the purity of the final state.
System scalability is fundamental for large-scale quantum computers (QCs) and is being pursued over a variety of hardware platforms. For QCs based on trapped ions, architectures such as the quantum charge-coupled device (QCCD) are used to scale the number of qubits on a single device. However, the number of ions that can be hosted on a single quantum computing module is limited by the size of the chip being used. Therefore, a modular approach is of critical importance and requires quantum connections between individual modules. Here, we present the demonstration of a quantum matter-link in whi…
We propose a potentially practical scheme for realization of an n-qubit (n>2) conditional phase flip (CPF) gate and implementation of Grover search algorithm in the ion-trap system. We demonstrate both analytically and numerically that, our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. We also show the merits of the proposal that the increase of the ion number can improve the fidelity and the success probability of the CPF gate. The required operations for Grover search are very close to the capabilities of current ion-trap techniq…
We prepare and detect the hyperfine state of a single 87Rb atom coupled to a fiber-based high finesse cavity on an atom chip. The atom is extracted from a Bose-Einstein condensate and trapped at the maximum of the cavity field, resulting in a reproducibly strong atom-cavity coupling. We use the cavity reflection and transmission signal to infer the atomic hyperfine state with a fidelity exceeding 99.92% in a read-out time of 100 microseconds. The atom is still trapped after detection.
The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a $^{171}\text{Yb}^+$ ion trapped in a microfabricated surface electrode ion trap. Gate error is characterized using a randomized benchmarking protocol, and an average error per randomized Clifford group gate of $3.6(3)\times1…
Conditional multi-qubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. (Phys. Rev. A 101, 022308) proposed an efficient single-step method for a prototypical multi-qubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the drivin…
