K. R. Brown

We present the design and characterization of a cryogenic vacuum chamber incorporating mechanical isolation from vibrations, a high numerical-aperture in-vacuum imaging objective, in-vacuum magnetic shielding, and an antenna for global radio-frequency manipulation of trapped ions. The cold shield near 4 K is mechanically referenced to an underlying optical table via thermally insulating supports and exhibits root-mean-square vibrations less than 7.61(4) nm. Using the in-vacuum objective, we can detect 397 nm photons from a trapped $^{40}\mathrm{Ca}^{+}$ ion with 1.77% efficiency and achieve 99.9963(4)% single-shot state-detection fidelity in 50 $μ$s. To characterize the efficacy of the magnetic shields, we perform Ramsey experiments on the ground state qubit and obtain a coherence time of 24(2) ms, which extends to 0.25(1) s with a single spin-echo pulse. XY4 and XY32 dynamical decoupling sequences driven via the radio-frequency antenna extend the coherence to 0.72(2) s and 0.81(3) s, respectively.

Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.

The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols.

State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with $^{40}$Ca$^+$ ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with $^{171}$Yb$^+$ ions in a second BGA trap.

The advent of microfabricated ion traps for the quantum information community has allowed research groups to build traps that incorporate an unprecedented number of trapping zones. However, as device complexity has grown, the number of digital-to-analog converter (DAC) channels needed to control these devices has grown as well, with some of the largest trap assemblies now requiring nearly one hundred DAC channels. Providing electrical connections for these channels into a vacuum chamber can be bulky and difficult to scale beyond the current numbers of trap electrodes. This paper reports on the development and testing of an in-vacuum DAC system that uses only 9 vacuum feedthrough connections to control a 78-electrode microfabricated ion trap. The system is characterized by trapping single and multiple $^{40}$Ca$^+$ ions. The measured axial mode stability, ion heating rates, and transport fidelities for a trapped ion are comparable to systems with external(air-side) commercial DACs.

We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171Yb+ hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit pi-rotations as fast as 1 us with less than 6 % variation in Rabi frequency over an 800 um microwave interaction region. Fully compensating pulse sequences further improve the uniformity of X-gates across this interaction region.

Microwave near-field quantum control of spin and motional degrees of freedom of 25Mg+ ions can be used to generate two-ion entanglement, as recently demonstrated in Ospelkaus et al. [Nature 476, 181 (2011)]. Here, we describe additional details of the setup and calibration procedures for these experiments. We discuss the design and characteristics of the surface-electrode trap and the microwave system, and compare experimental measurements of the microwave near-fields with numerical simulations. Additionally, we present a method that utilizes oscillating magnetic-field gradients to detect micromotion induced by the ponderomotive radio-frequency potential in linear traps. Finally, we discuss the present limitations of microwave-driven two-ion entangling gates in our system.

The practical construction of scalable quantum computer hardware capable of executing non-trivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault-tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

Anomalous heating of trapped atomic ions is a major obstacle to their use as quantum bits in a scalable quantum computer. The physical origin of this heating is not fully understood, but experimental evidence suggests that it is caused by electric-field noise emanating from the surface of the trap electrodes. In this study, we have investigated the role that adsorbates on the electrodes play by identifying contaminant overlayers, developing an in situ argon-ion beam cleaning procedure, and measuring ion heating rates before and after cleaning the trap electrodes' surfaces. We find a reduction of two orders of magnitude in heating rate after cleaning.

Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light. Similar control is difficult to achieve with radio frequency or microwave radiation because the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms' motion. The field gradients are negligible at these frequencies for freely propagating fields; however, stronger gradients can be generated in the near-field of microwave currents in structures smaller than the free-space wavelength. In the experiments reported here, we coherently manipulate the internal quantum states of the ions on time scales of 20 ns. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation suitable for general quantum computation. We implement both operations through the magnetic fields from microwave currents in electrodes that are integrated into the micro-fabricated trap structure and create an entangled state with fidelity 76(3) %. This approach, where the quantum control mechanism is integrated into the trapping device in a scalable manner, can potentially benefit quantum information processing, simulation and spectroscopy.

With a 9Be+ trapped-ion hyperfine-states qubit, we demonstrate an error probability per randomized single-qubit gate of 2.0(2) x 10^-5, below the threshold estimate of 10^-4 commonly considered sufficient for fault-tolerant quantum computing. The 9Be+ ion is trapped above a microfabricated surface-electrode ion trap and is manipulated with microwaves applied to a trap electrode. The achievement of low single-qubit-gate errors is an essential step toward the construction of a scalable quantum computer.

The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity [1-3] and the mechanical modes of a trapped atom [4] or macroscopic solid [5]. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields [6], and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states [7]. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 um (similar work is reported in a related paper [8]). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator [9-13].

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multi-qubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser beam control and motional state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.

Chiaverini et al. [Quant. Inf. Comput. 5, 419 (2005)] recently suggested a linear Paul trap geometry for ion trap quantum computation that places all of the electrodes in a plane. Such planar ion traps are compatible with modern semiconductor fabrication techniques and can be scaled to make compact, many zone traps. In this paper we present an experimental realization of planar ion traps using electrodes on a printed circuit board to trap linear chains of tens of 0.44 micron diameter charged particles in a vacuum of 15 Pa (0.1 torr). With these traps we address concerns about the low trap depth of planar ion traps and develop control electrode layouts for moving ions between trap zones without facing some of the technical difficulties involved in an atomic ion trap experiment. Specifically, we use a trap with 36 zones (77 electrodes) arranged in a cross to demonstrate loading from a traditional four rod linear Paul trap, linear ion movement, splitting and joining of ion chains, and movement of ions through intersections. We further propose an additional DC biased electrode above the trap which increases the trap depth dramatically, and a novel planar ion trap geometry that generates a two dimensional lattice of point Paul traps.

Universal ion trap computation on Decoherence Free Subspaces (DFS) using only two qubit operations is presented. The DFS is constructed for the collective dephasing model. Encoded single and two-qubit logical operations are implemented via the Sorensen-Molmer interaction. Alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction. This is universal over suitable encodings of one logical qubit into three physical qubits which are also DFS under collective decoherence.

Motivated by the recently demonstrated ability to attach quantum dots to polymers at well defined locations, we propose a condensed phase analog of the ion trap quantum computer: a scheme for quantum computation using chemically assembled semiconductor nanocrystals attached to a linear support. The linear support is either a molecular string (e.g., DNA) or a nanoscale rod. The phonon modes of the linear support are used as a quantum information bus between the dots. Our scheme offers greater flexibiliy in optimizing material parameters than the ion trap method but has additional complications. We discuss the relevant physical parameters, provide a detailed feasibility study, and suggest materials for which quantum computation may be possible with this approach. We find that Si is a potentially promising quantum dot material, already allowing 5-10 qubits quantum computer to operate with an error threshold of 10^-3.