Wigner crystals of ions as quantum hard drives

Atomic systems in regular lattices are intriguing systems for implementing ideas in quantum simulation and information processing. Focusing on laser cooled ions forming Wigner crystals in Penning traps, we find a robust and simple approach to engineering non-trivial 2-body interactions sufficient for universal quantum computation. We then consider extensions of our approach to the fast generation of large cluster states, and a non-local architecture using an asymmetric entanglement generation procedure between a Penning trap system and well-established linear Paul trap designs.Comment: 5 pages, 4 figure

Simulating Quantum Magnetism with Correlated Non-Neutral Ion Plasmas

By employing forces that depend on the internal electronic state (or spin) of an atomic ion, the Coulomb potential energy of a strongly coupled array of ions can be modified in a spin-dependent way to mimic effective quantum spin Hamiltonians. Both ferromagnetic and antiferromagnetic interactions can be implemented. We use simple models to explain how the effective spin interactions are engineered with trapped-ion crystals. We summarize the type of effective spin interactions that can be readily generated, and discuss an experimental implementation using single-plane ion crystals in a Penning trap.Comment: 10 pages, 5 figures, to be published in the Proceedings of 10th International Workshop on Non-Neutral Plasma

Scalable arrays of micro-Penning traps for quantum computing and simulation

We propose the use of 2-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions. This approach involves placing arrays of micro-structured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction. We solve for the normal modes of ion motion in such arrays, and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections. We use these techniques to investigate the feasibility of quantum simulation and quantum computation in fixed ion lattices. In homogeneous arrays, we show that sufficiently dense arrays are achievable, with axial, magnetron and cyclotron motions exhibiting inter-ion dipolar coupling with rates significantly higher than expected decoherence. With the addition of laser fields these can realize tunable-range interacting spin Hamiltonians. We also show how local control of potentials allows isolation of small numbers of ions in a fixed array and can be used to implement high fidelity gates. The use of static trapping fields means that our approach is not limited by power requirements as system size increases, removing a major challenge for scaling which is present in standard radio-frequency traps. Thus the architecture and methods provided here appear to open a path for trapped-ion quantum computing to reach fault-tolerant scale devices.Comment: 21 pages, 10 figures Changes include adding section IX (Implementation Example) and substantially rewriting section X (Scaling

Phase-coherent detection of an optical dipole force by Doppler velocimetry

We report phase-coherent Doppler detection of optical dipole forces using large ion crystals in a Penning trap. The technique is based on laser Doppler velocimetry using a cycling transition in $^{9}$Be$^{+}$ near 313 nm and the center-of-mass (COM) ion motional mode. The optical dipole force is tuned to excite the COM mode, and measurements of photon arrival times synchronized with the excitation potential show oscillations with a period commensurate with the COM motional frequency. Experimental results compare well with a quantitative model for a driven harmonic oscillator. This technique permits characterization of motional modes in ion crystals; the measurement of both frequency and phase information relative to the driving force is a key enabling capability -- comparable to lockin detection -- providing access to a parameter that is typically not available in time-averaged measurements. This additional information facilitates discrimination of nearly degenerate motional modes.Comment: Related manuscripts at http://www.physics.usyd.edu.au/~mbiercuk

Extending the memory times of trapped-ion qubits with error correction and global entangling operations

The technical demands to perform quantum error correction are considerable. The task requires the preparation of a many-body entangled state, together with the ability to make parity measurements over subsets of the physical qubits of the system to detect errors. Here we propose two trapped-ion experiments to realise error-correcting codes of variable size to protect a single encoded qubit from dephasing errors. Novel to our schemes is the use of a global entangling phase gate, which could be implemented in both Penning traps and Paul traps. We make use of this entangling operation to significantly reduce the experimental complexity of state preparation and syndrome measurements. We also show, in our second scheme, that storage times can be increased further by repeatedly teleporting the logical information between two codes supported by the same ion Coulomb crystal to learn information about the locations of errors. We estimate that a logical qubit encoded in such a crystal will maintain high coherence for times more than an order of magnitude longer than each physical qubit would.Comment: 18 pages, 8 figures. The authors list has changed since the first version of this draf

Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin pairs. These power-laws correspond physically to infinite-range (a=0), Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings. Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4. This demonstration coupled with the high spin-count, excellent quantum control and low technical complexity of the Penning trap brings within reach simulation of interesting and otherwise computationally intractable problems in quantum magnetism.Comment: 10 pages, 10 figures; article plus Supplementary Material

Double wells, scalar fields and quantum phase transitions in ions traps

Since Hund's work on the ammonia molecule, the double well potential has formed a key paradigm in physics. Its importance is further underlined by the central role it plays in the Landau theory of phase transitions. Recently, the study of entanglement properties of many-body systems has added a new angle to the study of quantum phase transitions of discrete and continuous degrees of freedom, i.e., spin and harmonic chains. Here we show that control of the radial degree of freedom of trapped ion chains allows for the simulation of linear and non-linear Klein-Gordon fields on a lattice, in which the parameters of the lattice, the non-linearity and mass can be controlled at will. The system may be driven through a phase transition creating a double well potential between different configurations of the ion crystal. The dynamics of the system are controllable, local properties are measurable and tunnelling in the double well potential would be observable.Comment: 6 pages, 5 figure