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Transport quantum logic gates for trapped ions  [PDF]
D. Leibfried,E. Knill,C. Ospelkaus,D. J. Wineland
Physics , 2007, DOI: 10.1103/PhysRevA.76.032324
Abstract: Many efforts are currently underway to build a device capable of large scale quantum information processing (QIP). Whereas QIP has been demonstrated for a few qubits in several systems, many technical difficulties must be overcome in order to construct a large-scale device. In one proposal for large-scale QIP, trapped ions are manipulated by precisely controlled light pulses and moved through and stored in multizone trap arrays. The technical overhead necessary to precisely control both the ion geometrical configurations and the laser interactions is demanding. Here we propose methods that significantly reduce the overhead on laser beam control for performing single and multiple qubit operations on trapped ions. We show how a universal set of operations can be implemented by controlled transport of ions through stationary laser beams. At the same time, each laser beam can be used to perform many operations in parallel, potentially reducing the total laser power necessary to carry out QIP tasks. The overall setup necessary for implementing transport gates is simpler than for gates executed on stationary ions. We also suggest a transport-based two-qubit gate scheme utilizing microfabricated permanent magnets that can be executed without laser light.
Microwave quantum logic gates for trapped ions  [PDF]
C. Ospelkaus,U. Warring,Y. Colombe,K. R. Brown,J. M. Amini,D. Leibfried,D. J. Wineland
Physics , 2011, DOI: 10.1038/nature10290
Abstract: 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.
Quantum logic gates with two-level trapped ions beyond Lamb--Dicke limit

Zheng Xiao-Juan,Luo Yi-Min,Cai Jian-Wu,

中国物理 B , 2009,
Abstract: In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb--Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.
Fast quantum logic gates with trapped ions interacting with external laser and quantized cavity field beyond the Lamb-Dicke regime  [PDF]
S. Shelly Sharma,A. Vidiella-Barranco
Physics , 2002, DOI: 10.1016/S0375-9601(03)00295-0
Abstract: A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $\eta_{L}=\eta_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.
A proposal of quantum logic gates using cold trapped ions in a cavity  [PDF]
F. L. Semiao,A. Vidiella-Barranco,J. A. Roversi
Physics , 2001, DOI: 10.1016/S0375-9601(02)00734-X
Abstract: We propose a scheme for implementation of logical gates in a trapped ion inside a high-Q cavity. The ion is simultaneously interacting with a (classical) laser field as well as with the (quantized) cavity field. We demonstrate that simply by tuning the ionic internal levels with the frequencies of the fields, it is possible to construct a controlled-NOT gate in a three step procedure, having the ion's internal as well as motional levels as qubits. The cavity field is used as an auxiliary qubit and basically remains in the vacuum state.
High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions  [PDF]
C. J. Ballance,T. P. Harty,N. M. Linke,D. M. Lucas
Physics , 2014,
Abstract: We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $\sim0.1\%$ level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between $97.1(2)\%$ (for a gate time $t_g=3.8\mu$s) and $99.9(1)\%$ (for $t_g=100\mu$s), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case.
Robust Trapped-Ion Quantum Logic Gates by Continuous Dynamical Decoupling  [PDF]
A. Bermudez,P. O. Schmidt,M. B. Plenio,A. Retzker
Physics , 2011, DOI: 10.1103/PhysRevA.85.040302
Abstract: We introduce a novel scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac-Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.
Spin-dependent forces on trapped ions for phase-stable quantum gates and motional Schrodinger-cat states  [PDF]
P. C. Haljan,K. -A. Brickman,L. Deslauriers,P. J. Lee,C. Monroe
Physics , 2004, DOI: 10.1103/PhysRevLett.94.153602
Abstract: Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that phase coherence of the resulting "Schr\"{o}dinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
Quantum gates with "hot" trapped ions  [PDF]
J. F. Poyatos,J. I. Cirac,P. Zoller
Physics , 1997, DOI: 10.1103/PhysRevLett.81.1322
Abstract: 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.
Simplified quantum logic with trapped ions  [PDF]
C. Monroe,D. Leibfried,B. E. King,D. M. Meekhof,W. M. Itano,D. J. Wineland
Physics , 1996, DOI: 10.1103/PhysRevA.55.R2489
Abstract: We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.
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