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Entanglement detection
 Physics Reports
"... How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalitie ..."
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How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
Engineered open systems and quantum simulations with atoms and ions
 Advances In Atomic, Molecular, and Optical Physics
, 2012
"... The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even manybody ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthin ..."
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The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even manybody ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the wellestablished concept of engineering of manybody Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in manybody quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems
Reduction of heating rate in a microfabricated ion trap by pulsedlaser cleaning
"... Abstract. Lasercleaning of the electrodes in a planar microfabricated ion trap has been attempted using ns pulses from a tripled Nd:YAG laser at 355nm. The effect of the laser pulses at several energy density levels has been tested by measuring the heating rate of a single 40Ca+ trapped ion as a f ..."
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Abstract. Lasercleaning of the electrodes in a planar microfabricated ion trap has been attempted using ns pulses from a tripled Nd:YAG laser at 355nm. The effect of the laser pulses at several energy density levels has been tested by measuring the heating rate of a single 40Ca+ trapped ion as a function of its secular frequency ωz. A reduction of the electricfield noise spectral density by ∼ 50 % has been observed and a change in the frequency dependence also noticed. This is the first reported experiment where the “anomalous heating ” phenomenon has been reduced by removing the source as opposed to reducing its thermal driving by cryogenic cooling. This technique may open the way to better control of the electrode surface quality in ion microtraps. ar
TwoDimensional Arrays of RF Ion Traps with Addressable Interactions
 New J. Phys
"... Abstract. We describe the advantages of 2dimensional, addressable arrays of spherical Paul traps. They would provide for the ability to address and tailor the interaction strengths of trapped objects in 2D and could establish a valuable new tool for quantum information processing. Simulations of tr ..."
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Abstract. We describe the advantages of 2dimensional, addressable arrays of spherical Paul traps. They would provide for the ability to address and tailor the interaction strengths of trapped objects in 2D and could establish a valuable new tool for quantum information processing. Simulations of trapping ions are compared to first tests using printed circuit board trap arrays loaded with dust particles. Pairwise interactions in the array are addressed by means of an adjustable radiofrequency (RF) electrode shared between trapping sites. By attenuating this RF electrode potential, neighboring pairs of trapped objects have their interaction strength increase and are moved closer to one another. In the limit of the adjustable electrode being held at RF ground, the two formerly spherical traps are merged into one linear Paul trap.
Ultrafast Control of Spin and Motion in Trapped Ions
, 2013
"... Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This ap ..."
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Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spindependent momentum kick. Finally, I explain how these spindependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
On the Formal Verification of Optical Quantum Gates in HOL
"... Abstract. Quantum computers are expected to handle hard computational problems and provide unbreakable security protocols. Among different quantum computer implementations, those based on quantum optics and nuclear magnetic resonance show good advancement in building large scale machines. However, ..."
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Abstract. Quantum computers are expected to handle hard computational problems and provide unbreakable security protocols. Among different quantum computer implementations, those based on quantum optics and nuclear magnetic resonance show good advancement in building large scale machines. However, the involvement of optical and nuclear techniques makes their development very critical. This motivates us to apply formal techniques, in particular theorem proving, in quantum circuits analysis. In this work, we present the formalization of multiinputs/multioutputs quantum gates (technically called multimodes optical circuits). This requires the implementation of tensor product over complexvalued functions. Firstly, we build a formal model of single optical beams and then extend it to cover circuits of multi optical beams, with the help of the developed tensor product algebra. As an application, we formally verify the behavior of the optical quantum CNOT gate and MachZehnder interferometer.
Optimal ILPBased Approach for Gate Location Assignment and Scheduling in Quantum Circuits
"... Physical design and synthesis are two key processes of quantum circuit design methodology. The physical design process itself decomposes into scheduling, mapping, routing, and placement. In this paper, a mathematical model is proposed for mapping, routing, and scheduling in iontrap technology in o ..."
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Physical design and synthesis are two key processes of quantum circuit design methodology. The physical design process itself decomposes into scheduling, mapping, routing, and placement. In this paper, a mathematical model is proposed for mapping, routing, and scheduling in iontrap technology in order to minimize latency of the circuit. The proposed model which is a mixed integer linear programming (MILP) model gives the optimal locations for gates and the best sequence of operations in terms of latency. Experimental results show that our scheme outperforms the other schemes for the attempted benchmarks.
Contributions to InformationBased Complexity and to Quantum Computing
, 2013
"... Multivariate continuous problems are widely encountered in physics, chemistry, finance and in computational sciences. Unfortunately, interesting real world multivariate continuous problems can almost never be solved analytically. As a result, they are typically solved numerically and therefore appr ..."
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Multivariate continuous problems are widely encountered in physics, chemistry, finance and in computational sciences. Unfortunately, interesting real world multivariate continuous problems can almost never be solved analytically. As a result, they are typically solved numerically and therefore approximately. In this thesis we deal with the approximate solution of multivariate problems. The complexity of such problems in the classical setting has been extensively studied in the literature. On the other hand the quantum computational model presents a promising alternative for dealing with multivariate problems. The idea of using quantum mechanics to simulate quantum physics was initially proposed by Feynman in 1982. Its potential was demonstrated by Shor’s integer factorization algorithm, which exponentially improves the cost of the best classical algorithm known. In the first part of this thesis we study the tractability of multivariate problems in the worst and average case settings using the real number model with oracles. We derive necessary and sufficient conditions for weak tractability for linear multivariate tensor product problems in those settings.