Conditional Spin Resonance with Trapped Ions

Abstract

Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a N -qubit molecule with adjustable coupling constants. I. MOTIVATIONDigital information processing builds upon elementary physical elements ("bits") that may occupy either one of two possible states labelled 0 and 1, respectively. If a quantum system, for example, an individual atom having discrete energy eigenstates, is chosen as elementary switch ("qubit" ), then the general state of this system will be a superposition of the two computational basis states, i.e. the states chosen to represent the logic 0 and 1. When applying the superposition principle to a register comprising N qubits, one immediately sees that such a register can exist in a superposition of 2 N states thus representing 2 N binary encoded numbers simultaneously. Any operation on this register will act on all states at once, effecting parallel processing on an exponentially growing (with N ) number of states. The outcome of a measurement on this register after such an operation will, of course, yield just one out of 2 N possible results with a certain probability.In order to take advantage of quantum parallelism for efficient computing, a second ingredient is necessary: interference. A useful quantum algorithm has to exploit this parallelism, and, at the same time, make different computational paths interfere such that only the correct result survives after the last computational step [1]. An important example is Shor's algorithm for the factorization of large numbers [2]. Once created, coherent superpositions have to remain intact while a quantum algorithm is carried out, i.e. qubits must not in an uncontrollable way interact with their environment. This would lead to decoherence, an important issue, not only in the realm of quantum information processing (QIP), but also related to the notion of measurement in quantum mechanics [3,4].A quantum computer is ideally suited for the simulation of quantum mechanical systems [5,6], for example, to determine eigenvalues and eigenvectors of many-body systems [7]. Calculating the dynamics of chaotic systems is another useful line of action for a quantum computer, even for one that consists of only a few qubits [8]. Beneficial both for fundamental research and applications is the ability of a quantum computer -comprising a modest number of qubits and working with limited accuracy -to simulate the dynamics of a macroscopic ensemble of classical particles, a task not suitable even for modern supercomputers [9].In the course of a quantum computation entangled states of qubits are created exhibiting correlations between individual qubits that possess no classical analog. Fundamental questions concerning the role of entanglement, not only in QIP, but also in the framewor...

Experimental quantum simulations of many-body physics with trapped ions

“…(Note that a similar proposal involving the same mathematics is given in [23].) However, the quantum Ising Hamiltonian contains an additional (simulated) magnetic field pointing in the x-direction.…”

Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation

“…The term ion spin "molecule" is used here to describe a pseudomolecule [9] exposed to a magnetic field gradient that induces pairwise coupling J ij between the internal qubit states (spins) of ion i and j (i, j = 1, 2, 3, ..., N with N the number of ions) [10,11]. An ion spin molecule is useful for quantum simulations, since spin chains with globally and locally adjustable coupling parameters can be realized and are well suited, for instance, for simulating magnetism of quantum systems [12].…”

Distinguishing between statistical and systematic errors in quantum process tomography

“…, and ñ |i . The time evolution (see equation (6)) is realized with the help of MAgnetic Gradient Induced Coupling (MAGIC) [34,36,38,39]. The evolution time takes 5.8 ms matching the J-coupling between 2 ions.…”