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Using a single, harmonically trapped $^9$Be$^+$ ion, we experimentallydemonstrate a technique for generation of arbitrary states of a two-levelparticle confined by a harmonic potential. Rather than engineering a singleHamiltonian that evolves the system to a desired final sate, we implement atechnique that applies a sequence of simple operations to synthesize the state

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Experimental Demonstration of a Technique to Generate Arbitrary Quantum Superposition States of a Harmonically Bound Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Particle

Experimental Demonstration of a Technique to Generate Arbitrary Quantum Superposition States of a Harmonically Bound Spin-1/2Particle