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arXiv:quant-ph/0307211

Quantized phase shifts and a dispersive universal quantum gate

Ferdinand Schmidt‐Kaler, Hartmut Häffner, S. Gulde, Mark Riebe, Gavin P. T. Lancaster, Jürgen Eschner, Christoph Becher, R. Blatt

Published Jul 29, 2003• 0 citations
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Abstract

A single 40Ca+ ion is trapped and laser cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's motional quantum state |n>. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state {S,D} is flipped depending on the motional qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numerical simulations for the generation of a maximally entangled state of five ions.

DOI
10.48550/arxiv.quant-ph/0307211

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A single 40Ca+ ion is trapped and laser cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's motional quantum state |n>. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state {S,D} is flipped depending on the motional qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numerical simulations for the generation of a maximally entangled state of five ions.
A single 40 Ca + -ion is trapped and laser-cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S 1/2 to D 5/2 transition causes a phase shift proportional to the ion's motional quantum state | n ⟩. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state { S , D } is flipped depending on the motional qubit state | n ⟩ = {|0⟩,|1⟩}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numerical simulations for the generation of a maximally entangled state of five ions.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.
We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.
A two-qubit quantum gate is realized using electronically excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase-locked lasers are used to excite a stimulated Raman transition between two metastable states D3/2{D}_{3/2}D3/2​ and D5/2{D}_{5/2}D5/2​ separated by 1.821.821.82 THz in a single trapped 40Ca^{40}\mathrm{Ca}40Ca+{}^{+}+ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.
We present an alternative scheme for the generation of a two-qubit quantum gate interaction between laser-cooled trapped ions. The scheme is based on the ac Stark shift (light shift) induced by laser light resonant with the ionic transition frequency. At specific laser intensities, the shift of the ionic levels allows the resonant excitation of transitions involving the exchange of motional quanta. We compare the performance of this scheme with respect to that of related ion-trap proposals and find that, for an experimental realization using traveling-wave radiation and working in the Lamb-Dicke regime, an improvement of over an order of magnitude in the gate switching rate is possible.