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arXiv:quant-ph/0104041 · Physical Review Letters

Ion-Trap Quantum Logic Using Long-Wavelength Radiation

Florian Mintert, Christof Wunderlich

Published Nov 29, 2001• 345 citations
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Abstract

A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogeneous magnetic field applied to an ion trap (i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and (ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency or microwave regime.

DOI
10.1103/physrevlett.87.257904

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A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogeneous magnetic field applied to an ion trap (i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and (ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency or microwave regime.
Am odified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin–spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin–spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped 171 Yb + ,w e hav ei mplemented an adaptive algorithm for state estimation involvin gs equential measurements on arbitrary qubit states.
We propose a design for a quantum-information processor where qubits are encoded into hyperfine states of ions held in a linear array of individually tailored linear microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single- and multiqubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the microtrap configurations we can tailor, in hardware, the qubit resonance frequencies and coupling strengths. We show that the system possesses a sideband transition structure which does not scale with the size of the processor, allowing scalable frequency discrimination between qubits. By using large magnetic field gradients, one can reset individual qubits in the ion chain via frequency selective optical pulses to implement quantum-error correction, thus avoiding the need for many tightly focused laser beams.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.
This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.
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 NNN-qubit molecule with adjustable coupling constants.