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Physical Review A

Tolerant-gate implementation for the trapped-ion quantum-information processor

K. Pahlke, Wolfgang M. Mathis

Published Jun 24, 2003• 2 citations
Publisher

Abstract

A sequence of five laser pulses is presented, implementing a controlled-NOT gate in a linear arrangement of trapped ions. This gate works if the quantum number of the collective vibration (phonon bus) is zero or one. We interpret this property as tolerance against errors caused by imperfect ground-state preparation. The periodicity of two Rabi frequencies is used in order to obtain this property. The gate implementation is designed in a way which does not correspond to the well-known phase-gate construction.

DOI
10.1103/physreva.67.062305

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A sequence of five laser pulses is presented, implementing a controlled-NOT gate in a linear arrangement of trapped ions. This gate works if the quantum number of the collective vibration (phonon bus) is zero or one. We interpret this property as tolerance against errors caused by imperfect ground-state preparation. The periodicity of two Rabi frequencies is used in order to obtain this property. The gate implementation is designed in a way which does not correspond to the well-known phase-gate construction.
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Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.
Abstract We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to 99 − 2 + 1 % . We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation < 20 phonons, trap frequency errors of +10%, and pulse area errors of −8%. The phase shift is not significantly affected up to < 10 phonons and pulse area errors of −2%. Both, contrast and phase shift are robust to timing errors up to −30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 µ s) by using two axial motional modes of a two-ion crystal through improved setups.