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Optics and Spectroscopy

Demonstrating the possibility of implementing the Toffoli gate in crystals doped by rare-earth metal ions

Ахмеджанов Ринат Абдулхаевич, Л. А. Гущин, I. V. Zelensky, Yu. P. Malakyan, Д. А. Собгайда

Published Jul 1, 2015• 1 citation
Publisher

Abstract

A scheme for the implementation of the Toffoli gate in inorganic crystals doped by rare-earth metal ions is proposed. A numerical analysis of the factors affecting the fidelity of the Toffoli gate implementation is carried out, and estimates for the available experimental parameters are obtained. A demonstration experiment is set up in which behavior similar to the Toffoli gate is shown for ensembles of Pr 3+ ions doped into a LaF 3 crystal.

DOI
10.1134/s0030400x15070024

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A scheme for the implementation of the Toffoli gate in inorganic crystals doped by rare-earth metal ions is proposed. A numerical analysis of the factors affecting the fidelity of the Toffoli gate implementation is carried out, and estimates for the available experimental parameters are obtained. A demonstration experiment is set up in which behavior similar to the Toffoli gate is shown for ensembles of Pr 3+ ions doped into a LaF 3 crystal.
We present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.
The paper reports on the experimental realization on the possibility of isolating ions in a selected frequency channel. In the scheme, this interaction is mediated by the change in permanent dipole moment experienced by the rare-earth ions when they are optically excited from the ground state to an excited state. The change in dipole moment changes the electric field experienced by ions situated close to the excited ion, thus their absorption frequencies are changed. The important aspect, in order to use this frequency shift for controlled logic, is that the shift is large enough for ions, originally resonant with a certain laser frequency, to be shifted out of resonance with this laser field. Excitation induced frequency shifts are experimentally observed, which opens the way for the realisation of the first quantum gate in this type of solid state materials.
Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits. We discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk for instantaneous spectral diffusion (ISD). Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when ISD is not considered and $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\rightarrow}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ over a broad range of dipole-dipole interaction strengths.
Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopants in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rare-earth-ion-doped crystals.