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Characterisation of EuCl_3.6H_2O for Multi-Qubit Quantum Processing

Rose L. Ahlefeldt, W. D. Hutchison, Matthew J. Sellars

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We describe a quantum computing architecture that uses satellite lines in rare earth doped EuCl3.6H2O as qubits. The crystallographic sites to which these lines belong are identified and this information is used to predict the performance of the quantum computing system.
DOI
10.1364/iqec.2011.i815

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This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com­ puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi­ cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char­ acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac­ tions were measured between a number of different satellite lines using a new two­ laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.
Quantum information uses special properties of quantum systems to manipulate or transmit data. This results in new processes, which are impossible to obtain with classical devices. For example, quantum computing and quantum storage, which are two important fields in quantum information research, aim respectively at performing very fast calculations and at storing quantum states of photons. These two applications could be obtained in solid-state systems using rare earth doped crystals. In this context, the most important property of these materials is the long coherence lifetimes of rare earth ion optical and hyperfine transitions. This allows one to create long-lived superposition states, which is a fundamental requirement for efficient quantum computing and storage. Promising results have already been demonstrated in rare earth doped crystals but it will be difficult to improve them with current materials. In this paper, we discuss the general and specific requirements for rare earth ions and crystals in order to perform quantum computing with a large number of quantum bits as well as all solid-state quantum storage. We also present the properties of a few recently studied crystals: Ho3+:YVO4, Ho3+:LuVO4 (quantum computing) and Tm3+:Y3Al5O12 (quantum storage).
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.