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arXiv:cond-mat/0703311 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Coherence and entanglement in two-qubit dynamics: interplay of the induced exchange interaction and quantum noise due to thermal bosonic environment

Vladimir Privman, Dmitry Solenov

Published Apr 27, 2007• 1 citation
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Abstract

We present a review of our recent results for the comparative evaluation of the induced exchange interaction and quantum noise mediated by the bosonic environment in two-qubit systems. We report new calculations for P-donor-electron spins in Si-Ge type materials. Challenges and open problems are discussed.
DOI
10.1117/12.717685

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Abstract — We review results in theoretical modeling of quantum systems in support of the studies of decoherence and qubit interactions for quantum information processing. The developed modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Field-theoretical techniques have been utilized to address decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We also describe general and specific research challenges, the solution of which will advance the field of modeling “open quantum systems ” to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
We outline selected trends and results in theoretical modeling of quantum systems in support of the developing research field of quantum information processing. The resulting modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Many-body field-theoretical techniques have been utilized to address a spectrum of diverse research topics. Specifically, the theory of decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers has been advanced. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We outline general and specific research challenges, the solution of which will advance the field of modeling "open quantum systems" to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.