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arXiv:cond-mat/0203039 · Modern Physics Letters B

SHORT-TIME DECOHERENCE AND DEVIATION FROM PURE QUANTUM STATES

VLADIMIR PRIVMAN

Published Jun 10, 2002• 22 citations
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Abstract

In systems considered for quantum computing, i.e., for control of quantum dynamics with the goal of processing information coherently, decoherence and deviation from pure quantum states, are the main obstacles to error correction. At low temperatures, usually assumed in quantum computing designs, some of the accepted approaches to evaluation of relaxation mechanisms break down. We develop a new formalism for the estimation of decoherence at short times, appropriate for evaluation of quantum computing architectures.

DOI
10.1142/s0217984902003920

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In systems considered for quantum computing, i.e., for control of quantum dynamics with the goal of processing information coherently, decoherence and deviation from pure quantum states, are the main obstacles to error correction. At low temperatures, usually assumed in quantum computing designs, some of the accepted approaches to evaluation of relaxation mechanisms break down. We develop a new formalism for the estimation of decoherence at short times, appropriate for evaluation of quantum computing architectures.
In the process of developing and operating quantum computing systems, quantum decoherence is a fundamental difficulty that poses a significant obstacle. The purpose of this study is to present a full understanding of quantum decoherence, which includes an examination of its impacts on quantum information processing as well as its origins and causes. Through our investigation of the dynamic relationship between decoherence and quantum error correction, we bring to light the significance of preserving coherence in order to ensure the reliability of quantum computation. In this study, we analyze a variety of sources of decoherence by means of theoretical models and practical research. These sources include environmental interactions, temperature fluctuations, and operational defects. Additionally, we address advanced strategies for minimizing decoherence, including as dynamical decoupling, error-correcting codes, and fault-tolerant quantum computing architectures. These techniques are discussed in this article. The results of our research highlight the significance of comprehending and effectively regulating quantum decoherence in order to develop quantum computing systems that are both scalable and attainable. By laying the groundwork for future research and development in the field of improving the robustness and performance of quantum computers, the purpose of this effort is being accomplished.
Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.