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arXiv:cond-mat/0303412 · Physical review. B, Condensed matter

Dephasing due to background charge fluctuations

Toshifumi Itakura, 康弘都倉

Published May 16, 2003• 91 citations

Abstract

In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.

DOI: 10.1103/physrevb.67.195320

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We analyze theoretically the decoherence of two interacting electrons in a double self-assembled quantum dot due to a random telegraph noise. For this purpose we have examined the pure dephasing rate by evaluating the decoherence factor. The latter has been shown to be different from that calculated within the Gaussian approximation in the strong coupling regime. In order to determine the influence of the random telegraph noise on the entanglement of the system states, the concurrence, the populations, and the entropy are evaluated as well. Our results show that telegraph noise can severely impact the coherence of charge qubits.

A quantum computer that can be constructed based on a superconducting nanocircuits has previously been proposed. We examine the effect of background charge fluctuations on a coupled Josephson charge qubit system used in such a computer. In previous work, the background charge fluctuations were found to be an important dephasing channel for a single Josephson qubit. We investigate the effect of fluctuations in the bias at the charge degeneracy point of a Josephson charge qubit system. Evaluated quantities are gate fidelity and diagonal elements of the qubit's density matrix. The fluctuation leads to gate error, however quantum gate operation becomes more accurate with increasing interaction between qubit systems.

It has been proposed that a quantum computer can be constructed based on electron spins in quantum dots or based on a superconducting nanocircuit. During two-qubit operations, the fluctuation of the coupling parameters is a critical factor. One source of such fluctuation is the stirring of the background charges. We focused on the influence of this fluctuation on a coupled spin qubit system. The induced fluctuation in exchange coupling changes the amount of entanglement, fidelity, and purity. In our previous study, the background charge fluctuations were found to be an important channel of dephasing for a single Josephson qubit.

We examine the dephasing rate of a Josephson charge qubit system due to background charge fluctuations. We consider single qubit and two-charge traps. The transition probability was controlled to a state where two traps were occupied. The transition probability was affected by the Coulomb blockade effect that occurs between two charge traps. To obtain the dephasing rate, we computed the spectra of random frequency modulation signals. Our results show that the interaction between charge traps suppresses dephasing.

Quantum information and quantum computation implementation in terms of electron charges and spin has attracted tremendous attention for the development of large-scale quantum information processing [1-5]. Artificial and tunable charge qubits fabricated in a semiconductor nanostructure are suitable for the purpose, since various parameters can be controlled by external gate voltages [6,7]. The rapid control of external gate voltage in two-electron double quantum dots has been demonstrated [8,9].Entanglement has recently emerged as a significant resource in quantum information and other applications. However an important problem is to ensure the robustness of this resource; that is, the ability to maintain it against decay. Decoherence is one of the fundamental limitation in quantum information science, and the understanding and the control of its dynamics appears as a crucial issue for the development of quantum information devices.For charge qubits in quantum dots, the effects of phonons and electromagnetic and background charge fluctuations are important in the decoherence process. The effect of phonons on the dynamics of two charge qubits has been examined [10,11].In this work, we analyze the effect of telegraph noise on the dynamical of two electrons in laterally coupled quantum dots. The resulting qubit is supposed to evolve in the basis spanned by the states |0〉 and |1〉 which describe the electron localized in the left and right dot respectively. We investigate theoretically the quantum dynamics of two interacting electrons driven by an oscillatory electric field. In order to study the effect of the telegraph noise on the entanglement we adopt the concurrence.

The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically decoupled qubit are studied. Distinct dynamics is found at different qubit working positions. Exact analytical formulas are derived at pure dephasing and approximate solutions are found at the general working position, for weakly and strongly coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on other parameters of the qubit-fluctuators system. These results can be used to determine potential microscopic models for the charge environment by performing noise spectroscopy.