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arXiv:1402.5177

Optimized Dynamical Decoupling in Ξ-Type n-Level Quantum Systems

Linping Chan, Shuang Cong

Published Feb 21, 2014• 0 citations
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Abstract

In this paper, we first design a type of Bang-Bang (BB) operation group to reduce the phase decoherence in a Ξ-type n-level quantum system based on the dynamical decoupling mechanism. Then, we derive two kinds of dynamical decoupling schemes: periodic dynamical decoupling (PDD) and Uhrig dynamical decoupling (UDD). We select the non-diagonal element of density matrix as a reference index, and investigate the behavior of quantum coherence of the Ξ-type n-level atom under these two dynamical decoupling schemes proposed. At last, we choose a Ξ-type six-level atom as a system controlled, and use the decoupling schemes proposed to suppress the phase decoherence. The simulation experiments and the comparison results are given.

DOI
10.48550/arxiv.1402.5177

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In this paper, we first design a type of Bang-Bang (BB) operation group to reduce the phase decoherence in a Ξ-type n-level quantum system based on the dynamical decoupling mechanism. Then, we derive two kinds of dynamical decoupling schemes: periodic dynamical decoupling (PDD) and Uhrig dynamical decoupling (UDD). We select the non-diagonal element of density matrix as a reference index, and investigate the behavior of quantum coherence of the Ξ-type n-level atom under these two dynamical decoupling schemes proposed. At last, we choose a Ξ-type six-level atom as a system controlled, and use the decoupling schemes proposed to suppress the phase decoherence. The simulation experiments and the comparison results are given.
In this paper, we derive the conditions of maintaining quantum coherence in arbitrary n-level atom in Ξ-configuration with Bang-Bang (BB) controls when the system exists the phase decoherence, the amplitude decoherence and the general decoherence (the amplitude damping and phase damping simultaneously), respectively. On this basis, we propose our BB decoupling scheme to suppress the phase decoherence in arbitrary n-level atom in Ξ-configuration. The corresponding decoupling operators are derived explicitly. At last we design the BB decoupling scheme to suppress phase decoherence for a six-level atom system in Ξ-configuration.
In this paper, we first present a brief derivation of the dynamical decoupling condition by means of designing control Hamiltonians, which is used to preserve arbitrary quantum states in the case of interactions with environment. According to different time intervals between the adjacent pulses, two important dynamical decoupling schemes: periodic dynamical decoupling (PDD) and Uhrig dynamical decoupling (UDD) are analyzed. Based on the comparison between PDD and UDD, we propose our optimized dynamical decoupling scheme with different time intervals between adjacent pulses which follow a normal distribution. At last numerical simulations are carried out in a three-level atom in Ξ -configuration, we select the non-diagonal element of density matrix as a reference index to compare the performances of suppressing the decoherence of these three strategies, and the results indicate that dynamical decoupling strategy proposed has better performances than that of PDD and UDD have under some low range of the loss of the quantum coherence.
In this paper, we first present a brief derivation of the dynamical decoupling conditions. On this basis, we propose our bang-bang (BB) decoupling scheme to suppress the general decoherence, that is, the amplitude damping and phase damping simultaneously, in arbitrary n-level atom in Ξ-configuration. At the same time, we also consider the physical pluses implementation so that the decoupling BB operators in our decoupling scheme are provided explicitly. At last, taking an eight-level atom in Ξ-configuration for example, we use the BB decoupling scheme proposed to suppress the general decoherence, and design the pulse sequences for the BB control operators.
Dynamical decoupling (DD) eliminates qubit-bath coupling by applying a sequence of instantaneous pulses. While qubit-bath couplings generally lead to qubit relaxation and dephasing, qubit-qubit couplings are often used to manipulate or control quantum states. We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. We find that universal control is possible using Heisenberg interaction in both periodically decoupled system and Uhrig decoupled system, and the available control operations under two kinds of DD sequences obey the same commutation relation. In the UDD case, we also derive a rough bound for control errors.