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Annalen der Physik

Protecting Quantum State in Time‐Dependent Decoherence‐Free Subspaces Without the Rotating‐Wave Approximation

Qi‐Cheng Wu, Ye‐Hong Chen, Bi‐Hua Huang, Zhi‐Cheng Shi, Jie Song, Yan Xia

Published Jul 12, 2017• 13 citations
Publisher

Abstract

Abstract In this paper, we propose a scheme to protect quantum state by utilizing the time‐dependent decoherence‐free subspaces (TDFSs) theory without the rotating‐wave approximation (RWA). A coherent control is designed to drive the quantum system into the TDFSs, moreover, the singularities of the designed coherent control can be avoided by appropriately choosing the control parameters. From an experimental view point, the influences of variations of the control parameters and the imperfect initial state are discussed in detail. Numerical simulations confirm that the scheme can protect the quantum information from both the environmental decoherence and the control errors. In addition, by comparing with the scheme employing RWA, we show that the weak coherent control field is not suitable to create the TDFS, the counter‐rotating terms in the strong coherent control are helpful to protect the quantum information.

DOI
10.1002/andp.201700186

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Abstract In this paper, we propose a scheme to protect quantum state by utilizing the time‐dependent decoherence‐free subspaces (TDFSs) theory without the rotating‐wave approximation (RWA). A coherent control is designed to drive the quantum system into the TDFSs, moreover, the singularities of the designed coherent control can be avoided by appropriately choosing the control parameters. From an experimental view point, the influences of variations of the control parameters and the imperfect initial state are discussed in detail. Numerical simulations confirm that the scheme can protect the quantum information from both the environmental decoherence and the control errors. In addition, by comparing with the scheme employing RWA, we show that the weak coherent control field is not suitable to create the TDFS, the counter‐rotating terms in the strong coherent control are helpful to protect the quantum information.
Abstract In this paper, a scheme is put forward to design pulses which drive a three‐level system based on the reverse engineering with Lewis‐Riesenfeld invariant theory. The scheme can be applied to a three‐level system even when the rotating‐wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.
We apply the time-dependent decoherence-free subspace theory to a Markovian open quantum system in order to present a proposal for a quantum-state engineering program. By quantifying the purity of the quantum state, we verify that the quantum-state engineering process designed via our method is completely unitary within any total engineering time. Even though the controls on the open quantum system are not perfect, the asymptotic purity is still robust. Owing to its ability to completely resist decoherence and the lack of restraint in terms of the total engineering time, our proposal is suitable for multitask quantum-state engineering program. Therefore, this proposal is not only useful for achieving the quantum-state engineering program experimentally, it also helps us build both a quantum simulation and quantum information equipment in reality.
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Abstract The interconversion of a variety of entangled states can facilitate the information transmission and decline the risk of error rates. Here two faithful protocols to achieve deterministic interconversion between three‐logic‐qubit W state and three‐logic‐qubit Greenberger–Horne–Zeilinger state in decoherence‐free subspace (DFS), resorting to the state‐selective property of the quantum dot (QD)‐cavity systems and robust‐fidelity quantum control gates are presented. Moreover, the single‐photon detectors introduced can effectively herald and mitigate potential failures from imperfect interaction between the QD‐cavity system and photons, significantly enhancing experimental feasibility. Through comprehensive analysis and evaluation, the protocols demonstrate exceptional conversion efficiencies and deliver near‐perfect fidelities. Additionally, the DFS makes system coherence over extended periods to overcome the decoherence effect caused by specific environmental noise, paving the way for quantum information processing.
We present a scheme to drive a finite-dimensional quantum system into the decoherence-free subspaces (DFS) by Lyapunov control. Control fields are established by Lyapunov function. This proposal works well for both closed and open quantum systems, with replacing the DFS by desired subspaces for closed systems. An example which consists of a four-level system with three degenerate states driven by three lasers is presented to gain further insight on the scheme. Numerical simulations for the dynamics of the system are performed and the results are good.
We present a method aimed at protecting unitary dynamics in the presence of decoherence, by integrating leakage elimination operators (LEOs) into the system's evolution to create dynamical leakage-free paths. Deriving the dynamical equation for an open quantum system with general drives can be challenging. Our approach avoids the rotating wave approximation and instead uses the coarse-grained averaging technique to derive a quantum master equation for such systems. The combination of the coarse-graining approach and LEO operators appears suitable to study Markovian control methods. We show that employing LEO pulses in specific subspaces can reduce errors arising from undesired transitions due to decoherence. Notably, satisfactory final fidelity can still be achieved even when the reservoir is at a finite temperature. By looking into the dynamical equation governing the quantum state on the dynamical leakage-free path, we provide analytical insights into the effectiveness of the LEO method in suppressing decoherence effects.