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IET Control Theory and Applications

Deterministic generation of symmetric multi‐qubit Dicke states: an application of quantum feedback control

Jiahua Wei, Bo Qi, Hong‐Yi Dai, Jian‐Hua Huang, Ming Zhang

Published Sep 1, 2015• 13 citations
Publisher

Abstract

In this study, the authors explore how to deterministically generate symmetric multi‐qubit Dicke states such as symmetric W‐states, from arbitrary initial states in a cavity quantum electrodynamics (QED) system with the aid of measurement‐based quantum feedback control. The concrete implementation procedures of the feedback strategy, which is constructed in the form of only two constant modes, are presented in detail. In addition, the feasibility of the control scheme in preparing symmetric multi‐qubit Dicke states is explicitly demonstrated by theoretical studies and numerical simulations.

DOI
10.1049/iet-cta.2014.1314

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In this study, the authors explore how to deterministically generate symmetric multi‐qubit Dicke states such as symmetric W‐states, from arbitrary initial states in a cavity quantum electrodynamics (QED) system with the aid of measurement‐based quantum feedback control. The concrete implementation procedures of the feedback strategy, which is constructed in the form of only two constant modes, are presented in detail. In addition, the feasibility of the control scheme in preparing symmetric multi‐qubit Dicke states is explicitly demonstrated by theoretical studies and numerical simulations.
Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit WWW state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processing but also to create and stabilize the target WWW state through adaptive quantum feedback control. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than 0.90.90.9 can be achieved and maintained for a considerably long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented.
We discuss a general physical mechanism for arbitrary control of the quantum states of multiple qubits in the symmetric Dicke subspace. The qubit-qubit coupling leads to unequal energy spacing in the symmetric Dicke subspace. This allows one to manipulate a prechosen transition with an external driving source, with other transitions remaining off-resonant. Any entangled state in the symmetric Dicke subspace can be created from the initial ground state by tuning the driving source. We illustrate the idea in cavity QED, but it should be applicable to other related systems.
We investigate the generation of a multibody Dicke state in a coupled cavity system subject to environmental noise. Based on quantum feedback control, cavity decay may play a constructive role in obtaining the intended state. The required interaction time need not be accurately controlled. In addition, the feedback operations are only applied to a single atom in one cavity during the whole evolution process, and it is not necessary to change the control strategy as the number of atoms increases. Thus, our proposal can exploit the core advantage of coupled cavities to implement a scalable control scheme for preparing multibody entanglement.
Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.