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arXiv:1005.2810 · Physical Review A

Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control

Zhuo Liu, Lülin Kuang, Kai Hu, Luting Xu, Suhua Wei, Lingzhen Guo, Xin-Qi Li

Published Sep 29, 2010• 28 citations
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Abstract

In a solid-state circuit QED system, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of a moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved feedback scheme. We show that this is essential to achieve a desirable control effect by the use of dispersive measurement.

DOI
10.1103/physreva.82.032335

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In a solid-state circuit QED system, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of a moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved feedback scheme. We show that this is essential to achieve a desirable control effect by the use of dispersive measurement.
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In a solid-state circuit QED system, we extend the previous study of generating and stabilizing a two-qubit Bell state [Phys. Rev. A 82, 032335 (2010)] to a three-qubit GHZ state. In a dispersive regime, we employ the homodyne joint readout for multiple qubits to infer the state for further processing, and in particular we use it to stabilize the state directly by means of an alternate-flip-interrupted Zeno (AFIZ) scheme. Moreover, the state-of-the-art feedback action based on the filtered current enables not only a deterministic generation of the pre-GHZ state in the initial stage, but also a fast recovery from occasional error in the later stabilization process. We show that the proposed scheme can maintain the state with high fidelity if the efficient quantum measurement and rapid single-qubit rotations are available.
Circuit QED is a promising solid-state quantum computing architecture. It also has excellent potential as a platform for quantum control---especially quantum feedback control---experiments. However, the current scheme for measurement in circuit QED is low efficiency and has low signal-to-noise ratio for single-shot measurements. The low quality of this measurement makes the implementation of feedback difficult, and here we propose two schemes for measurement in circuit QED architectures that can significantly improve signal-to-noise ratio and potentially achieve quantum-limited measurement. Such measurements would enable the implementation of quantum feedback protocols and we illustrate this with a simple entanglement-stabilization scheme.
We demonstrate and contrast two approaches to the stabilization of qubit entanglement by feedback.Our demonstration is built on a feedback platform consisting of two superconducting qubits coupled to a cavity, which are measured by a nearly quantum-limited measurement chain and controlled by high-speed classical logic circuits.This platform is used to stabilize entanglement by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements.In view of the instrumental roles that these two feedback paradigms play in quantum error correction and quantum control, we directly compare them on the same experimental setup.Furthermore, we show that a second layer of feedback can be added to each of these schemes, which heralds the presence of a high-fidelity entangled state in real time.This "nested" feedback brings about a marked entanglement fidelity improvement without sacrificing success probability.
Measurement-based heralded entanglement schemes have served as the primary link between physically separated qubits in most quantum information platforms. However, the impossibility of performing a deterministic Bell measurement with linear optics bounds the success rate of the standard protocols to at most 50%, which means that the entanglement of the unheralded state is zero. Here we show that the ability to perform feedback during the measurement process enables unit success probability in a single shot. Our primary feedback protocol, based on photon counting retains the same robustness as the standard Barrett-Kok scheme, while doubling the success probability even in the presence of loss. In superconducting circuits, for which homodyne detectors are more readily available than photon counters, we give another protocol that can deterministically entangle remote qubits given existing parameters. In constructing the latter protocol, we derive a general expression for locally optimal control that applies to any continuous, measurement-based feedback problem.