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arXiv:cond-mat/0603573 · Physical Review B

Quantum coherence control of solid-state charge qubit by means of a suboptimal feedback algorithm

Jinshuang Jin, Xin-Qi Li, YiJing Yan

Published Jun 2, 2006• 10 citations
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Abstract

The quantum coherence control of a solid-state charge qubit is studied by using a suboptimal continuous feedback algorithm within the Bayesian feedback scheme. For the coherent Rabi oscillation, the present algorithm suggests a simple bang-bang control protocol, in which the control parameter is modulated between two values. For the coherence protection of the idle state, the present approach is applicable to arbitrary states, including those lying on the equator of the Bloch sphere which are out of control in the previous Markovian feedback scheme.

DOI
10.1103/physrevb.73.233302

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The quantum coherence control of a solid-state charge qubit is studied by using a suboptimal continuous feedback algorithm within the Bayesian feedback scheme. For the coherent Rabi oscillation, the present algorithm suggests a simple bang-bang control protocol, in which the control parameter is modulated between two values. For the coherence protection of the idle state, the present approach is applicable to arbitrary states, including those lying on the equator of the Bloch sphere which are out of control in the previous Markovian feedback scheme.
In the context of a charge qubit under continuous monitoring by a single electron transistor, we propose an unraveling of the generalized quantum Markovian master equation into an ensemble of individual quantum trajectories for stochastic point process. A suboptimal feedback algorism is implemented into individual quantum trajectories to protect a desired pure state. Coherent oscillations of the charge qubit could be maintained in principle for an arbitrarily long time in case of sufficient feedback strength. The effectiveness of the feedback control is also reflected in the detector's noise spectrum. The signal-to-noise ratio rises significantly with increasing feedback strength such that it could even exceed the Korotkov-Averin bound in quantum measurement, manifesting almost ideal quantum coherent oscillations of the qubit. The proposed unraveling and feedback protocol may open up the prospect to sustain ideal coherent oscillations of a charge qubit in quantum computation algorithms.
We discuss the operation of the one-qubit quantum feedback loop, which may be used for initialization of a qubit in a solid-state quantum computer. The continuous monitoring of a quantum state, which makes the feedback possible, is done by means of a weak continuous measurement and processing of the obtained information via quantum Bayesian equations. The properly designed quantum feedback loop can keep the desired phase of a single-qubit quantum coherent oscillations for infinitely long time, even in presence of a dephasing environment. Various nonidealities reduce the fidelity of the feedback synchronization. We report our study of the effects of finite available bandwidth and time delay on the one-qubit quantum feedback performance, and also discuss the effect of environment-induced dephasing.
We analyze the newly proposed quantum feedback loop for a solid-state qubit, based on monitoring the quadrature components of the current from a weakly coupled detector, which continuously measures the qubit. Similar to the earlier proposal of the "Bayesian" feedback, the feedback loop is used to maintain the coherent (Rabi)oscillations in a qubit for an arbitrarily long time; however, this is done in a significantly simpler way, which requires much smaller bandwidth of the control circuitry. The price for simplicity is a less-than-ideal operation: the fidelity is limited to about 95%. The feedback loop operation can be experimentally verified by appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization. The quadrature-based quantum feedback seems to be within the reach of the present-day technology.
Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.