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arXiv:1111.4801 · Physical Review A

Maintaining quantum coherence in the presence of noise through state monitoring

Thomas Konrad, Hermann Uys

Published Jan 4, 2012• 20 citations
arXivHTMLPDF

Abstract

Unsharp measurements allow the estimation and tracking of quantum wave functions in real time with minimal disruption of the dynamics. Here we demonstrate that high-fidelity state monitoring, and hence quantum control, is possible, even in the presence of classical dephasing and amplitude noise, by simulating such measurements on a two-level system undergoing Rabi oscillations. Finite estimation fidelity is found to persist indefinitely after the decoherence times set by the noise fields in the absence of measurement.

DOI
10.1103/physreva.85.012102

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Unsharp measurements allow the estimation and tracking of quantum wave functions in real time with minimal disruption of the dynamics. Here we demonstrate that high-fidelity state monitoring, and hence quantum control, is possible, even in the presence of classical dephasing and amplitude noise, by simulating such measurements on a two-level system undergoing Rabi oscillations. Finite estimation fidelity is found to persist indefinitely after the decoherence times set by the noise fields in the absence of measurement.
In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level and multi-level systems, i.e., the high-fidelity quantum dynamics can be maintained. Furthermore, we discuss the influence of noise strength and measurement strength on the degree of precise quantum control. Crucially, the measurement-feedback scheme is quite universal in that it can be applied to precise quantum control for any dimension systems. Thus, it naturally finds extensive applications in quantum information processing.
We investigate the quantum control of two qubits interacting with a Markovian environment and evolving as an XXX state. The control is implemented via a simple applied field, whose profile is determined by means of the piecewise time-independent quantum control method. The goal is to make either the population or the system concurrence to follow a specified tracking control trajectory. By considering the system under the influence of three kinds of noise---phase damping, amplitude damping, or a combination of both---we unveil the conditions (like energy balance) under which the quantum control is properly achieved and fidelity (monitored through the trace distance) is kept satisfactorily high, even if the qubits interact differently with the dissipative medium. We further find that the effects of phase damping, a type of noise which notoriously destroys coherence and entanglement, can be mitigated if during the control the system is also exposed to amplitude damping. Of potential interest for the usage of entanglement as resource for quantum information, our results indicate that distinct entanglement measures and coherence can be maintained relatively high (even at long times) as a consequence of the tracking quantum control process.
We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the backaction of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing interatomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate interatomic interactions, the entire many-body state---modified by the measurement---is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the interatomic interactions enhance the information gained via the measurement.
Motivated by the technical requirements of quantum information processing and nanotechnology, the control of individual quantum systems such as single atoms, ions or even photons has become a highly desirable aim.The monitoring of quantum systems-a direct test and in many cases a prerequisite of their control-has been investigated so far only for certain observables such as the position or momentum of quantum particles.Here, we describe a method to monitor in real time the complete state of a quantum particle with unknown initial state moving in a known potential.The method is based on successively updating an estimate by the results of a continuous position measurement.We demonstrate by numerical simulations that even in a chaotic potential tracking the wave function of a particle is possible, and we show with an example that the monitoring scheme appears to be robust against sudden random perturbations.
This paper investigates the application of quantum decoherence control techniques to enhance distributed quantum computing. The core challenge in distributed quantum computing lies in mitigating the detrimental effects of quantum decoherence, which rapidly degrades the delicate quantum states of qubits, hindering computation accuracy and fidelity. This research proposes a novel approach utilizing precisely controlled interactions between qubits to suppress decoherence and establish robust entanglement, ultimately facilitating accurate and efficient distributed quantum computation. The theoretical framework outlines key control strategies and associated mathematical formulations, demonstrating the potential for significant improvements in performance. Specifically, we explore the use of tailored pulse sequences designed to minimize dephasing and minimize the impact of environmental noise. The proposed method leverages a feedback control system to dynamically adjust the control parameters based on real-time decoherence monitoring. The presented formalism includes the Bloch equations and their extensions to account for controlled interactions, providing a rigorous foundation for the theoretical analysis. We demonstrate the feasibility of achieving high-fidelity entanglement and quantum gates in a distributed system, paving the way for scalable quantum computation. Finally, we discuss the limitations and future directions of this approach, emphasizing the need for advanced noise mitigation techniques and improved qubit coherence times.
We investigate the possibility to monitor the dynamics of an open quantum system with the help of a small probe system, coupled via dephasing coupling to the open system of interest. As an example, we consider a dissipative harmonic oscillator and a single qubit as probe system. Qubit plus oscillator are described by a finite temperature quantum master equation, where the dynamics of the whole system can be obtained analytically. We find that the short time behavior of the reduced qubit state (its coherence) provides exhaustive information on the dissipative dynamics of the oscillator. Observing this coherence for two initial states with different out-of-equilibrium temperatures, one can determine all coupling constants and the equilibrium temperature fixed by the external heat bath. In addition, the dephasing coupling to the qubit probe, may be considered as a perturbation of the dissipative oscillator. The corresponding quantum fidelity can be calculated analytically, also. Hence, we find the precise relation between the behavior of the reduced qubit state (its coherence) and that fidelity.