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Observing single quantum trajectories of a superconducting quantum bit


The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture—a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a ‘quantum trajectory’1,2 determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories3 of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier4,5, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics6,7,8. Moreover, our experiments suggest a new means of implementing ‘quantum steering’9—the harnessing of action at a distance to manipulate quantum states through measurement.

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Figure 1: Single-quadrature weak measurements.
Figure 2: Correlation of tomography results with measurement values.
Figure 3: Quantum trajectories.


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We thank H. Wiseman, A. N. Korotkov, E. M. Levenson-Falk and N. Roch for discussions, and R. Vijay for contributions to preliminary experiments. This research was supported in part by the Army Research Office, Office of Naval Research and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Office. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US government.

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Authors and Affiliations



K.W.M. and S.J.W. performed the experiment, analysed the data and wrote the manuscript. C.M. had the idea for the experiment and edited the manuscript. All work was carried out under the supervision of I.S.

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Correspondence to K. W. Murch.

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The authors declare no competing financial interests.

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This file contains Supplementary Methods, Supplementary Figures 1-4, Supplementary Text and Data and an additional reference. (PDF 223 kb)

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Murch, K., Weber, S., Macklin, C. et al. Observing single quantum trajectories of a superconducting quantum bit. Nature 502, 211–214 (2013).

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