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arXiv:1206.6946 · Physical Review Letters

Measurement-Induced Qubit State Mixing in Circuit QED from Up-Converted Dephasing Noise

D. H. Slichter, Rajamani Vijay, Steven J. Weber, Samuel Boutin, Maxime Boissonneault, Jay Gambetta, Alexandre Blais, Irfan A. Siddiqi

Published Oct 9, 2012• 113 citations
arXivHTMLPDF

Abstract

We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f~1 GHz and find agreement with values extrapolated from a 1/f(α) fit to the measured flux noise spectral density below 1 Hz.

DOI
10.1103/physrevlett.109.153601

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We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f~1 GHz and find agreement with values extrapolated from a 1/f(α) fit to the measured flux noise spectral density below 1 Hz.
Dispersive readout of the transmon qubit in circuit QED is known to lose its quantum non-demolition character at small to moderate measurement drive amplitudes. This phenomenon is understood to originate from Laundau-Zener transitions at accidental multi-photon resonances, where nnn drive photons can promote the transmon by mmm levels. This interpretation has been shown to be in agreement with experiments characterizing the dispersive readout of a single transmon. The impact of these measurement-induced state transition (MIST) of a transmon embedded in a multi-qubit chip, however, remains largely unexplored. Here, we show that the presence of other components, such as qubits and couplers, can affect the MIST threshold of a measured transmon. To arrive at these results, we present a general method to characterize measurement-induced transition when the qubit under readout is coupled to other circuit elements, a ubiquitous situation in circuit QED-based quantum processors. As an example, we consider the case of two transmon qubits, and we show that the spectator qubit can be impacted by the measurement-induced transition of the readout qubit and, conversely, that the presence of the spectator qubit can lower the MIST threshold of the readout qubit. Finally, we explore how adding a coupler mode between the two qubits further modifies these effects.
We theoretically study measurement-induced dephasing of a superconducting qubit in the circuit QED architecture and compare the results to those obtained experimentally by Schuster et al. [Phys. Rev. Lett. 94, 123602 (2005)]. Strong coupling of the qubit to the resonator leads to a significant ac Stark shift of the qubit transition frequency. As a result, quantum fluctuations in the photon number populating the resonator cause dephasing of the qubit. We find good agreement between the predicted line shape of the qubit spectrum and the experimental results. Furthermore, in the strongly dispersive limit, where the Stark shift per photon is large compared to the cavity decay rate and the qubit linewidth, we predict that the qubit spectrum will be split into multiple peaks, with each peak corresponding to a different number of photons in the cavity.
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Superconducting electrical circuits can be used to study the physics of cavity quantum electrodynamics (QED) in new regimes, therefore realizing circuit QED. For quantum-information processing and quantum optics, an interesting regime of circuit QED is the dispersive regime, where the detuning between the qubit transition frequency and the resonator frequency is much larger than the interaction strength. In this paper, we investigate how nonlinear corrections to the dispersive regime affect the measurement process. We find that in the presence of pure qubit dephasing, photon population of the resonator used for the measurement of the qubit act as an effective heat bath, inducing incoherent relaxation and excitation of the qubit. Measurement thus induces both dephasing and mixing of the qubit, something that can reduce the quantum nondemolition aspect of the readout. Using quantum trajectory theory, we show that this heat bath can induce quantum jumps in the qubit state. Nonlinear effects can also reduce the achievable signal-to-noise ratio of a homodyne measurement of the voltage.
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Dispersive readout is widely used to perform high-fidelity measurement of superconducting qubits. Much work has been focused on the qubit readout fidelity, which depends on the achievable signal-to-noise ratio and the qubit relaxation time. As groups have pushed to increase readout fidelity by increasing readout photon number, dispersive readout has been shown to strongly affect the postmeasurement qubit state. Such effects hinder the effectiveness of quantum error correction, which requires measurements that both have high readout fidelity and are quantum nondemolition (QND). Here, we experimentally investigate non-QND effects in the fluxonium. We map out the state evolution of fluxonium qubits in the presence of resonator photons and observe that these photons induce transitions in the fluxonium both within and outside the qubit subspace. We numerically model our system and find that transitions to higher-excited states and coupling to an external spurious mode are necessary to explain observed non-QND effects.