Readout-Induced Suppression and Enhancement of Superconducting Qubit Lifetimes

Ted Thorbeck, Zhihao Xiao, Archana Kamal, and Luke C. G. Govia

Phys. Rev. Lett. 132, 090602 – Published 29 February 2024

Abstract

It has long been known that the lifetimes of superconducting qubits suffer during readout, increasing readout errors. We show that this degradation is due to the anti-Zeno effect, as readout-induced dephasing broadens the qubit so that it overlaps “hot spots” of strong dissipation, likely due to two-level systems in the qubit’s bath. Using a flux-tunable qubit to probe the qubit’s frequency-dependent loss, we accurately predict the change in lifetime during readout with a new self-consistent master equation that incorporates the modification to qubit relaxation due to measurement-induced dephasing. Moreover, we controllably demonstrate both the Zeno and anti-Zeno effects, which can explain both suppression and the rarer enhancement of qubit lifetimes during readout.

Received 12 September 2023
Accepted 23 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.090602

Physics Subject Headings (PhySH)

Quantum measurements Quantum nondemolition measurement

Superconducting devices Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Ted Thorbeck ^1,*, Zhihao Xiao ², Archana Kamal², and Luke C. G. Govia ³

¹IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
²Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
³IBM Quantum, IBM Almaden Research Center, San Jose, California 95120, USA

^*ted.thorbeck@ibm.com

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Issue

Vol. 132, Iss. 9 — 1 March 2024

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Images

Figure 1
Fundamentals of Zeno and anti-Zeno effects. (a) The qubit decay rate in the absence of readout $γ_{q} (ω)$ is dominated by a few hot spots, likely due to TLSs. During readout the qubit’s frequency is Stark shifted by $ν_{S} ({\bar{n}}_{r})$ and broadened at the dephasing rate $γ_{ϕ} ({\bar{n}}_{r})$ , as shown by the Lorentzian centered about the Stark-shifted qubit frequency ${\tilde{ω}}_{q} ({\bar{n}}_{r})$ . Here the Lorentzian overlaps a hot spot that the qubit is not sensitive to at its natural frequency, thus increasing the decay rate. (b) To display the Zeno effect, the natural qubit frequency must be resonant with a hot spot, so that during readout the qubit becomes less sensitive to the hot spot. (c) Schematic of how the decay rate during readout $Γ ({\bar{n}}_{r})$ depends on the readout strength, in terms of the average number of photons in the resonator, for both the Zeno and anti-Zeno effects.
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Figure 2
Predicting $Γ ({\bar{n}}_{r})$ using the Kofman-Kurizki formula. (a) Fixed-delay $T_{1}$ experiment, with $t_{delay} = 30 μ s$ , to measure the qubit decay rate $γ_{q} (ω)$ using flux to shift the qubit frequency by $Δ ω (Φ)$ about the natural qubit frequency, $ω_{q} / 2 π = 4.884 GHz$ . We convert qubit population at the end of the experiment $p_{1}$ to a decay rate using $γ_{q} = - \log (p_{1}) / t_{delay}$ , neglecting heating and imperfect initialization. (b) Fixed-delay $T_{1}$ experiment with a pseudomeasurement pulse, of strength ${\bar{n}}_{r}$ , during the delay to measure the decay rate during readout $Γ ({\bar{n}}_{r})$ . (a),(b) Interleaved into a single experiment, lasting about 100 s, to prevent drift in $γ_{q} (ω)$ . (c),(e),(g) Results of $γ_{q} (ω)$ sweep in blue. (d),(f),(h) Experimental results of $Γ ({\bar{n}}_{r})$ sweep in blue, with the Kofman-Kurizki prediction in black. A flux offset applied during pseudomeasurement tone shifts the portion of $γ_{q} (ω)$ that is sampled during readout, to switch between the Zeno and anti-Zeno effects. The vertical black line on the left shows the flux-tuned qubit frequency at ${\bar{n}}_{r} = 0$ , black arrow on right. The colored Lorentzians show the portions of $γ_{q} (ω)$ involved in evaluating the Kofman-Kurizki formula at ${\bar{n}}_{r} \approx 1$ and 4, as shown by the colored arrows on the right.
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Figure 3
Breakdown of the Kofman-Kurizki prediction. (a),(b) Repetition of the experiment from Fig. 2, taken about a month later, showing the failure of the Kofman-Kurizki formula to predict the measured $Γ ({\bar{n}}_{r})$ . Here the orange Lorentzian shows the dephasing broadened range of the qubit when the Stark shift is approximately equal to the detuning to the TLS, at about ${\bar{n}}_{r} \approx 2$ . (c) Qubit $p_{1}$ during swap spectroscopy, showing oscillations between the qubit and the TLS. (d) Swap spectroscopy for the TLS at $Δ / 2 π = - 11 MHz$ in (a). Delay between the $X$ pulse and the measurement tone was fixed at $50 μ s$ , so $p_{1}$ does not approach unity at $t_{pulse} = 0$ in (c).
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Figure 4
Zeno and anti-Zeno effects for a qubit coupled to a coherent defect. (a) Variable-delay $T_{1}$ experiment, with logarithmic spacing to fit $Γ$ over orders of magnitude, as a function of both the magnitude of the flux noise applied to the qubit and the qubit-defect detuning. The qubit frequency is fixed at $ω_{q} / 2 π = 4.291 GHz$ , while the flux through the defect is swept. (b) Two line cuts through (c): blue for qubit on resonance with the defect, showing the Zeno effect, and orange for the qubit far from resonance with the defect, showing the anti-Zeno effect. (c) Measured $Γ$ as a function of dephasing rate and qubit-defect detuning. Points near zero detuning and zero applied flux noise are not shown because vacuum-Rabi oscillations do not fit a simple exponential. (d) Theory prediction of $Γ$ using Eq. (2) and parameters independently measured in the Supplemental Material [51].
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