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arXiv:2305.10508 · Physical Review Letters

Readout-Induced Suppression and Enhancement of Superconducting Qubit Lifetimes

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

Published Feb 29, 2024• 34 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.132.090602

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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.
Measurement backaction degrades dispersive readout of superconducting qubits even at modest drive strengths, often via the reduction of qubit lifetimes during readout. In this work, we theoretically and experimentally study this degradation and show how it can result from the interplay between detuned two-level systems (TLSs) and a drive-renormalized qubit spectrum. For modest to strong readout, the qubit emission spectrum becomes non-Lorentzian and depends sensitively on the readout drive frequency (even when measurement rate is fixed). We combine the readout-modified qubit emission spectrum with time-dependent perturbation theory to predict qubit lifetimes in the presence of a TLS bath. Master equation simulations and experimental measurements on a frequency-tunable transmon confirm these predictions quantitatively. In particular, we find that driving at the resonator frequency associated with the qubit ground state yields the narrowest qubit emission spectrum and the least lifetime degradation for a fixed measurement rate, providing a practical guideline for optimizing readout protocols in future quantum processors.
The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample different portions of the bath. We compare the Zeno effects arising from dispersive energy measurements and purely dephasing "quasimeasurements," showing energy measurements are not necessary to accelerate or suppress the decay process.
Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number-nonconserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e., Kerr interactions) shows that number-nonconserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly nonlinear degrees of freedom.
For quantum information processing, each physical system has a different advantage as regards implementation, so hybrid systems that benefit from the advantage of several systems would provide a promising approach. One common hybrid approach involves combining a superconducting qubit as a controllable qubit and another quantum system with a long coherence time as a memory qubit. The use of a superconducting qubit gives us excellent controllability of the quantum states, and the memory qubit is capable of storing information for a long time. It has been believed that selective coupling can be realized between a superconducting qubit and a memory qubit by tuning the energy splitting between them. However, we have shown that this detuning approach has a fundamental drawback as regards energy leakage from the memory qubit. Even if the superconducting qubit is effectively separated by reasonable detuning, a non-negligible incoherent energy relaxation in the memory qubit occurs via residual weak coupling when the superconducting qubit is affected by severe dephasing. This energy transport from the memory qubit to the control qubit can be interpreted as the appearance of the anti--quantum Zeno effect induced by the fluctuation in the superconducting qubit. We also discuss possible ways to avoid this energy relaxation process, which is feasible with existing technology.
Scaling up superconducting quantum processors with optimized performance requires a sufficient flexibility in the choice of operating points for single and two qubit gates to maximize their fidelity and cope with imperfections. Flux control is an efficient technique to manipulate the parameters of tunable qubits, in particular to activate entangling gates. At flux sensitive points of operation, the ubiquitous presence of 1/f flux noise however gives rise to dephasing by inducing fluctuations of the qubit frequency. We show how two-tone modulation of the flux bias, a bichromatic modulation, gives rise to a continuum of dynamical sweet spots where dephasing due to slow flux noise is suppressed to first order for a wide range of time-averaged qubit frequencies. The qubits can be operated at these dynamical sweet spots to realize protected entangling gates and to avoid collisions with two-level-system defects.
Quantum measurements play a central role in quantum information processing. Understanding the mechanism of the quantum measurements is essential to both improve the visibility of the readout and decrease the projection error during measurement. Here, we describe and demonstrate an experimental protocol for quantifying a measurement backaction when we readout a superconducting flux qubit using a Josephson bifurcation amplifier. The coupling with the Josephson bifurcation amplifier induces a dephasing on the flux qubit during the readout. We have succeeded in estimating and controlling the strength of such a measurement-induced dephasing by changing the pulse height of the microwave driving. Our results are crucial for designing a suitable quantum readout technique for the realization of practical quantum devices.