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arXiv:1101.0862 · Physical Review B

Measurement of energy decay in superconducting qubits from nonequilibrium quasiparticles

M. Lenander, H. Wang, Radoslaw C. Bialczak, Erik A. Lucero, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, Martin P. Weides, J. Wenner, Tsuyoshi Yamamoto, Yi Yin, Jie Zhao, Andrew N. Cleland, John M. Martinis

Published Jul 1, 2011• 101 citations
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Abstract

Quasiparticles are an important decoherence mechanism in superconducting qubits, and can be described with a complex admittance that is a generalization of the Mattis-Bardeen theory. By injecting nonequilibrium quasiparticles with a tunnel junction, we verify qualitatively the expected change of the decay rate and transition frequency in a phase qubit. With their relative change in agreement to within 4 % of prediction, the theory can be reliably used to infer quasiparticle density. We describe how settling of the decay rate may allow determination of whether qubit energy relaxation is limited by nonequilibrium quasiparticles.

DOI
10.1103/physrevb.84.024501

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Quasiparticles are an important decoherence mechanism in superconducting qubits, and can be described with a complex admittance that is a generalization of the Mattis-Bardeen theory. By injecting nonequilibrium quasiparticles with a tunnel junction, we verify qualitatively the expected change of the decay rate and transition frequency in a phase qubit. With their relative change in agreement to within 4 % of prediction, the theory can be reliably used to infer quasiparticle density. We describe how settling of the decay rate may allow determination of whether qubit energy relaxation is limited by nonequilibrium quasiparticles.
As low-loss nonlinear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represents an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and nonequilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible nonequilibrium quasiparticle distribution. We also derive expressions for the shift in qubit frequency in the presence of quasiparticles.
We calculate the energy decay rate of Josephson qubits and superconducting resonators from nonequilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n(qp) = 10/microm(3), which suggests that nonequilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators-a small reduction in decay rate with increasing temperature.
Quasiparticle tunneling across a Josephson junction sets a limit for the lifetime of a superconducting qubit state. We develop a general theory of the corresponding decay rate in a qubit controlled by a magnetic flux. The flux affects quasiparticles tunneling amplitudes, thus making the decay rate flux-dependent. The theory is applicable for an arbitrary quasiparticle distribution. It provides estimates for the rates in practically important quantum circuits and also offers a new way of measuring the phase-dependent admittance of a Josephson junction.
We study decoherence in superconducting qubits due to quasiparticle tunneling which is enhanced by two known deviations from the equilibrium BCS theory. The first process corresponds to tunneling of an already existing quasiparticle across the junction. The quasiparticle density is increased, e.g., because of an effective quasiparticle doping of the system. The second process is quasiparticle tunneling by breaking of a Cooper pair. This can happen at typical energies of superconducting qubits if there is an extended quasiparticle density inside the gap. We calculate the induced energy decay and pure dephasing rates in typical qubit designs. Assuming the lowest reported value of the nonequilibrium quasiparticle density in Aluminum, we find for the persistent-current flux qubit decay times of the order of recent measurements. Using the typical subgap density of states in Niobium we also reproduce observed decay times in the corresponding Niobium flux qubits.
Quasiparticles, especially the ones near the Josephson junctions in the superconducting qubits, are known as an important source of decoherence. By injecting quasiparticles into a quantum chip, we characterized the diffusion feature by measuring the energy relaxation time and the residual excited-state population of a transmon qubit. From the extracted transition rates, we phenomenologically modeled the quasiparticle diffusion in a superconducting circuit that contained “hot” nonequilibrium quasiparticles in addition to low-energy ones.
Superconducting qubits based on Josephson junctions have emerged as a leading hardware platform in the quest to realize large-scale quantum computers. However, qubit decoherence remains a major hurdle on the path toward fault-tolerant quantum computing. In particular, excess quasiparticle (QP) excitations constitute a significant source of dissipation in superconducting quantum devices. The empirically observed QP density in these systems is orders of magnitude larger than that predicted by Bardeen-Cooper-Schrieffer (BCS) theory. Moreover, QP poisoning due to high-energy particle impacts can cause correlated errors that simultaneously affect multiple qubits, thereby impeding quantum error correction. Although QP-induced decoherence has been extensively studied in widely implemented transmon qubits, its impact on fluxonium qubits, a leading alternative architecture, remains far less explored. In this thesis, we investigate energy relaxation in fluxonium qubits induced by controlled QP poisoning using an on-chip Josephson injector junction that generates Cooper-pair-breaking phonons and photons. We separately measure the relaxation and excitation rates, instead of the conventional energy relaxation time. For specific injection parameters, we observe an apparent reversal of the rates, with the excitation rate exceeding the relaxation rate. We further measure the rates as a function of external flux to disentangle the effects of QP tunneling across the small junction and the junction array superinductor. Across all measured samples, differing in qubit spectra and injection conditions, we infer roughly an order of magnitude higher QP density at the small junction than in the array junctions. Our findings advance the understanding of QP-induced decoherence in fluxonium qubits and provide insight for reconciling discrepancies in reported bounds on QP densities, potentially enabling the development of QP mitigation strategies tailored to fluxonium qubits.