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arXiv:cond-mat/0304255 · Physical Review Letters

Quasiparticle Decoherence in d -Wave Superconducting Qubits

M. H. S. Amin, Anatoly Yu. Smirnov

Published Jan 6, 2004• 43 citations
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Abstract

It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.

DOI
10.1103/physrevlett.92.017001

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It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.
We study the Josephson junction between two d -wave superconductors, which is discussed as an implementation of a qubit. We propose an approach to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles, which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.
Superconducting qubits hold promise for quantum computing, but their operation is challenged by various sources of noise, including excitations known as quasiparticles. Qubits with gap asymmetry larger than their transition energy are less susceptible to quasiparticle decoherence as the quasiparticles are mostly trapped in the low-gap side of the junction. Because of this trapping, the gap asymmetry can contribute to maintaining the quasiparticles out of equilibrium. Here we address the temperature dependence of the quasiparticle densities in the two sides of the junction. We show that four qualitatively different regimes are possible with increasing temperature: (i) nonequilibrium, (ii) local quasiequilibrium, (iii) global quasiequilibrium, and (iv) full equilibrium. We identify shortcomings in assuming global quasiequilibrium when interpreting experimental data, highlighting how measurements in the presence of magnetic field can aid the accurate determination of the junction parameters, and hence the identification of the nonequilibrium regimes. Quasiparticle poisoning challenges the operation of superconducting qubits, but errors can be suppressed by engineering gap asymmetry between the electrodes of the qubit’s Josephson junction. The authors present a model of the qubit-quasiparticle system valid beyond the low-temperature limit and identify different nonequilibrium regimes, which can affect the interpretation of experimental data.
Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike the transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection and isolating the quasiparticle-induced contribution by subtracting the background transition rates. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle densities in the small junction and the junction array and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.
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.
The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over 10310^3103 seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions.
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.