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Decoherence in Josephson-junction qubits due to critical-current fluctuations

2004; American Physical Society; Volume: 70; Issue: 6 Linguagem: Inglês

10.1103/physrevb.70.064517

1550-235X

D. J. Van Harlingen, T. L. Robertson, B. L. T. Plourde, P. A. Reichardt, Trevis A. Crane, John Clarke,

Spectroscopy and Quantum Chemical Studies

We compute the decoherence caused by $1∕f$ fluctuations at low frequency $f$ in the critical current ${I}_{0}$ of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency, ${S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ is the spectral density of the critical-current noise at $1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time $t$ scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in ${I}_{0}$ and area $\mathcal{A}$, and show that their values of ${S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We empirically extrapolate ${S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ to lower temperatures using a scaling $T(\mathrm{K})∕4.2$. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at $100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.