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t∗=π/(2g)=1/(4×10 MHz)=25.0 nst^\ast = \pi/(2g) = 1/(4\times10\ \mathrm{MHz}) = 25.0\ \mathrm{ns}

Why this formula appears here

Putting numbers to the swing keeps it honest rather than decorative. Take ω\omega/2π\pi = 5\ GHz\mathrm{GHz} and g/2π\pi = 10\ MHz\mathrm{MHz} , both squarely inside the range of qubit and resonator frequencies and coupling strengths reported across circuit quantum electrodynamics architectures, which span a few gigahertz in frequency and from a fraction of a megahertz up to several hundred megahertz in coupling depending on the regime [ 12 ] . The swap time is t∗t^\ast = π\pi/(2g) = 1/(4×\times10\ MHz\mathrm{MHz}) = 25.0\ ns\mathrm{ns} , and the ledger’s swing at that instant is ℏ\hbarω\omega/2 ≈\approx 1.66×\times10^{-24}\ J\mathrm{J} ≈\approx 10.3\ μ\mueV\mathrm{eV} — an exact analytic evaluation under the stated…

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t∗=π/(2g)=1/(4×10 MHz)=25.0 nst^\ast = \pi/(2g) = 1/(4\times10\ \mathrm{MHz}) = 25.0\ \mathrm{ns}

Equation 104 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Putting numbers to the swing keeps it honest rather than decorative. Take ω\omega/2π\pi = 5\ GHz\mathrm{GHz} and g/2π\pi = 10\ MHz\mathrm{MHz} , both squarely inside the range of qubit and resonator frequencies and coupling strengths reported across circuit quantum electrodynamics architectures, which span a few gigahertz in frequency and from a fraction of a megahertz up to several hundred megahertz in coupling depending on the regime [ 12 ] . The swap time is t∗t^\ast = π\pi/(2g) = 1/(4×\times10\ MHz\mathrm{MHz}) = 25.0\ ns\mathrm{ns} , and the ledger’s swing at that instant is ℏ\hbarω\omega/2 ≈\approx 1.66×\times10^{-24}\ J\mathrm{J} ≈\approx 10.3\ μ\mueV\mathrm{eV} — an exact analytic evaluation under the stated…

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