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$5\,\mathrm{GHz}$

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A concrete number anchors the scale before the subtler chaining question is addressed. A superconducting transmon-style qubit with a transition frequency near 5\, $\mathrm{GHz}$ carries a local energy gap $\langle$ H $\rangle$ - $E_0$ =hf $\approx$ 3.3 $\times$ 10^{-24}\, $\mathrm J$ . Substituted into the instantaneous rate 2( $\langle$ H $\rangle$ - $E_0$ )/ $\pi$ $\hbar$ , this gives an upper ceiling of roughly 2 $\times$ 10^{10} orthogonal state changes per proper second; over one proper microsecond of continuous operation, $N_\perp$ $\lesssim$ 2 $\times$ 10^4 . Real superconducting processors run single-qubit gates in tens of nanoseconds, a realized rate several orders of magnitude below this ceiling. The Levitin-Toffoli bound is, in…

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5\,\mathrm{GHz}

Equation 29 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

A concrete number anchors the scale before the subtler chaining question is addressed. A superconducting transmon-style qubit with a transition frequency near 5\, $\mathrm{GHz}$ carries a local energy gap $\langle$ H $\rangle$ - $E_0$ =hf $\approx$ 3.3 $\times$ 10^{-24}\, $\mathrm J$ . Substituted into the instantaneous rate 2( $\langle$ H $\rangle$ - $E_0$ )/ $\pi$ $\hbar$ , this gives an upper ceiling of roughly 2 $\times$ 10^{10} orthogonal state changes per proper second; over one proper microsecond of continuous operation, $N_\perp$ $\lesssim$ 2 $\times$ 10^4 . Real superconducting processors run single-qubit gates in tens of nanoseconds, a realized rate several orders of magnitude below this ceiling. The Levitin-Toffoli bound is, in…