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⟨H⟩−E0=hf≈3.3×10−24 J\langle H\rangle-E_0=hf\approx3.3\times10^{-24}\,\mathrm J

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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\,GHz\mathrm{GHz} carries a local energy gap ⟨\langle H⟩\rangle-E0E_0=hf≈\approx3.3×\times10^{-24}\,J\mathrm J . Substituted into the instantaneous rate 2(⟨\langle H⟩\rangle-E0E_0)/π\piℏ\hbar , this gives an upper ceiling of roughly 2×\times10^{10} orthogonal state changes per proper second; over one proper microsecond of continuous operation, N⊥N_\perp≲\lesssim2×\times10^4 . 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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⟨H⟩−E0=hf≈3.3×10−24 J\langle H\rangle-E_0=hf\approx3.3\times10^{-24}\,\mathrm J

Equation 30 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

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

A concrete number anchors the scale before the subtler chaining question is addressed. A superconducting transmon-style qubit with a transition frequency near 5\,GHz\mathrm{GHz} carries a local energy gap ⟨\langle H⟩\rangle-E0E_0=hf≈\approx3.3×\times10^{-24}\,J\mathrm J . Substituted into the instantaneous rate 2(⟨\langle H⟩\rangle-E0E_0)/π\piℏ\hbar , this gives an upper ceiling of roughly 2×\times10^{10} orthogonal state changes per proper second; over one proper microsecond of continuous operation, N⊥N_\perp≲\lesssim2×\times10^4 . 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…

Meanings in this article

  • E0E_0: the ground-state energy of H [ 2 , 1 ].
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