Equation 31 · Part 5 · A Horizon Is a Toll Booth, Not a Loophole

subscript

2(\langle H\rangle-E_0)/\pi\hbar

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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