Calculus×Computing
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Quantum computing

Level AdvancedDifficulty ★★★★★Application⌖ Open in the map

What is it?

Computing with qubits: states are unit vectors of complex amplitudes, gates are unitary matrices (exponentials e−iHte^{-iHt}), measurement samples with probabilities ∣α∣2|\alpha|^2. Shor's algorithm relies on a quantum Fourier transform. Mostly linear algebra; calculus enters through complex exponentials, Fourier analysis and the physics of the hardware.

Formulas

∣ψ⟩=α∣0⟩+β∣1⟩,∣α∣2+∣β∣2=1|\psi\rangle = \alpha|0\rangle + \beta|1\rangle, \quad |\alpha|^2 + |\beta|^2 = 1

The mathematics behind it

  • Complex numbers★★★★★fundamental

    Qubit amplitudes are complex numbers; interference is addition of complex phases.

  • Taylor and Maclaurin series★★★★★advanced

    Gates are e−iHte^{-iHt}, matrix exponentials defined by their power series.

Further reading

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.

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