Mathematical quick reference

Key formulas and notation

A supplementary study guide. Formulas here are typeset using the bundled offline KaTeX engine; original lecture pages remain the authoritative source.

Quantum state

$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle,\quad |\alpha|^2+|\beta|^2=1$$

{c} · Study reference; see the full lecture for context and assumptions.

Unitary operations

$$U^\dagger U=I$$

{c} · Study reference; see the full lecture for context and assumptions.

Tensor product

$$(A\otimes B)(C\otimes D)=AC\otimes BD$$

{c} · Study reference; see the full lecture for context and assumptions.

Bell state

$$|\Phi^+\rangle=\frac{|00\rangle+|11\rangle}{\sqrt2}$$

{c} · Study reference; see the full lecture for context and assumptions.

Measurement probabilities

$$P(x)=|\langle x|\psi\rangle|^2$$

{c} · Study reference; see the full lecture for context and assumptions.

Quantum Fourier transform

$$\operatorname{QFT}_N|x\rangle=\frac1{\sqrt N}\sum_{y=0}^{N-1}e^{2\pi ixy/N}|y\rangle$$

{c} · Study reference; see the full lecture for context and assumptions.

Phase estimation

$$U|u\rangle=e^{2\pi i\theta}|u\rangle$$

{c} · Study reference; see the full lecture for context and assumptions.

Grover search

$$O(\sqrt N)$$

{c} · Study reference; see the full lecture for context and assumptions.

Quantum error correction

$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$

{c} · Study reference; see the full lecture for context and assumptions.

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