Quantum Physics & Computing formula — definition, units and applicable conditions

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Quantum Physics & Computing

time-dependent Schrödinger equation

i\hbar\frac{\partial\psi}{\partial t}=\hat H\psi

describes the evolution of the state of a closed quantum system over time.

Quantum Physics & Computing

P(i)=\lvert\langle i\mid\psi\rangle\rvert^2

converts the amplitude of the normalized state on the measurement basis into a probability.

Quantum Physics & Computing

|\psi\rangle=\cos\frac\theta2|0\rangle+e^{i\phi}\sin\frac\theta2|1\rangle

uses two angles to represent the single-qubit pure state, omitting the global phase.

Quantum Physics & Computing

\Delta x\,\Delta p\ge\frac\hbar2

The standard deviations of position and momentum cannot be arbitrarily small at the same time.