quantum_intro.md

Brief introduction to quantum computing

Classical computers, as we know them, work by manipulating bits that hold the value of either zero or one.

Quantum computers, on the other hand, utilize qubits—a quantum-world counterpart of bits. Qubits also can hold values of zero and one, but it can also be in a superposition of the two states, meaning that it can be partially in both states at once.

Qubits are typically represented using a pair of complex numbers labeled α and β. These two values relate to the probabilities at which the given qubit will be measured as zero or one.

Typically, we represent the zero state as

$\left\lvert 0 \right\rangle = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$

the one state as

$\left\lvert 1 \right\rangle = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$

while superposed qubits can be represented as

$\left\lvert \psi \right\rangle = \begin{bmatrix} \alpha \\ \beta \end{bmatrix}$

where squares of α and β add up to 1

$\left|\alpha\right|^2 + \left|\beta\right|^2 = 1$

It is important to note that even though a qubit can hold any of virtually infinite states, when we measure it, it always collapses into one of the two basic states—zero or one.