## The More You Know: Quantum Circuit

Quantum Circuits are used to visualize a prescription of quantum gates acting on a quantum state. They describe the changes of the quantum data as it undergoes successive discrete operations.

The data in a Quantum Circuit is usually encoded in a $n$-qubit state (other Quantum Circuit models can use $m$-level quantum systems instead of these $2$-level systems) which is set to a known vale, i.e. $|000...\rangle$. Thus, for every qubit in the circuit a horizontal rail, a wire, is drawn to represent its evolution, time flows from left to right.

Wires in a Quantum Circuit initialized to the $n$-qubit quantum state $|000...\rangle$.

Additionally, a Quantum Circuit is built from elementary quantum gates (unitary operations) acting on a fixed number of qubits. Since Quantum Circuits are read from left to right, leftmost gates act first.

Single-qubit and Two-qubit quantum gates in a Quantum Circuit.

Then, a description of the Quantum System consists of

1. Input: A controlled input $n$-qubit state.
2. Evolution: Prescribed sequence of Unitary Single-qubit and Two-qubit logic quantum gates which give the evolution of the initial quantum state.
3. Output: Readout (measurement) of the state of the $n$ qubits.

Quantum Circuits where drawn using this LaTeX package.