{c}
{tag=Universal quantum gates}

Set of <quantum logic gate> composed of the <Clifford gates> plus the <Toffoli gate>. It forms a set of <universal quantum gates>.


Clifford plus T

Course plan:
* <Programmer's model of quantum computers>{full}
* look at a <Qiskit hello world>
  * e.g. ours: <qiskit/hello.py>{file}
* learn about <quantum circuits>.
  * <tensor product in quantum computing>
  * First we learn some <quantum logic gates>. This shows an alternative, and extremely important view of a quantum computer besides a matrix multiplication: as a circuit. Fundamental subsections:
    * <quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially>{full}
    * <quantum logic gates are needed for physical implementation>{full}
    * <universal quantum gates>{full}
    * <quantum circuits vs classical circuits>{full}
    * Examples of specific gates:
      * <Single-qubit gates>:
        * <Pauli gate>
          * <Pauli-X gate>
        * <Hadamard gate>
      * <Controlled quantum gate>
        * <CNOT gate>
      * <Bell state>
        * <Bell circuit>
  * <quantum algorithms>
    * <Quantum Fourier transform>{full}
    * <Shor's algorithm>{full}


Introduction to quantum computing

{wiki}

A <quantum circuit> is a <graph> of <quantum logic gates>.

<Quantum circuits> are the prevailing <model of quantum computing> as of the 2010's - 2020's


Quantum circuit

{wiki}

= Quantum gate
{synonym}

At <quantum computing is just matrix multiplication>{full} we saw that making a quantum circuit actually comes down to designing one big <unitary matrix>.

We have to say though that that was a bit of a lie.

Quantum programmers normally don't just produce those big matrices manually from scratch.

Instead, they use </quantum logic gates>.

The following are the main reasons for that:
* <quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially>{full}
* <quantum logic gates are needed for physical implementation>{full}


Ciro Santilli @cirosantilli 37

 Incoming links: Quantum logic gate