{c}
{wiki}

One of the four following states:

$$
\begin{aligned}
\ket{\Phi^+} &= \frac{1}{\sqrt{2}} (\ket{00} &+ \ket{11})
\ket{\Phi^-} &= \frac{1}{\sqrt{2}} (\ket{00} &- \ket{11})
\ket{\Psi^+} &= \frac{1}{\sqrt{2}} (\ket{01} &+ \ket{10})
\ket{\Psi^-} &= \frac{1}{\sqrt{2}} (\ket{01} &- \ket{10})
\end{aligned}
$$

When unqualified as in "the Bell state", it generally just means $\ket{\Phi^+}$.

The Bell states are entangled and <non-separable>. Intuitively, we can see that when we measure that state, the values of the first and second bit are strictly correlated. This is the hallmark of <quantum computation>: making up states where qubits are highly correlated to match a specific algorithmic answer, and opposed to uniformly random noise. For example, the <Bell state circuit> is a common <hello world>, e.g. it is used in the official <Qiskit hello world>.


Bell state

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}


Ciro Santilli @cirosantilli 35

 Incoming links: Qiskit hello world