Algorithmic cooling
A qubit (or quantum bit) is a unit of information that can be in a superposition of two states, denoted as formula_1 and formula_2. The general superposition can be written as formula_3where formula_4 and formula_5. If one measures the state of the qubit in the orthonormal basis composed of formula_1 and formula_2, one gets the result formula_1 with probability formula_9 and the result formula_2 with probability formula_11.
Bell state
Although there are many possible ways to create entangled Bell states through quantum circuits, the simplest takes a computational basis as the input, and contains a Hadamard gate and a CNOT gate (pictured below). As an example, the quantum circuit pictures takes the two qubit input formula_7and transformed it to the first Bell state (1). Explicitly, the Hadamard gate transforms formula_7 into a superposition of formula_9. This will then act as a control input to the CNOT gate, which only inverts the target when the control is 1. Thus, the CNOT gate transforms the second qubit as follows formula_10.