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.
Superconducting quantum computing
where formula_23 is the shape of the microwave pulse in time, formula_24 is the resonance frequency of the second qubit, formula_25 are the Pauli matrices, formula_26 is the coupling coefficient between the two qubits via the resonator, formula_27 is the qubit detuning, formula_28 is the stray (unwanted) coupling between qubits and formula_29 is Planck constant divided by formula_30. The time integral over formula_23 determines the angle of rotation. Unwanted rotations due to the first and third terms of the Hamiltonian can be compensated with single qubit operations. The remaining part is exactly the controlled-X gate.