9.8 Universality for quantum gates
The existence of a universal set of gates for quantum computing is mostly academic for a coding book, but it is worth a short discussion to complement the classical situation.
Unlike the classical case, there is an infinite number of 1-qubit quantum gates. The RXφ, RYφ, and RZφ give us such a set, where 0 ≤ φ < 2π. If we can’t generate these precisely, we need to approximate them as closely as we wish. We modify our definition to say that a set of quantum gates is universal if we can create a circuit with those gates and approximate any n-qubit quantum gate to arbitrary precision. [TCN]
We need qubit entanglement, which does not have a classical counterpart.
Finally, below the elegant gates like X, Y, Z, H, and CNOT, we need to understand which gates engineers implemented in the hardware in any...
