# A question about a real programmable quantum computer

In the theory of universal quantum gates,I have known a common universal gate set is the Clifford + T gate set, which is composed of the CNOT, H, S and T gates. Then there is a concept called "accuracy", which means use the composition of this set of gates can achieve any accuracy of the gate we want to approximately simulate.

However, in real quantum computer hardware, for example, ion-trapped quantum computers, the two parameterized gates in this paper can be regareded as universal quantum gates to realize any quantum gates (https://arxiv.org/pdf/1603.07678.pdf), and the concept of "accuracy" is also no longer mentioned.

It mentioned a concept of "fidelity" instead. So does that means, the process of simulation will be 100% right if we don't take the influence of hardware realization into account? If so, why do we still need to learn so much about "universal quantum gates"?

The reason that accuracy is a concern for the CNOT/H/T gate set is that it is a discrete set, so for a rotation of some irrational angle (in multiples of $$\pi$$), I believe you would generically need infinite gates to exactly match it. The reason this gate set is still considered is that due to the Eastin-Knill theorem, Quantum Error Correcting Codes can only allow a discrete logical gate set, so in Fault-Tolerant Quantum Computers, a discrete set might be the best that we can do.