Solovay-Kitaev theorem
The Solovay-Kitaev theorem says that with any Universal Gate Set, we can approximate a quantum gate on $n$ qubits to precision $ε$ using $Θ (2^n log^c(1/ε))$ gates for some constant $c$.
The dependence on the number of qubits $2^n$ is expected because an operator on $n$ qubits is a Matrix of $2^n \times 2^n$ entries. The dependence on the precision $log^c(1/ε)$ is great. The precision $\epsilon$ is the “distance” between the approximate quantum gate and the actual quantum gate, which we want to be small. So $1/\epsilon$ is big, but taking the Logarithm of it makes it small. The Polylog is also considered small. Thus this dependence means our approximation quickly converges on the actual quantum gate.