So any universal gate set can replicate any other, since both are universal, but different architectures generally have different physical gates. While Clifford+T is a universal gate set that is very nice to think about theoretically, it isn't generally close to the one used in the lab.

In most experimental setups, the physical level universal gate set used is composed of arbitrary angle Pauli rotations, along with a single entangling gate which is either always maximally entangling, or also variable angle.

For trapped ion systems, we use single qubit Paulis along with a gate known as the Mølmer-Sørenson gate. This gate is a rotation about the XX axis of two qubits which uses the shared motion of the ions in the trap to get distant entanglement.

Superconductors use different entangling gates, if I remember correctly IBM uses a gate called the 'Rip gate' which I think is a ZX rotation gate, and on the Google Sycamore chip, they use a gate which ends up being a combination of CZ and iSWAP.

To understand how these are universal gate sets, lets use the ion trap gate set to build the pieces of the initial set you described, Clifford+T. First, lets condense that set into the three elements [H, CNOT, T]. A T gate is just a Z rotation, so by having the arbitrary Pauli rotations we are covered there. A Hadamard gate is an X rotation followed by a Y rotation, so we have that one as well. Through this we have all possible single qubit gates already. Now to get the CNOT, we can wrap the XX gate in 4 single qubit Paulis, as described in Fig. 1 of this paper. As a result we have a full universal set. The only difference for the SC gate sets would be a different decomposition of CNOT.

So any universal gate set can replicate any other, since both are universal, but different architectures generally have different physical gates. While Clifford+T is a universal gate set that is very nice to think about theoretically, it isn't generally close to the one used in the lab.

In most experimental setups, the physical level universal gate set used is composed of arbitrary angle Pauli rotations, along with a single entangling gate which is either always maximally entangling, or also variable angle.

For trapped ion systems, we use single qubit Paulis along with a gate known as the Mølmer-Sørenson gate. This gate is a rotation about the XX axis of two qubits which uses the shared motion of the ions in the trap to get distant entanglement.

Superconductors use different entangling gates, if I remember correctly IBM uses a gate called the 'Cross-Resonance gate' which I think is a ZX rotation gate, and on the Google Sycamore chip, they use a gate which ends up being a combination of CZ and iSWAP.

To understand how these are universal gate sets, lets use the ion trap gate set to build the pieces of the initial set you described, Clifford+T. First, lets condense that set into the three elements [H, CNOT, T]. A T gate is just a Z rotation, so by having the arbitrary Pauli rotations we are covered there. A Hadamard gate is an X rotation followed by a Y rotation, so we have that one as well. Through this we have all possible single qubit gates already. Now to get the CNOT, we can wrap the XX gate in 4 single qubit Paulis, as described in Fig. 1 of this paper. As a result we have a full universal set. The only difference for the SC gate sets would be a different decomposition of CNOT.