Is there a name for a gate that 'moves' one qubit to a new position via multiple SWAP gates?

Question

Let's say there is a qubit at position $i$, and I want to move it to position $i'$. Without loss of generality, let's say $i < i'$. By 'move it' I mean, perform multiple $SWAP$ operations so that every qubit at positions $i<j<i'$ is moved over one position, so that they are moved to position $j' = j - 1$, and the qubit at position $i$ is moved to the qubit position $i'$.

This would be implemented using $i' - i$ number of $SWAP$ gates. Denote $SWAP_{k,k+1}$ as the $SWAP$ gate swapping qubits at positions $k$ and $k+1$. In Python-style pseudocode, this would be the way to implement the gate I am describing:

for k in range(i,i'):
    SWAP(k,k+1)

I feel like there should be a name for the gate I am describing. If not, I want to call it something like $MOVETO_{i,i'}$ or $SHIFT_{i,i'}$.

Any suggestions?

Answer 1

Note that the first SWAP places qubit $i+1$ at position $i$. The second one places qubit $i+2$ at position $i+1$. Eventually, the qubit number $k$ will be at place $k-1$ for $k>i$, while qubit $i$ will be placed at position $i'$.

Thus, this operation already has a name: it's a circular shift, or bitwise rotation. Specifically, it's a left circular shift by 1 position.