What type of Quantum Gate is this I'm trying to work out if this is a certain type of 'known' Quantum Gate
$|1\rangle|1\rangle $ goes to $|1\rangle|1\rangle $ 
$|1\rangle|0\rangle $ goes to $|1\rangle|0\rangle $ 
$|0\rangle|1\rangle $ goes to $|0\rangle|1\rangle $ 
$|0\rangle|0\rangle $ goes to -$|0\rangle|0\rangle $ 
So only the last state changes. I initially thought this was a controlled - not gate, but I realise now it's not. Is it maybe a phase shifter gate? 
 A: That gate is, up to conventions on whether you control on $|1⟩$ or $|0⟩$, a controlled-Z gate. With the most usual convention the CZ gate adds a $\pi$ phase to the $|1⟩$ state of the controlled qubit only when the control qubit is also in $|1⟩$. To switch to this convention, you could sandwich your gate between Pauli X gates on both qubits, but honestly, it doesn't matter - it's a CZ gate up to relabelling of the qubits.
It also bears mention that CZ gates are arguably more common than CNOT gates, as it's generally easier to add phases than to perform well-controlled bit flips. From the Cirac-Zoller gate onwards, many (most?) proposed and implemented CNOT gates are, at heart, CZ gates sandwiched between Hadamard gates on the controlled qubit.
One more thing to keep in mind is that you should not call this a controlled-phase gate, since that usually refers to a controlled phase of $e^{i\pi/2}$, instead of a sign change.
A: If you absolutely have to decompose it into named gates then it looks like parallel Pauli x gates followed by a controlled Pauli z followed by parallel Pauli x gates again
