Basis is for this post ist the paper https://arxiv.org/pdf/1902.00445.pdf
I want to do something similar using graph data encoded in quantum states. The circuit structure should look like this (first Grover iteration incl. the oracle):
GDBstands for a "Graph-Database", meaning a QRAM so that the qubits $|Graph\rangle$ encode some kind of graph in
mqubits. These states represent the adjacency matrix and the edge weights.
- $|\psi_1\rangle$ (see the red vertical line) looks like (assuming
n=2so 4 different graphs):
- $GDB^\dagger$ uncomputes the Graph-Database and the gate
Groverstands for the usual "inversion about average"
- The big "marking"-gate in middle is my question mark! Let me skip that for now.
- The entire algorithm involves more than one iteration to update the threshold used in the marking-gate accordingly (see the paper). Finally, the
Indexof the graph that satisfies some kind of maximum or minimum requirement among all graphs should be measured with high probability, as usual in the amplitude amplification algorithm (Grover).
Now the actual question is a bit strange, I admit. Can anyone image a graph-related problem where such a circuit could be useful, that is, what exactly could I do in the marking-gate? Any suggestion is welcome. It may be far from a real usecase. The key point is really to use the graph-encoding.
There are, of course, a number of "workspace" qubits that are not shown in the circuit above.