Clustering in Hilbert space of a quantum optimization problem

Understand

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric.

• Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem.
• This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful.
• Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground state space which grow with the system size.