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Topological sensitivity in the diagonal compiler
The diagonal compiler included as part of #498 makes its choice of where to insert CNOTs based solely on most frequently sighted ZZ Pauli pairs. This has the benefit of producing low-CNOT-count circuits, but there's no reason to think that they're low-depth or that they do a good job of respecting chip topology.
Investigate this insertion strategy. Can it be modified to be topology-sensitive? Can it be modified to improve circuit depth rather than total CNOT count?
Here's a related paper that also makes use of certain Hamiltonians' large isotropy groups: https://arxiv.org/abs/2104.00728 .