Commits on May 22, 2024

1. Add DenseLayout trial to SabreLayout …

   Building on the work done in Qiskit#10829, Qiskit#10721, and Qiskit#12104 this commit adds
   a new trial to all runs of `SabreLayout` that runs the dense layout
   pass. In general the sabre layout algorithm starts from a random layout
   and then runs a routing algorithm to permute that layout virtually where
   swaps would be inserted to select a layout that would result in fewer
   swaps. As was discussed in Qiskit#10721 and Qiskit#10829 that random starting point
   is often not ideal especially for larger targets where the distance
   between qubits can be quite far. Especially when the circuit qubit count
   is low relative to the target's qubit count this can result it poor
   layouts as the distance between the qubits is too large. In qiskit we
   have an existing pass, `DenseLayout`, which tries to find the most
   densely connected n qubit subgraph of a connectivity graph. This
   algorithm necessarily will select a starting layout where the qubits are
   near each other and for those large backends where the random starting
   layout doesn't work well this can improve the output quality.
   
   As the overhead of `DenseLayout` is quite low and the core algorithm is
   written in rust already this commit adds a default trial that uses
   DenseLayout as a starting point on top of the random trials (and any
   input starting points). For example if the user specifies to run
   SabreLayout with 20 layout trials this will run 20 random trials and
   one trial with `DenseLayout` as the starting point. This is all done
   directly in the sabre layout rust code for efficiency. The other
   difference between the standalone `DenseLayout` pass is that in the
   standalone pass a sparse matrix is built and a reverse Cuthill-McKee
   permutation is run on the densest subgraph qubits to pick the final
   layout. This permutation is skipped because in the case of Sabre's
   use of dense layout we're relying on the sabre algorithm to perform
   the permutation.
   
   Depends on: Qiskit#12104

   

   mtreinish committed May 22, 2024
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