Track Sabre decay heuristic on physical qubits

The custom `decay` heuristic is supposed to penalise increases in depth
in the output.  The output space of qubits are the physical qubits, so
the depth is defined in relation to those.  Since its introduction in
Qiskitgh-4537, this heuristic has instead been tracking the depth on the
virtual qubits, which due to the swaps is not necessarily related to the
depth in the output.

Notably, this commit actually makes the depth for routing large
volumetric circuits slightly _worse_ on average (at least for heavy-hex
topologies).  This may be because the effect on the heuristic is
overweighted, or that the depth tracking resets after each gate is
routed (and occasionally in between) to be flat across all qubits,
rather than reflecting the actual depth each qubit is subject to.

crates/accelerate/src/sabre_swap/mod.rs

@@ -415,8 +415,8 @@ fn swap_map_trial(
                 qubits_decay.fill(1.);
                 num_search_steps = 0;
             } else {
-                qubits_decay[best_swap[0]] += DECAY_RATE;
-                qubits_decay[best_swap[1]] += DECAY_RATE;
+                qubits_decay[layout.logic_to_phys[best_swap[0]]] += DECAY_RATE;
+                qubits_decay[layout.logic_to_phys[best_swap[1]]] += DECAY_RATE;
             }
         }
         // If we exceeded the number of allowed attempts without successfully routing a node, we
@@ -735,7 +735,8 @@ fn choose_best_swap(
                     + EXTENDED_SET_WEIGHT * extended_set.score(swap, layout, dist)
             }
             Heuristic::Decay => {
-                qubits_decay[swap[0]].max(qubits_decay[swap[1]])
+                qubits_decay[layout.logic_to_phys[swap[0]]]
+                    .max(qubits_decay[layout.logic_to_phys[swap[1]]])
                     * (absolute_score
                         + layer.score(swap, layout, dist)
                         + EXTENDED_SET_WEIGHT * extended_set.score(swap, layout, dist))

releasenotes/notes/sabre-decay-physical-ad2f470cd45d69f3.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    The ``"decay"`` heuristic of :class:`.SabreSwap` and :class:`.SabreLayout` now tracks the depth
+    correctly on physical qubits rather than mistakenly tracking the "depth" of swaps on virtual
+    qubits.

test/python/transpiler/test_sabre_layout.py

@@ -60,7 +60,7 @@ def test_5q_circuit_20q_coupling(self):
         pass_.run(dag)
 
         layout = pass_.property_set["layout"]
-        self.assertEqual([layout[q] for q in circuit.qubits], [11, 10, 16, 5, 17])
+        self.assertEqual([layout[q] for q in circuit.qubits], [16, 7, 11, 12, 13])
 
     def test_6q_circuit_20q_coupling(self):
         """Test finds layout for 6q circuit on 20q device."""