Preference-Conditioned Reinforcement Learning for Noise-Aware Qubit Routing on Constrained Quantum Processors

Compiling a logical quantum circuit onto a processor with restricted qubit connectivity requires inserted SWAP operations, and on present-day hardware the cost of each insertion depends on which physical coupling carries it, on how much it lengthens the critical path and on how many two-qubit gates it adds. Routing heuristics minimise a single proxy, usually the SWAP count, and treat calibration data as an afterthought. This paper formulates routing as a Markov decision process whose reward is the negative increment of a scalarised cost over two-qubit gate count, two-qubit depth and an error-equivalent gate count computed from per-edge and per-qubit calibration data, and trains one proximal-policy-optimisation agent conditioned on the preference vector, so that the trade-off surface is reachable at compile time without retraining. The policy scores every coupling edge with a shared network and is therefore independent of processor size: a single agent trained on random circuits transfers to a 27-qubit heavy-hexagon lattice, a 16-qubit grid and a 16-qubit chain. The evaluation is deliberately strict: 40 quantum Fourier transform, Grover and random circuits, three topologies, 5 calibration snapshots, a noise-aware initial layout shared with every baseline, identical post-routing optimisation, paired Wilcoxon tests with Holm correction, and verification of every small output against the logical unitary. Against SABRE configured with its decay heuristic and 20 trials, the greedy-decoded agent routes with a median two-qubit gate count of +1.5% and a median estimated success probability of −0.5% (p = 0.61), i.e. parity rather than superiority, while outperforming the one-step heuristic built on the same features by +4.6% gates; sampling four decodes gives −1.2% depth and +0.3% ESP at equal gate count (p = 0.002). The preference vector changes the routing of 66% of configurations in the intended direction over a narrow range, and a density-matrix simulation of 1869 compiled circuits confirms that the error model used in the reward ranks circuits consistently with simulated fidelity (within-circuit Spearman rank correlation of 0.91). Two negative findings are reported: calibration features yield no measurable gain at a balanced preference, and the full Qiskit optimisation-level-3 pipeline remains 15.6% ahead on gate count through gate-level passes that routing cannot supply.