Diagnosing Simulation and Hardware Barriers to Cross-Size Transfer in Equivariant Quantum Reinforcement Learning

Abstract

Equivariant quantum circuits (EQCs) parameterise reinforcement-learning policies for combinatorial optimisation with a size-independent parameter count, suggesting policies trained on small instances may transfer to larger ones. Whether such transfer survives realistic execution has not been measured end-to-end. We train EQC policies on Euclidean Travelling Salesman instances and evaluate identical checkpoints across statevector simulation, matrix-product-state simulation, noisy simulation, a protocol-matched noiseless emulator, and trapped-ion hardware. Within the validated regime, zero-shot five-to-ten-city transfer beats target-size training in all six evaluations. Beyond it, three barriers emerge: bond-dimension truncation destroys policy quality even without transfer; larger size jumps degrade performance consistently with a conditional diagnostic bound; and finite-shot execution inflates the transfer gap from $\sim 5\%$ to $31.3\%$ (sampling noise alone) to $45.3\%$ hardware), because action margins lie below the shot-noise floor and collapse as $n^{-2.1}$. A cross-platform campaign across four hardware vendors confirms the penalty is set by native two-qubit gate count and error mitigation, not shot budget. A shot-complexity bound formalises the obstruction. We claim no quantum advantage; we provide the diagnostic standard such claims should meet.

45 pages, 16 figures