  We show that in the mathematical framework of the quantum theory the
classical pigeonhole principle can be violated more directly than previously
suggested, i.e., in a setting closer to the traditional statement of the
principle. We describe how the counterfactual reasoning of the paradox may be
operationally grounded in the analysis of the tiny footprints left in the
environment by the pigeons. After identifying the drawbacks of recent
experiments of the quantum pigeonhole effect, we argue that a definitive
experimental violation of the pigeonhole principle is still needed and propose
such an implementation using modern quantum computing hardware: a
superconducting circuit with transmon qubits.
