A Quantum Trophic Eigenspectrum Sampler for Ensemble Stability Certification of Ecological Food Webs

I present QTES, the Quantum Trophic Eigenspectrum Sampler, a quantum approach to ensemble level stability certification of ecological food webs. Classical assessment of May stability across a stochastic ensemble of community matrices costs work that grows linearly with the ensemble size. QTES reframes the task as a quantum marked ensemble search, where a stability oracle flags an unstable realization, amplitude amplification finds rare destabilizing configurations in about the square root of the ensemble size, and amplitude estimation returns the unstable fraction with improved precision over classical Monte Carlo. The primitives are established, so the contribution is their assembly for an application that has not been addressed, with one finding from the prototype. The natural oracle, which thresholds the dominant singular value, fails for ecological matrices, because the self regulation that stabilises a matrix also inflates its singular values. Over four hundred random matrices this proxy separates stable from unstable with a score of only 0.68, while the resolvent test reaches 0.90 using the same machinery. I ran the two quantum components on Amazon Braket SV1 at four to nine qubits with two thousand shots. Phase estimation recovers the dominant singular value to about 1.6 percent, Grover amplification agrees with theory within sampling error, and amplitude estimation recovers the unstable fraction to within about 0.0025. The asymptotic speedups are theoretical and inherit the standard assumptions of quantum Monte Carlo.