Stochastic Hamiltonian Modulation of Energy-Marked Quantum States: An Ensemble-Based Numerical Assessment
Abstract
Abstract Noise-assisted quantum dynamics can produce useful transport and detection effects, but conclusions drawn from individual stochastic trajectories may not persist under ensemble averaging. We assess a closed-system model in which selected computational-basis states are assigned unit energy in a diagonal Hamiltonian and coupled by a transverse term whose scalar amplitude is independently sampled from a zero-mean Gaussian distribution at each timestep. Four configurations containing 2, 3, and 10 qubits were simulated using sparse exponential propagation. For each original parameter setting, 100 seeded trajectories were compared with zero-perturbation and constant-coupling controls. At the originally proposed weak perturbation strengths, none of the four configurations showed a statistically resolved increase in final marked-state population: all 95% confidence intervals included the uniform baseline. Perturbation-strength sweeps revealed configuration-dependent responses at larger amplitudes, including increased population for one three-qubit configuration, but no universal marked-state amplification or established stochastic-resonance regime. The marked set must also be supplied when constructing the Hamiltonian, so eliminating an explicit phase-oracle circuit does not eliminate its information-encoding role. These results recast the model as an exploratory study of stochastically modulated energy-marked dynamics rather than an oracle-free search algorithm. The work…
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