Solving the Vehicle Routing Problem (VRP) in Stochastic Transportation Networks (STNs), a core task in Intelligent Transportation Systems (ITS), introduces estimation challenges for stochastic path travel times and the resulting VRP objective function. These challenges have typically been addressed through computationally expensive sampling-based techniques such as Monte Carlo simulation, whose performance depends on sample size, the sampling strategy, and the underlying travel time distributions. To address these issues, this study proposes and validates a quantum computing technique, Quantum Amplitude Estimation (QAE) for path-level travel time estimation in STNs. Without relying on sampling or prior assumptions of the travel time distribution, the proposed framework encodes all feasible travel time realizations into a quantum superposition, enabling a theoretical quadratic speed-up over Monte Carlo simulation. Four QAE variants are implemented in IBM's Qiskit framework, namely Canonical AE (CAE), Iterative AE (IAE), Maximum Likelihood AE (MLAE), and Faster AE (FAE), together with four rotation-angle scaling strategies for handling different discrete travel time distributions. Experiments on a small-scale STN show that the choice of scaling method and rotation-angle range significantly affects estimation accuracy, while the four QAE variants produce comparable estimates across all tested conditions, with IAE exhibiting the most stable overall performance. The results provide practical guidance on parameter selection for future hybrid quantum-classical optimization frameworks in ITS applications.Solving the Vehicle Routing Problem (VRP) in Stochastic Transportation Networks (STNs), a core task in Intelligent Transportation Systems (ITS), introduces estimation challenges for stochastic path travel times and the resulting VRP objective function. These challenges have typically been addressed through computationally expensive sampling-based techniques such as Monte Carlo simulation, whose performance depends on sample size, the sampling strategy, and the underlying travel time distributions. To address these issues, this study proposes and validates a quantum computing technique, Quantum Amplitude Estimation (QAE) for path-level travel time estimation in STNs. Without relying on sampling or prior assumptions of the travel time distribution, the proposed framework encodes all feasible travel time realizations into a quantum superposition, enabling a theoretical quadratic speed-up over Monte Carlo simulation. Four QAE variants are implemented in IBM's Qiskit framework, namely Canonical AE (CAE), Iterative AE (IAE), Maximum Likelihood AE (MLAE), and Faster AE (FAE), together with four rotation-angle scaling strategies for handling different discrete travel time distributions. Experiments on a small-scale STN show that the choice of scaling method and rotation-angle range significantly affects estimation accuracy, while the four QAE variants produce comparable estimates across all tested conditions, with IAE exhibiting the most stable overall performance. The results provide practical guidance on parameter selection for future hybrid quantum-classical optimization frameworks in ITS applications.

quant-pharXiv:2608.06145Aug 7, 20260 citations

Quantum Optimal Transport Amplitude Method (QOTAM)

Fidele Twagirayezu

We propose the _Quantum Optimal Transport Amplitude Method_ (QOTAM), a new framework in which scattering amplitudes arise from a complex optimal-transport problem on on-shell kinematic space. Incoming and outgoing wavepackets define probability distributions, and we introduce a complex kernel $K(q|p)$ whose modulus squared transports $\rho_{\rm in}$ to $\rho_{\rm out}$ while its phase encodes the classical action. The physical amplitude is obtained from the variational principle $\delta\mathcal{S}[K]=0$ , where $\mathcal{S}[K]$ includes a transport cost, an $iS_{\rm cl}/\hbar$ phase term, and regularizers enforcing locality and factorization. Tree amplitudes emerge from linear response of the optimal kernel, and the formulation admits efficient numerical realization via entropically regularized optimal transport. QOTAM offers a geometric–variational approach to scattering with potential applications to high-multiplicity and non-perturbative regimes.We propose the _Quantum Optimal Transport Amplitude Method_ (QOTAM), a new framework in which scattering amplitudes arise from a complex optimal-transport problem on on-shell kinematic space. Incoming and outgoing wavepackets define probability distributions, and we introduce a complex kernel $K(q|p)$ whose modulus squared transports $\rho_{\rm in}$ to $\rho_{\rm out}$ while its phase encodes the classical action. The physical amplitude is obtained from the variational principle $\delta\mathcal{S}[K]=0$, where $\mathcal{S}[K]$ includes a transport cost, an $iS_{\rm cl}/\hbar$ phase term, and regularizers enforcing locality and factorization. Tree amplitudes emerge from linear response of the optimal kernel, and the formulation admits efficient numerical realization via entropically regularized optimal transport. QOTAM offers a geometric–variational approach to scattering with potential applications to high-multiplicity and non-perturbative regimes.

QeiosNov 21, 20251 citation

Quantum Entropies and Their Maximizations

Masanori Ohya

Springer eBooksJan 1, 19930 citations

K(q|p)

whose modulus squared transports

\rho_{\rm in}

\rho_{\rm out}

while its phase encodes the classical action. The physical amplitude is obtained from the variational principle

\delta\mathcal{S}[K]=0

, where

\mathcal{S}[K]

includes a transport cost, an

iS_{\rm cl}/\hbar

phase term, and regularizers enforcing locality and factorization. Tree amplitudes emerge from linear response of the optimal kernel, and the formulation admits efficient numerical realization via entropically regularized optimal transport. QOTAM offers a geometric–variational approach to scattering with potential applications to high-multiplicity and non-perturbative regimes.