An interior-point method is introduced to compute dynamical quantum optimal transport geodesics on density matrices, shown to approximate some quantum chemistry problems after parameter tuning.
On Quantum Optimal Transport
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Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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An algorithm for dynamical quantum optimal transport with applications to quantum chemistry
An interior-point method is introduced to compute dynamical quantum optimal transport geodesics on density matrices, shown to approximate some quantum chemistry problems after parameter tuning.
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.