k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Carlen and Jan Maas
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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.
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.
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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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 and divergences of order $p$ by quantum channels
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
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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.