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.
T owards optimal transport for quantum densities
6 Pith papers cite this work, alongside 2 external citations. Polarity classification is still indexing.
6
Pith papers citing it
2
external citations · external index
citation-role summary
background 1
citation-polarity summary
verdicts
UNVERDICTED 6roles
background 1polarities
background 1representative citing papers
A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
Two quantum Wasserstein distance definitions coincide for qubits with single-operator cost functions, implying the self-distance equals the Wigner-Yanase skew information.
Proves equalities among quantum Wasserstein distances obtained from optimizations over general versus separable bipartite states and shows relations to Uhlmann-Jozsa fidelity and superfidelity, including equality for qubits.
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.
citing papers explorer
-
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.
-
General method for obtaining the energy minimum of spin Hamiltonians for separable states
A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
-
Relations between different definitions of the quantum Wasserstein distance for qubits
Two quantum Wasserstein distance definitions coincide for qubits with single-operator cost functions, implying the self-distance equals the Wigner-Yanase skew information.
-
Quantum Wasserstein distance and its relation to several types of fidelities
Proves equalities among quantum Wasserstein distances obtained from optimizations over general versus separable bipartite states and shows relations to Uhlmann-Jozsa fidelity and superfidelity, including equality for qubits.
-
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.
-
Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.