We study long wave limits for general Schrodinger maps systems into Kahler manifolds with a constraining potential vanishing on a Lagrangian submanifold. We obtain KdV type systems set on the tangent space of the submanifold. Our general theory is applied to study the long wave limit of the Gross-Pitaevskii equation, a…
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8 results for “antiferromagnetic”
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities with noise can be captured as a special case of learning graphical models. This lea…
Paper explores limits of graph property testing in Ising models.
problem Understanding information-theoretic limits of graph property testing in Ising models.
method Combinatorial constructs and correlation-based tests.
result Property testing is more challenging for general Ising models than ferromagnets.
Algorithm learns RBMs with arbitrary external fields, improving on previous constraints.
problem Learning RBMs with arbitrary external fields, improving on previous constraints.
method Greedy algorithm that maximizes covariance between observed nodes sharing latent neighbors.
result Algorithm can learn RBMs with arbitrary external fields, improving on previous constraints.
Developed a message-passing algorithm for simulating nonstoquastic Hamiltonians in quantum annealing.
problem Challenges in simulating nonstoquastic Hamiltonians in quantum annealing.
method Message-passing algorithm using a time-dependent Hamiltonian.
result Validated the algorithm's performance through comparison to the replica method.
Develops quantum circuits for faster learning with symmetry considerations.
problem Speeding up learning quantum states with symmetry considerations.
method Utilizes Okounkov-Vershik approach and Young-Jucys-Murphy elements to develop -equivariant convolutional quantum circuits.
result Proves -CQA generates any unitary in any given irrep sector, universal for SU() symmetry.
New algorithm samples from Ising models efficiently, even with outliers.
problem Sampling from Ising models with general interaction matrices.
method Combines MCMC and variational inference techniques.
result First polynomial time sampling algorithms for low-rank Ising models.
GE-autoencoder identifies spontaneous symmetry breaking in systems.
problem Locating phase boundaries and identifying spontaneously broken symmetries in systems.
method Group-equivariant autoencoder using group theory to constrain parameters and learn invariant order parameters.
result GE-autoencoder accurately determines spontaneous symmetry breaking and estimates critical temperatures more efficiently.