We define a very general class of estimators for the conditional moment problem, which we term the variational method of moments (vmm), and provide conditions under which these are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model.
We additionally provide algorithms for valid statistical inference based on the same kind of variational reformulations, both for kernel-and neural-net-based varieties, and demonstrate the strong performance of our proposed estimation and inference algorithms in a detailed series of synthetic experiments.
Ground-state preparation for a given hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization.
We consider an approach to simulate dissipative non-hermitianhamiltonian quantum dynamics using hamiltonian simulation techniques to efficiently recover the ground state of a target hamiltonian.
Contrastive representation learning seeks to acquire useful representations by estimating the shared information between multiple views of data.
Here, the choice of data augmentation is sensitive to the quality of learned representations : as harder the data augmentations are applied, the views share more task-relevant information, but also task-irrelevant one that can hinder the generalization capability of representation.
We study in detail the consequences of constraining a quantum particle to a helix, catenary, helicoid, or catenoid, exploring the relations between these curves and surfaces using differential geometry.
Initially, we use the variationalmethod to estimate the energy of the particle in its ground state, and then, we obtain better approximations with the use of the confluent heun functionthrough numerical calculations.
We present a simple gradient-descent-based algorithm that can be used as an optimization subroutine in combination with imaginary time evolution, which by construction guarantees a monotonic decrease of the energy in each iteration step.
Using this result we find a closed expression for the energy functional and its gradientof a general fermionic quantum many-body hamiltonian.