Efficient inference in the transverse field Ising model

Abstract

In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories (paths). A key feature, novel in the context of similar algorithms, is the explicit separation of the classical and quantum parts of the distributions. Numerical simulations show accurate results in comparison with the sampled solution of the cavity equations, the exact diagonalization of the Hamiltonian (when possible) and other approximate inference methods in the literature. The computational complexity of this new algorithm scales linearly with the connectivity of the underlying lattice, enabling the study of highly connected networks, as the ones often encountered in quantum machine learning problems.

References in corpus (5)

• Quantum Boltzmann Machine
• Topological phases and quantum computation
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Cavity method for quantum spin glasses on the Bethe lattice
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited