Speaker
Description
Tensor networks offer efficient representations of high-dimensional objects and are widely used in quantum many-body physics, optimization, and machine learning. This seminar explores how tensor-network techniques constructions can be applied to a range of combinatorial problems. First, it presents an implementation of Schnorr’s algorithm for RSA integer factorization, using tensor networks to obtain approximate solutions to a collection of closest-vector problem instances; the method is demonstrated by factoring semiprimes of up to 100 bits. The second part develops a quantum-computational framework for equational reasoning, where equivalence classes of symbolic expressions are represented as ground states of suitable Hamiltonians. This framework supports the solution of the word problem, the enumeration of equivalent expressions, and the analysis of equivalence-class structure. The seminar concludes with an application to maximally compact polymers, encoding ensembles of Hamiltonian cycles on two-dimensional lattices in the amplitudes of a quantum state to estimate thermodynamic quantities, with potential applications to simplified descriptions of protein folding and soft-matter systems.