FrancescoSlongo

The quadratic unconstrained binary optimization (QUBO) encoding makes it possible to sample classical many-body systems that are otherwise intractable for conventional Monte Carlo, specifically self-assembled melts of rigid lattice ring polymers, where high density, chain stiffness and topological constraints drive real-space autocorrelation times to diverge.

Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling cost with the size of the self-assembled ring melts. DOI: 10.1126/sciadv.adi0204 ↗

A general method for computing canonical averages of physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO), built on a histogram-reweighting scheme applicable to QUBO-based sampling restricted to specific intervals of an order parameter such as physical energy.

The scheme accurately recovers the density of states, in turn allowing expectation values to be computed in the conjugate ensemble (e.g. at fixed temperature) for systems otherwise intractable with real-space sampling. Applied to space-filling melts of lattice ring polymers mapped in QUBO form, the method reveals that the ring catenation probability is nonmonotonic with bending rigidity. DOI: 10.1103/PhysRevResearch.7.023116 ↗

A Monte Carlo method for studying topological entanglements in polymer melts, overcoming the computational limitations associated with equilibrium sampling of long polymer chains. The approach exploits a self-assembly ensemble and strictly local moves to efficiently propagate backbone reconnections across scales while preserving the number of linear chains, achieving near-linear scaling of the decorrelation time with system size.

Applied to fully-packed lattice melts, the method enables the equilibration of systems containing more than one billion monomers and provides access to the universal melt regime. The characterization of intra- and inter-chain entanglements reveals that they arise from localized knots and links rather than global tangles, with the Gauss linking integral between neighbouring chains growing only as N^1/4. DOI: 10.1038/s41467-026-74480-4 ↗