We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first-and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.

Summary The C ++ library HOPS (Highly-Optimized Polytope Sampling) provides implementations of efficient and scalable algorithms for sampling convex-constrained models that are equipped with arbitrary target functions. For uniform sampling, substantial performance gains were achieved compared to the state-of-the-art. The ease of integration and utility of non-uniform sampling is showcased in a Bayesian inference setting, demonstrating how HOPS interoperates with third-party software. Availability and Implementation Source code is available at https://github.com/modsim/hops/, tested on Linux and MS Windows, includes unit tests, detailed documentation, example applications, and a Dockerfile. Supplementary information Supplementary data are available at Bioinformatics online.

Summary Random flux sampling is a powerful tool for the constraint-based analysis of metabolic networks. The most efficient sampling method relies on a rounding transform of the constraint polytope, but no available rounding implementation can round all relevant models. By removing redundant polytope constraints on the go, PolyRound simplifies the numerical problem and rounds all the 108 models in the BiGG database without parameter tuning, compared to about 50% for the state-of-the-art implementation. Availability The implementation is available on gitlab: https://gitlab.com/csb.ethz/PolyRound Supplementary information Supplementary data are available at Bioinformatics online.