Trilinos is a community-developed, open-source software framework that facilitates building large-scale, complex, multiscale, multiphysics simulation code bases for scientific and engineering problems. Since the Trilinos framework has undergone substantial changes to support new applications and new hardware architectures, this document is an update to “An Overview of the Trilinos project” by Heroux et al. (ACM Transactions on Mathematical Software, 31(3):397–423, 2005). It describes the design of Trilinos, introduces its new organization in product areas, and highlights established and new features available in Trilinos. Particular focus is put on the modernized software stack based on the Kokkos ecosystem to deliver performance portability across heterogeneous hardware architectures. This article also outlines the organization of the Trilinos community and the contribution model to help onboard interested users and contributors.

We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class. We then provide a complete characterization of quantum channels T that are universally image additive in the sense that for any quantum channel S, the image of T ⊗ S is the convex hull of the tensor product of the images of T and S. These channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical-quantum channels.

Quantum memories can be regarded as quantum channels that transmit information through time without moving it through space. Aiming at a reliable storage of information, we may thus not only encode at the beginning and decode at the end, but also intervene during the transmission-a possibility not captured by the ordinary capacities in quantum Shannon theory. In this paper, we introduce capacities that take this possibility into account and study them, in particular, for the transmission of quantum information via dynamical semigroups of Lindblad form. When the evolution is subdivided and supplemented by additional continuous semigroups acting on arbitrary block sizes, we show that the capacity of the ideal channel can be obtained in all cases. If the supplementary evolution is reversible, however, this is no longer the case. Upper and lower bounds for this scenario are proven. Finally, we provide a continuous coding scheme and simple examples showing that adding a purely dissipative term to a Liouvillian can sometimes increase the quantum capacity.

We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any prescribed value of the entropy difference, both for quantum and classical systems. We outline implications for information theory and thermodynamics, such as a necessary condition for a process to be close to thermodynamic reversibility, or an easily computable lower bound on the classical channel capacity. Furthermore, we derive a tight upper bound, uniform for all states of a given dimension, on the variance of the surprisal, whose thermodynamic meaning is that of heat capacity.

Communication in multi- and many-core processors has long been a bottleneck to performance due to the high cost of long-distance electrical transmission. This difficulty has been partially remedied by architectural constructs such as caches and novel interconnect topologies, albeit at a steep cost in terms of complexity. Unfortunately, even these measures are rendered ineffective by certain kinds of communication, most notably scatter and gather operations that exhibit highly nonlocal data access patterns. Much work has gone into examining how the increased bandwidth density afforded by chip-scale silicon photonic interconnect technologies affects computing, but photonics have additional properties that can be leveraged to greatly accelerate performance and energy efficiency under such difficult loads. This paper describes a novel synchronized global photonic bus and system architecture called P-sync that uses photonics' distance independence to greatly improve performance on many important applications previously limited by electronic interconnect. The architecture is evaluated in the context of a non-local yet common application: the distributed Fast Fourier Transform. We show that it is possible to achieve high efficiency by tightly balancing computation and communication latency in P-sync and achieve upwards of a 6× performance increase on gather patterns, even when bandwidth is equalized.

In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero-error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.