Theory of Change

Horizon 2045 (H2045) is a 25-year initiative to end the nuclear weapons century. We urgently need to manage the intertwined existential risks of the Anthropocene—the geological era that began with the 1945 Trinity Test and is characterized by humankind’s newfound capacity to destroy itself along with all life on the planet. Recent research has shown that concerns about existential threats have become palpable, as has the desire to solve human-made problems and move to a brighter future. This offers an important opportunity: By considering nuclear weapons in the context of other dangers, we can dismantle conventional wisdom that nuclear weapons are tools for maintaining global stability, drawing new energy to the effort to rid ourselves of them. What makes H2045 unique is that we bring a new theory of change. Rather than centering solely on nuclear weapons, our theory of change creates common ground for organizations and thought leaders who share our vision: Humanity can, and will, move beyond the existential challenges we now face. By shifting our sole focus from nuclear challenges to a broader conception of global security, we increase the surface area for collaboration and shared learning. In so doing, we lay the groundwork for a much larger-scale effort. This document is an invitation to think with us. It is the product of a collaborative effort. It is a snapshot of a work in process. It raises more questions than it answers. It is intended to shake the current paradigm. It uses speculative techniques to bring alternate futures to life. It may cause discomfort. It may cause inspiration. We think this kind of work is important in shaping debates, changing narratives, and provoking change. We invite you to use this document as a jumping off point for thinking big and long term. It does not need to be read all at once. You may skip to the section that seems most intriguing and start there. What questions does it raise for you? What questions remain to be asked and answered? What answers might you have? There is a great deal that must be done. In our next phase we will be working to translate these insights into pragmatic solutions. Inspiration and vision light the way for that journey. H2045 will expand to include others in the development of a vision that inspires change.https://digitalcommons.risd.edu/cfc_projectsprograms_globalsecurity_horizon2045/1001/thumbnail.jp

Algorithms and Bounds for Very Strong Rainbow Coloring

A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in such a coloring is the strong rainbow connection number (\src(G)) of the graph. When proving upper bounds on \src(G), it is natural to prove that a coloring exists where, for \emph{every} shortest path between every pair of vertices in the graph, all edges of the path receive different colors. Therefore, we introduce and formally define this more restricted edge coloring number, which we call \emph{very strong rainbow connection number} (\vsrc(G)). In this paper, we give upper bounds on \vsrc(G) for several graph classes, some of which are tight. These immediately imply new upper bounds on \src(G) for these classes, showing that the study of \vsrc(G) enables meaningful progress on bounding \src(G). Then we study the complexity of the problem to compute \vsrc(G), particularly for graphs of bounded treewidth, and show this is an interesting problem in its own right. We prove that \vsrc(G) can be computed in polynomial time on cactus graphs; in contrast, this question is still open for \src(G). We also observe that deciding whether \vsrc(G) = k is fixed-parameter tractable in $k$ and the treewidth of $G$. Finally, on general graphs, we prove that there is no polynomial-time algorithm to decide whether \vsrc(G) \leq 3 nor to approximate \vsrc(G) within a factor $n^{1-\varepsilon}$, unless P$=$NP

After the A-Bomb

RISD’s Center for Complexity launches Horizon 2045, a 25-year project aimed at eliminating the threat of nuclear war.https://digitalcommons.risd.edu/cfc_projectsprograms_globalsecurity_horizon2045/1000/thumbnail.jp

Restricted Complexity, General Complexity

Why has the problematic of complexity appeared so late? And why would it be justified

Time complexity and gate complexity

We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version of t-QCT is also considered as optimality by sub-Riemannian geodesic length. The work has two aims: one is to develop a t-QCT itself based on physically natural concept of time, and the other is to pursue the possibility of using t-QCT as a tool to estimate the complexity in conventional gate-optimal quantum computation theory (g-QCT). In particular, we investigate to what extent is true the statement: time complexity is polynomial in the number of qubits if and only if so is gate complexity. In the analysis, we relate t-QCT and optimal control theory (OCT) through fidelity-optimal computation theory (f-QCT); f-QCT is equivalent to t-QCT in the limit of unit optimal fidelity, while it is formally similar to OCT. We then develop an efficient numerical scheme for f-QCT by modifying Krotov's method in OCT, which has monotonic convergence property. We implemented the scheme and obtained solutions of f-QCT and of t-QCT for the quantum Fourier transform and a unitary operator that does not have an apparent symmetry. The former has a polynomial gate complexity and the latter is expected to have exponential one because a series of generic unitary operators has a exponential gate complexity. The time complexity for the former is found to be linear in the number of qubits, which is understood naturally by the existence of an upper bound. The time complexity for the latter is exponential. Thus the both targets are examples satisfyng the statement above. The typical characteristics of the optimal Hamiltonians are symmetry under time-reversal and constancy of one-qubit operation, which are mathematically shown to hold in fairly general situations.Comment: 11 pages, 6 figure