Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

Empirical Determination of Bang-Bang Operations

Strong and fast "bang-bang" (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for empirically determining the set of required BB pulses, that relies on quantum process tomography. In this manner an experimenter may tailor his or her BB pulses to the quantum system at hand, without having to assume a model Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum

Diverse perspectives on interdisciplinarity from the Members of the College of the Royal Society of Canada

Various multiple-disciplinary terms and concepts (although most commonly “interdisciplinarity”, which is used herein) are used to frame education, scholarship, research, and interactions within and outside academia. In principle, the premise of interdisciplinarity may appear to have many strengths; yet, the extent to which interdisciplinarity is embraced by the current generation of academics, the benefits and risks for doing so, and the barriers and facilitators to achieving interdisciplinarity represent inherent challenges. Much has been written on the topic of interdisciplinarity, but to our knowledge there have been few attempts to consider and present diverse perspectives from scholars, artists, and scientists in a cohesive manner. As a team of 57 members from the Canadian College of New Scholars, Artists, and Scientists of the Royal Society of Canada (the College) who self-identify as being engaged or interested in interdisciplinarity, we provide diverse intellectual, cultural, and social perspectives. The goal of this paper is to share our collective wisdom on this topic with the broader community and to stimulate discourse and debate on the merits and challenges associated with interdisciplinarity. Perhaps the clearest message emerging from this exercise is that working across established boundaries of scholarly communities is rewarding, necessary, and is more likely to result in impact. However, there are barriers that limit the ease with which this can occur (e.g., lack of institutional structures and funding to facilitate cross-disciplinary exploration). Occasionally, there can be significant risk associated with doing interdisciplinary work (e.g., lack of adequate measurement or recognition of work by disciplinary peers). Solving many of the world’s complex and pressing problems (e.g., climate change, sustainable agriculture, the burden of chronic disease, and aging populations) demand thinking and working across long-standing, but in some ways restrictive, academic boundaries. Academic institutions and key support structures, especially funding bodies, will play an important role in helping to realize what is readily apparent to all who contributed to this paper—that interdisciplinarity is essential for solving complex problems; it is the new norm. Failure to empower and encourage those doing this research will serve as a great impediment to training, knowledge, and addressing societal issues