Research Directions and Foundations in Topological Quantum Computation Methods
نویسنده
چکیده
We give a short overview of the recent research perspectives and mathematical foundations in topological quantum computation theory. In particular, we will be interested in braid representation theory, topological invariants of braids, approximation with braiding generators and quantum hashing with the icosahedral group. Mathematics Subject Classification: 16T25; 20F36; 54H13; 57M25; 57M27; 81P68; 81P94; 94A60
منابع مشابه
Mathematical Foundations of Topological Quantum Computation
We explore the mathematical foundations of topological quantum computation, a quantum computation model that is based on principles of topology which as a result is more resistant to quantum decoherence than existing models. From the generalization of the topological basis for the two common particle exchange statistics, we explore the possibility of particles that exhibit arbitrary exchange st...
متن کاملDialogue Categories and Frobenius Monoids
Higher topological quantum field theory and categorical quantum mechanics
متن کاملar X iv : 0 70 4 . 22 41 v 1 [ qu an t - ph ] 1 8 A pr 2 00 7 Why should anyone care about computing with anyons ?
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behavior, and we establish their relation to quantum computation. Possible directions for the physical realization of topological syste...
متن کاملar X iv : 0 70 4 . 22 41 v 2 [ qu an t - ph ] 8 S ep 2 00 7 Why should anyone care about computing with anyons ?
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behavior, and we establish their relation to quantum computation. Possible directions for the physical realization of topological syste...
متن کاملNames of
This project developed new results in the topology and foundations of quantum algorithms. It made major developments in the program for topological quantum field computation, including the design of substantially simplified lattice models with topological phases, and new insights into the universality classes of such models. Lattice gas simulations of various classical and quantum systems were ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013