arXiv subjects

James L. Ulrich

Publications and source records attributed to James L. Ulrich.

2 recordsLinked to original sources

arXiv2016

Posner computing: a quantum neural network model

We present a construction, rendered in Quipper, of a quantum algorithm which probabilistically computes a classical function from n bits to n bits. The construction is intended to be of interest primarily for the features of Quipper it highlights. However, intrigued by the utility of quantum information processing in the context of neural networks, we present the algorithm as a simplest example of a particular quantum neural network which we first define. As the definition is inspired by recent work of Fisher concerning possible quantum substrates to cognition, we precede it with a short description of that work.

quant-ph↗

arXiv2006

Ore revisited: an algorithmic investigation of the simple commutator promise problem

Motivated by a desire to test the security of the pubic key exchange protocol of I. Anshel, M. Anshel, and D. Goldfeld, (``An Algebraic Method for Public-Key Cryptography'', Mathematical Research Letters, vol. 6, pp. 1-5, 1999), we study algorithmic approaches to the simple commutator decision and promise problems (SCDP/SCPP) for the braid groups B_n. We take as our point of departure a seminal paper of O. Ore, (``Some Remarks on Commutators'', Proceedings of the American Mathematical Society, Vol. 2, No. 2, pp.307-314, 1951), which studies the SCPP for the symmetric groups. Our results build on the work of H. Cejtin and I. Rivin, (``A Property of Alternating Groups'', arXiv:math.GR/0303036).

math.GR↗