28 citations · 112 across the 11 of their papers we have counts for
11 papers
New efficient algorithm for the isometric embedding of 2-surface metrics in 3 dimensional Euclidean space
Wolfgang Tichy, Jonathan R. McDonald, Warner A. Miller
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve t…
Simplicial Ricci Flow
Warner A. Miller, Jonathan R. McDonald, Paul M. Alsing +2
We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the…
On exterior calculus and curvature in piecewise-flat manifolds
Jonathan R. McDonald, Warner A. Miller, Paul M. Alsing +3
Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex to…
Is the Measurement Based Quantum Computing Search Algorithm Really Grover's Algorithm?
A. Matthew Smith, P. M. Alsing, J. R. McDonald +1
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qua…
A geometric view of quantum cellular automata
Jonathan R. McDonald, Paul M. Alsing, Howard A. Blair
Nielsen, et al. [1, 2] proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of o…
Quantum computing in a piece of glass
Warner A. Miller, Grigoriy Kreymerman, Christopher Tison +2
Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use…