49 citations · 133 across the 8 of their papers we have counts for
8 papers
Improved Error Bounds for the Adiabatic Approximation
Donny Cheung, Peter Hoyer, Nathan Wiebe
Since the discovery of adiabatic quantum computing, a need has arisen for rigorously proven bounds for the error in the adiabatic approximation. We present in this paper, a rigorou…
Cellular Automata as a Model of Physical Systems
Donny Cheung, Carlos A. Perez-Delgado
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as…
On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography
Donny Cheung, Dmitri Maslov, Jimson Mathew +1
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over . We improve over earlier algorithms by cons…
Local Unitary Quantum Cellular Automata
Carlos A. Perez-Delgado, Donny Cheung
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute w…
Convex Separation from Optimization via Heuristics
Lawrence M. Ioannou, Benjamin C. Travaglione, Donny Cheung
Let be a full-dimensional convex subset of . We describe a new polynomial-time Turing reduction from the weak separation problem for to the weak optimization…
Models of Quantum Cellular Automata
Carlos A. Perez-Delgado, Donny Cheung
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with…