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Total: 51 results found.

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1. Simulations of quantum double models
(Uncategorized/Publication)
... of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations in a spin lattice model originally due to Kitaev to prepare a ground 'vacuum' state ...
2. Simulations of quantum double models
(Uncategorized/Publication)
... of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations in a spin lattice model originally due to Kitaev to prepare a ground 'vacuum' state ...
3. The entropic boundary law in BF theory
(Uncategorized/Publication)
We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, ...
We use a result of Y Furuta to show that for almost all positive integers m, the cyclotomic field Q(exp(2 pi i/m)) has an infinite Hilbert p-class field tower with high rank Galois groups at each step, ...
We give a lower bound on the size of the product set of two arbitrary subsets of the set of Farey fractions of a given order and apply it to study the distribution of elements of multiplicative groups ...
We study the confinement of low group velocity band-edge modes in a photonic crystal slab. We use a rigorous, three dimensional, finite-difference time-domain method to compute the electromagnetic properties ...
... depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local ...
... quantized, where two light fields are treated as quantum. In the semi-classical regime, the dispersive properties of the scheme are analyzed in detail, and the conditions leading to group velocity matching ...
For a positive integer n, we let phi(n) and lambda(n) denote the Euler function and the Carmichael function, respectively. We define xi(n) as the ratio phi(n)/lambda(n) and study various arithmetic properties ...
... order t in the multiplicative group Z(m)(*), gcd(a, m) = 1, S(x, y) is the set of y-smooth integers n  ...
... efficiency in generating large nonlinear cross-phase shifts compared. The dispersive properties of those schemes are analyzed in detail, and the conditions leading to group velocity matching for two of ...
We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous results. ...
Let p be a prime and 79 an integer of order t in the multiplicative group modulo p. In this paper, we continue the study of the distribution of Diffie-Hellman triples (V-x, V-y, V-xy) by considering the ...
14. On the bit security of the Diffie-Hellman key
(Uncategorized/Publication)
Let F-p be a finite field of p elements, where p is prime. The bit security of the Diffie-Hellman function over subgroups of F*(p) and of an elliptic curve over F-p, is considered. It is shown that if ...
... are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings. ...
... a slightly weaker form of this conjecture. Finally, we generalize our entanglement analysis to any unitary group. ...
We show that an algorithm of V. Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important ...
... of the unitary group is explicitly computable and allows for study of the monotone's dynamics. The side factors k(1) and k(2) of this concurrence canonical decomposition (CCD) are concurrence symmetries, ...
... and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (CCD) SU(2(n))=KAK. The group K fixes a bilinear form related to the ...
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