Related papers: Generating Ray Class Fields of Real Quadratic Fiel…
Large sets of equiangular lines are constructed from sets of mutually unbiased bases, over both the complex and the real numbers.
In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…
By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\geq3$.…
We propose a construction of $d^2$ complex equiangular lines in $\mathbb{C}^d$, also known as SICPOVMs, conjectured by Zauner to exist for all d. The construction gives a putatively complete list of SICs with Weyl-Heisenberg symmetry in all…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
Lagrangians for gauge fields and matter fields can be constructed from the infinite dimensional Kac-Moody algebra and group. A continuum regularization is used to obtain such generic lagrangians, which contain new nonlinear and asymmetric…
The paper presents a method to generate some families of linear codes over finite fields of characteristics greater than two in the widest class due to the size of Grassmann manifold, i.e. when the dimension is equal to codimension. Our…
This is a revised version of ANT-0045. If K is a number field of degree n with discriminant D, if K=Q(a) then H(a)>c(n)|D|^(1/(2n-2)) where H(a) is the height of the minimal polynomial of a. We ask if one can always find a generator a of K…
We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic…
A functioning quantum computer will be a machine that builds up, in a programmable way, nonclassical correlations in a multipartite quantum system. Linear optics quantum computation (LOQC) is an approach for achieving this function that…
We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…
$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
In this article we continue the investigation of the length of the narrow $2$-class field tower of real quadratic number fields $\mathrm{k}$ whose discriminants are not a sum of two squares and for which their $2$-class groups are…
We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude…
We study real hyperfields, focusing in particular on those that are finite with cyclic positive cones. All real hyperfields have characteristic zero, although they can still be classified using the C-characteristic, an invariant that…