A quantum compiling algorithm is an algorithm for decomposing (“compiling”) an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose Uin is an NB-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For NB > 10, expressing Uin as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary ma...

An element u of a norm-unital Banach algebra A is said to be unitary if u is invertible in A and satisfies ‖u‖ = ‖u−1‖ = 1. The norm-unital Banach algebra A is called unitary if the convex hull of the set of its unitary elements is norm-dense in the closed unit ball of A . If X is a complex Hilbert space, then the algebra BL(X) of all bounded linear operators on X is unitary by the Russo–Dye th...

We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...

ESPRIT is a high-resolution signal parameter estimation technique based on the translational invariance structure of a sensor array. Previous ESPRIT algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary. Here, we present a simple and efficient method to constrain the estimated phase factors to the unit circle, if centro-symmetric arr...

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.

In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

In a recent preprint by Deutsch et al. 5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2-qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of g-qubit unitary operations for xed g. We consider approximation of unitary operations on subspaces as well as approximatio...

One can prove the following two propositions: (1) Let V be a real unitary space, A, B be finite subsets of V , and v be a vector of V . Suppose v ∈ Lin(A∪B) and v / ∈ Lin(B). Then there exists a vector w of V such that w ∈ A and w ∈ Lin(((A ∪ B) \ {w}) ∪ {v}). (2) Let V be a real unitary space and A, B be finite subsets of V . Suppose the unitary space structure of V = Lin(A) and B is linearly ...

In this correspondence, we propose some new designs of 2 2 unitary space-time codes of sizes 6; 32; 48; 64 with best known diversity products (or product distances) by partially using sphere packing theory. In particular, we present an optimal 2 2 unitary space-time code of size 6 in the sense that it reaches the maximal possible diversity product for 22 unitary space-time codes of size 6. The ...