An element of a group acting on a graph is called invertor if it transfers an edge of the graph to its inverse. In this paper, we show that if G is a group acting on a tree X with inversions such that G does not fix any element of X, then an element g of G is invertor if and only if g is not in any vertex stabilizer of G and g2 is in an edge stabilizer of G. Moreover, if H is a finitely generat...

A subgroup H of a group G is called malnormal in G if it satisfies the condition that if g ∈G and h∈H, h≠ 1 such that ghg−1 ∈H, then g ∈H. In this paper, we show that if G is a group acting on a tree X with inversions such that each edge stabilizer is malnormal in G, then the centralizer C(g) of each nontrivial element g of G is in a vertex stabilizer if g is in that vertex stabilizer. If g is ...

In this Section we state some facts concerning stabilizer groups and stabilizer states. Let Pn be the n-qubit Pauli group. Any element of Pn has the form iP1⊗ · · · ⊗Pn, where each factor Pa is either the identity or a singlequbit Pauli operator X,Y, Z and m ∈ Z4. An abelian subgroup G ⊆ Pn is called a stabilizer group if −I / ∈ G. Each stabilizer group has the form G = 〈G1, . . . , Gr〉 for som...

This paper presents a systematic approach for the design of power system stabilizer using genetic algorithm and investigates the robustness of the GA based PSS. The proposed approach employs GA search for optimal setting of PSS parameters. The performance of the proposed GPSS under small and large disturbances, loading conditions and system parameters is tested. The eigenvalue analysis and nonl...

How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large, the state will be close to maximally entangled with probability exponentially close to 1. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code. Finally, we show that typically very few ...

Increasing interest has been seen in applying power system stabilizer to power systems problems from the number of publications on this topic in recent decade years. As a relatively new research topic a need is felt to pay more attention to the basic principles of the theory, identification of problems and design of Power System Stabilizer. This paper presents a survey of few decade publication...

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...

This paper presents an adaptive Power System Stabilizer (PSS) using an Adaptive Network Based Vague Inference System (ANVIS). An Adaptive Vague Set Based Controller Power System Stabilizer (AVCPSS) has been evaluated. This AVCPSS is capable of providing appropriate stabilization signals over a broad range of operating conditions and disturbances. A Vague Controller (VC) is synthesized by using ...