We show that the space of density matrices for n-qubit states, considered as a (2)-dimensional real vector space, has a basis consisting of density matrices of stabilizer states. We describe an application of this result to automated verification of quantum protocols. 1 Definitions and Results We are working with the stabilizer formalism [5], in which certain quantum states on sets of qubits ar...

A local stabilizer protocol that takes any on-line or oo-line distributed algorithm and converts it into a synchronous self-stabilizing algorithm with local monitoring and repairing properties is presented. Whenever the self-stabilizing version enters an inconsistent state, the inconsistency is detected, in O(1) time, and the system state is repaired in a local manner. The expected computation ...

We give a geometric description of binary quantum stabilizer codes. In the case of distance d = 4 this leads to the notion of a quaternary quantum cap. We describe several recursive constructions for quantum caps, determine the quantum caps in PG(3, 4) and the cardinalities of quantum caps in PG(4, 4). ∗research partially supported NSA grant H98230-10-1-0159 †The research of this author takes p...

An explicit lattice realization of a non-Abelian topological memory is presented. The correspondence between logical and physical states is seen directly by use of the stabilizer formalism. The resilience of the encoded states against errors is studied and compared to that of other memories. A set of non-topological operations are proposed to manipulate the encoded states, resulting in universa...

Many economists believe that credit market distortions create a financial accelerator which destabilizes the economy. This paper shows that when credit market distortions arise from adverse selection they sometimes stabilize the economy rather than destabilize it. The stabilizing forces are closely related to forces that cause overinvestment in static models. When investment projects are equity...

v Abstract. The chemical stability tests currently used for propellants suffer from some drawback. In this paper an attempt has been made to recast the existing system of stability testing in order to improve the reliability factor. A new stability concept has also been brought out based on the action of the stabilizer and its derivatives with the decomposed products of the nitric esters, the c...

Formality, Informality, and Social Welfare An industry is modeled in which entrepreneurs, who are heterogeneous in ability, may produce formally or informally. It is shown how the formal-informal mix depends on the distribution of ability, product demand and various parameter values. The industry equilibrium is compared to one in which informality is prohibited. With relatively high product dem...

We show how to construct quantum stabilizer and subsystem codes from algebro-geometric toric codes extending the known construction of subsystem codes from cyclic codes and extending the construction of stabilizer codes from toric codes in an earlier work by one of the authors. Since algebrogeometric toric codes are higher dimensional extensions of cyclic codes, we obtain this way a new and ric...

This paper is motivated by the computer-generated nonadditive code described in Rains et al [RHSN97]. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. ...