Gauge color codes in two dimensions

We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes where gauge fixing through local measurements dynamically determines which gates are transversal. Although the operations are local, the underlying code is not topological in structure, which is how the construction circumvents no-go constraints imposed by the Bravyi-K\"onig and Pastawski-Yoshida theorems. We provide strong evidence that the encoding has no error threshold in the conventional sense, though it is still possible to have logical gates with error probability much lower than that of physical gates.Comment: 15 pages, 9 figure

Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization

We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal observables. We review the concept of an entanglement witness from the geometrical point of view and use this geometry to show that the set of separable states is not a polytope and to characterize the class of entanglement witnesses (observables) that detect entangled states on opposite sides of the set of separable states. All this serves to motivate a classical algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. The idea of such an algorithm, which is an efficient reduction of the quantum separability problem to a global optimization problem, was introduced in PRA 70 060303(R), where it was shown to be an improvement on the naive approach for the quantum separability problem (exhaustive search for a decomposition of the given state into a convex combination of separable states). The last section of the paper discusses in more generality such algorithms, which, in our case, assume a subroutine that computes the global maximum of a real function of several variables. Despite this, we anticipate that such algorithms will perform sufficiently well on small instances that they will render a feasible test for separability in some cases of interest (e.g. in 3-by-3 dimensional systems)

09421 Abstracts Collection -- Algebraic Methods in Computational Complexity

From 11.10. to 16.10.2009, the Dagstuhl Seminar 09421 ``Algebraic Methods in Computational Complexity \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Delay-Coordinates Embeddings as a Data Mining Tool for Denoising Speech Signals

In this paper we utilize techniques from the theory of non-linear dynamical systems to define a notion of embedding threshold estimators. More specifically we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We describe a particular variation of the embedding threshold estimator implemented in a windowed Fourier frame, and we apply it to speech signals heavily corrupted with the addition of several types of white noise. Our experimental work seems to suggest that, after training on the data sets of interest,these estimators perform well for a variety of white noise processes and noise intensity levels. The method is compared, for the case of Gaussian white noise, to a block thresholding estimator