Related papers: Encoding subshifts through sliding block codes
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We use the wrinkling theorem proven in Y. Eliashberg and N. Mishachev, "Wrinkling of smooth mappings and its applications - I", Invent. Math., 130(1997), 345-369, to fully describe the homotopy type of the space of S-immersions, i.e.…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
Superstring perturbation theory is traditionally carried out by using picture-changing operators (PCO's) to integrate over odd moduli. Naively the PCO's can be inserted anywhere on a string worldsheet, but actually a constraint must be…
Position encoding is the primary mechanism which induces notion of sequential order for input tokens in transformer architectures. Even though this formulation in the original transformer paper has yielded plausible performance for general…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…
We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden…
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…
The problem of when the vanishing of a (generalized) Schur complement of a block matrix (corresponding to the leading principal subblock) implies that the other (generalized) Schur complement (corresponding to the trailing principal…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in…
In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…
We study the protection of information in nearly critical topological quantum codes, constructed by perturbing topological stabilizer codes towards continuous quantum phase transitions. Our focus is on the transverse-field toric code…
We take the paradigm of interacting spin chains, the Heisenberg spin-$\frac{1}{2}$ XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An…
We consider tiles (dimers) each of which covers two vertices of a rectangular lattice. There is a normalized translation invariant weighting on the shape of the tiles. We study the pressure, p, or entropy, (one over the volume times the…
We propose a mechanism that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in…
Utilizing a shared embedding space, emerging multimodal models exhibit unprecedented zero-shot capabilities. However, the shared embedding space could lead to new vulnerabilities if different modalities can be misaligned. In this paper, we…
In this paper we develop a new approach to the investigation of the bi-partite entanglement entropy in integrable quantum spin chains. Our method employs the well-known replica trick, thus taking a replica version of the spin chain model as…
Electromagnetic slot models are employed to efficiently simulate electromagnetic penetration through openings in an otherwise closed electromagnetic scatterer. Such models, which incorporate varying assumptions about the geometry of the…
We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for…