Search · four archives
Search · four archives
20 papers · ranked by Valyu relevance
da Silva, Eduardo Brandani, Brizola, Evandro Mazetto
In this work, we present new constructions for topological subsystem codes using semiregular Euclidean and hyperbolic tessellations. They give us new families of codes, and we also provide a new family of codes obtained through an already existing construction, due to Sarvepalli and Brown. We also prove new results…
Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley + 2 more
'Nathanan Tantivasadakarn' 'Dominic J. Williamson'] Abstract: We construct Pauli topological subsystem codes characterized by arbitrary twodimensional Abelian anyon theories – this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the…
Pradeep Kiran Sarvepalli, Kenneth R. Brown
Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs that satisfy certain constraints. Finding such hypergraphs and computing their…
Hiteshvi Manish Solanki, Pradeep Kiran Sarvepalli
Topological subsystem color codes (TSCCs) are an important class of topological subsystem codes that allow for syndrome measurement with only 2-body measurements. It is expected that such low complexity measurements can help in fault tolerance. While TSCCs have been studied over depolarizing noise model, their…
Vinuta V. Gayatri, Pradeep Kiran Sarvepalli
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some subsystem codes. Later Bravyi et al. proposed a subsystem surface code. Building upon…
Aleksander Kubica, Michael Vasmer
Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges. Here, we introduce a new topological…
Justyna Łodyga, Paweł Mazurek, Andrzej Grudka, Michał Horodecki
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical…
Hendrik Poulsen Nautrup, Nicolai Friis, Hans J. Briegel
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular…
Edson Donizete de Carvalho, Waldir Silva Soares Jr., Eduardo Brandani da Silva, Amin Sakzad + 1 more
'Eduardo Brandani da Silva' 'Amin Sakzad' 'Khoa Nguyen'] In this work, we show that an n-dimensional sublattice $Λ′=mΛ$ of an n-dimensional lattice $Λ$ induces a $G=Z_{m}^{n}$ tessellation in the flat torus $(T_{β′}=Rn/Λ′)$, where the group G is isomorphic to the lattice partition $(Λ/Λ′)$. As a consequence, we obtain…
Heejun Kim, Daniel C. McNamee, Nayeong Jeong, Sang Wan Lee
The brain navigates complex environments by combining entorhinal grid codes with hippocampal place codes. Although grid codes effectively represent a current environment’s geometry, their capacity to generalize across topologically analogous environments with different reward and state structures remains poorly…
Michael Vasmer, Dan E. Browne, Aleksander Kubica
We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting…
Felipe Coelho Argolo
Conant-Ashby’s (‘good regulator’) theorem states that a simple regulator of a system must behave as an image of it. Notably, evolutionary features present in living beings often mirror natural processes, yielding symmetries between biological structures and the external environment. For instance, nervous cells can…
Authors not listed
RNA molecules fold into complex three-dimensional structures that determine their function. A wide range of mathematical frameworks, such as chord diagrams, fatgraphs, and context-free grammars, have been used to represent these structures; however, these models have largely been developed from mathematical motivations…
Authors not listed
Because topology plays a key role in many chemical and physical properties of materials, identification of topology from crystalline structures is a common and important task in materials science. We present here a new web application, CrystalNets, whose user-friendly interface allows scientists to identify and…
Lihong Cao
The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While “Concept Cells” in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their…
Authors not listed
Topological band theory based on the variety of reciprocal space invariants provides an insightful framework for quantum material characterization in condensed matter physics. Its bulk-boundary correspondence principle has become a reliable tool for predicting Fermi level properties. Here, we investigate a recently…
Arnau Rodríguez-Rubio, Andrea Savoini, Florian Modicom, Patrick Butler + 1 more
As recognized in the early 1960s, catenanes composed of two achiral rings that are oriented (Cnh symmetry) as a result of the sequence of atoms they contain are topologically chiral. Here we present the first synthesis of a highly enantioenriched catenane containing a related but overlooked “co-conformationally…
Brittany Story, Biswajit Sadhu, Henry Adams, Aurora Clark
Recent work (J. Chem. Phys. 154, 114114) has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in $3N$-dimensions. This includes information about all transition paths between local minima (connected by critical points of index > 1), and…
Jun Kitazono, Ryota Kanai, Masafumi Oizumi
To understand the nature of the complex behavior of the brain, one important step is to identify “cores” in the brain network, where neurons or brain areas strongly interact with each other. Cores can be considered as essential sub-networks for brain functions. In the last few decades, an information-theoretic approach…
Zhenghong Chen
Persistent homology, building its foundation on homology theory, has been successfully applied various fields containing computation of topology. Here, we derive and implement persistent homology theory to specefic topological spaces with G-invariant covering, whereby persistence over quotient space can be canonically…