19 papers · ranked by Valyu relevance
Christopher Chamberland, Guanyu Zhu, Theodore J. Yoder, Jared Hertzberg + 1 more
'Jared Hertzberg' 'Andrew W. Cross'] In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such a layout is particularly suitable for…
Debasmita Bhoumik, Ritajit Majumdar, Dhiraj Madan, Dhinakaran Vinayagamurthy + 2 more
'Dhinakaran Vinayagamurthy' 'Shesha Raghunathan' 'Susmita Sur‐Kolay'] Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be efficiently…
Umesh Uttamrao Shinde, Ravikumar Bandaru
The error correction model’s main purpose in heavy hexagonal quantum codes is to improve their reliability for quantum computing applications. Existing challenges include finding the optimal decoder for quantum error correction in heavy hexagonal codes. This research propels the frontier of quantum error correction…
C. Benito, Esperanza López, Borja Peropadre, A. Bermúdez
heavy-hexagonal lattice Authors: ['C. Benito' 'Esperanza López' 'Borja Peropadre' 'A. Bermúdez'] Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The…
Umesh Uttamrao Shinde, Ravikumar Bandaru
Heavy hexagonal coding is a type of quantum error-correcting coding in which the edges and vertices of a low-degree graph are assigned auxiliary and physical qubits. While many topological code decoders have been presented, it is still difficult to construct the optimal decoder due to leakage errors and qubit…
James R. Wootton
Matching codes are stabilizer codes based on Kitaev's honeycomb lattice model. The hexagonal form of these codes are particularly well-suited to the heavy-hexagon device layouts currently pursued in the hardware of IBM Quantum. Here we show how the stabilizers of the code can be measured solely through the 2-body…
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…
R.G. Rebecca, Giorgio A. Ascoli, Nate M. Sutton, Holger Dannenberg
Spatial periodicity in grid cell firing has been interpreted as a neural metric for space providing animals with a coordinate system in navigating physical and mental spaces. However, the specific computational problem being solved by grid cells has remained elusive. Here, we provide mathematical proof that spatial…
Ben Sorscher, Gabriel C. Mel, Samuel A. Ocko, Lisa Giocomo + 1 more
The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might mechanistically emerge in a generic manner from neural circuits, and what their computational significance might be. Here we forge an intimate link between the computational problem of…
Vemund Schøyen, Constantin Bechkov, Markus Borud Pettersen, Erik Hermansen + 4 more
The brain’s ability to navigate is often attributed to spatial cells in the hippocampus and entorhinal cortex. Grid cells, found in the entorhinal cortex, are known for their hexagonal spatial activity patterns and are traditionally believed to be the neural basis for path integration. However, recent studies have cast…
Sangil Lee, Linda Q. Yu, Caryn Lerman, Joseph W. Kable
Across many studies, ventromedial prefrontal cortex (vmPFC) activity has been found to correlate with subjective value during value-based decision-making. Recently, however, vmPFC has also been shown to reflect a hexagonal gridlike code during navigation through physical and conceptual space. This raises the…
Samir F. Matar, Vladimir L. Solozhenko
Based on superdense C6 with quartz (qtz) topology, new ultrahigh-density hexagonal binary phases, qtz BN and qtz SiC, have been identified from full geometry structure relaxations and ground state energies using calculations based on the quantum density functional theory (DFT) with gradient GGA exchange-correlation XC…
Bo Zhang, Jia Liu
The phenomenon of neuronal replay, the sequential reactivation of hippocampal place cells for past experiences, have been proposed to organize learned knowledges into a cognitive map. Here we used the spin-glass model to simulate the formation of the hexagonal pattern of grid cells, the metric of cognitive map, when…
Dong Chen, Kai-Jia Sun, Liang Wang, Zhanjun Zhang + 3 more
Grid cells constitute a crucial component of the “GPS” in the mammalian brain. Recent experiments revealed that grid cell activity is anchored to environmental boundaries. More specifically, these results revealed a slight yet consistent offset of 8 degrees relative to boundaries of a square environment. The causes and…
Samir F. Matar, Vladimir L. Solozhenko
Hexagonal carbon allotropes C6, C9 and C12 with qtz, sta and lon topologies, respectively, were predicted on the basis of crystal chemistry and first principles (DFT) calculations. The new allotropes are mechanically (elastic properties) and dynamically (phonons) stable phases and are characterized by ultra-high…
Samir F. Matar, Vladimir L. Solozhenko
In the framework of a crystallochemical approach, new hexagonal (P63/mc) sp3-bonded BN polytypes (4H, 6H and 8H) and ternary BC2N were proposed by rationalized substitutions of C for B and N in hexagonal carbon allotrope C8 (4C carbon) with cfc topology, and density functional theory calculations of their ground states…
Martí Garçon, Andreas Phanopolous, George Sackman, Chris Richardson + 4 more
New heterometallic hydride complexes that involve the addition of {Mg–H} and {Zn–H} bonds to group 10 transition metals (Pd, Pt) are reported. The side-on coordination of a single {Mg–H} to Pd forms a well-defined σ-complex. In contrast, addition of three {Mg–H} or {Zn–H} bonds to Pd or Pt results in the formation of…
Sebastian Günther, Patrick Zeller, Bernhard Böller, Joost Wintterlin
A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer-based analyses are required. The lattice vector of…
Sam Coates, Ron Lifshitz, Akihisa Koga, R. McGrath + 2 more
'Ryuji Tamura'] Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting…