Topological order in an exactly solvable 3D spin model
By Sergey Bravyi, Bernhard Leemhuis, Barbara M. Terhal. 2010
201 citations recorded by the source corpus.
Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on {Omega}(R{sup 2}) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such stringsmore » must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.« less
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/bf59f9006d63b2699fa92f4fd691b21ffc555249
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Fracton phases of matter (2020, background): “[7] Sergey Bravyi, Bernhard Leemhuis, and Barbara M.”
- Quantum memories at finite temperature (2014, methodology): “A similar model whose ground-state degeneracy depends on microscopic details (Bravyi et al., 2011b) is introduced by Chamon in Ref.”
- Fractons (2018, background): “[6] Sergey Bravyi, Bernhard Leemhuis, and Barbara M.”
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality (2016, background): “Thus far, two broad classes of fracton topological orders have been found: Type I fracton phases, such as the Chamon-BravyiLeemhuis-Terhal (CBLT) model [14,15] and the Majorana cubic model [18], have fracton excitations appearing at the corners of membrane operators; composites of fractons form topo”
- Local stabilizer codes in three dimensions without string logical operators (2011, methodology): “[15] Sergey Bravyi, Bernhard Leemhuis, and Barbara M.”
- Quantum error correction for quantum memories (2013, unknown): “tection. Various two-dimensional topological stabilizer codes will be discussed in Section III, while some 3D examples of topological codes are the Haah code (Bravyi and Haah, 2013), the Chamon code (Bravyi et al., 2011), the 3D toric code (Castelnovo and Chamon, 2008) and the 4D toric code (Dennis ”