Protected qubits and Chern-Simons theories in Josephson junction arrays

By B. Douçot, M. Feigel'man, L. Ioffe, A. Ioselevich. 2004

149 citations recorded by the source corpus.

We present general symmetry arguments that show the appearance of doubly degenerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special ${\mathbb{Z}}_{2}$ Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d8cf566f8f90dff2253eb062fa6f58874cd70090

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Citations in the corpus

Circuit QED: Superconducting Qubits Coupled to Microwave Photons (2015, background): “In particular, the possibility of topological protection (Kitaev, 2003; Ioffe and Feigelman, 2002; Ioffe et al., 2002; Doucot et al., 2003; Doucot et al., 2005) is beginning to be explored in superconducting qubits (Gladchenko et al.”
Artificial flat band systems: from lattice models to experiments (2018, background): “In two-dimensional systems, the suppression of single pair transport can be used to achieve superconducting qubits that are topologically protected from local noise by parity symmetry [105, 106].”
Non-Abelian Anyons and Topological Quantum Computation (2007, background): “Some possible current candidates are quasi-two dimensional chiral pwave superconductors such as Sr2RuO4, p-wave Feshbach resonance induced fermionic cold atom superfluids, ultra-cold atoms in optical lattices (possibly realizing the Kitaev model or extended Hubbard models), and Josephson junction ar”
Superconducting nanocircuits for topologically protected qubits (2008, background): “Recently, an alternative approach to qubit protection has been propose”