Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders.

Modern hybrid superconductor-semiconductor Josephson junction arrays are a promising platform for analog quantum simulations. Their controllable and nonsinusoidal energy-phase relation opens the path to implement nontrivial interactions and study the emergence of exotic quantum phase transitions. Here, we propose the analysis of an array of hybrid Josephson junctions defining a two-leg ladder geometry for the quantum simulation of the tricritical Ising phase transition. This transition provides the paradigmatic example of minimal conformal models beyond Ising criticality and its excitations are intimately related to Fibonacci non-Abelian anyons and topological order in two dimensions. We study this superconducting system and its thermodynamic phases based on bosonization and matrix-product-state techniques. Its effective continuous description in terms of a three-frequency sine-Gordon quantum field theory suggests the presence of the targeted tricritical point and the numerical simulations confirm this picture. Our results indicate which experimental observables can be adopted in realistic devices to probe the physics and the phase transitions of the model. Additionally, our proposal provides a useful one-dimensional building block to design exotic topological order in two-dimensional scalable Josephson junction arrays.

Electronic Transport in Double-Nanowire Superconducting Islands with Multiple Terminals.

We characterize in situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends suggest the presence of a subgap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals, and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.

Readout of Parafermionic States by Transport Measurements.

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.

Non-Abelian anions from degenerate landau levels of ultracold atoms in artificial gauge potentials.

We show that non-Abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-Abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: The non-Abelian part of the vector potential makes the Landau levels nondegenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-Abelian quantum Hall states appear: These ground states, including deformed Moore-Read states (characterized by Ising anyons as quasiholes), are studied for both fermionic and bosonic gases.

Topological quantum hashing with the icosahedral group.

We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/epsilon)), we can approximate all SU(2) matrices to an average error epsilon with a cost of O(log(1/epsilon)) in time. The algorithm is applicable to generic quantum compiling.