Related papers: Methods for simulating string-net states and anyon…

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…

We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold…

Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as…

Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high…

Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…

Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. The central challenge is how to encode a highly-complex quantum-many-body wave…

Topological boundary states exhibit distinctive properties, including unidirectional propagation and noise robustness, which hold significant potential for advancing the performance of quantum science and technology. Here, we demonstrate…

Anyons are particles obeying statistics of neither bosons nor fermions. Non-Abelian anyons, whose exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a great attention because of possible…

The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical"…

Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…

With the discovery of Majorana quasiparticles in semiconductor-superconductor hybrid structures, topologically protected qubits have emerged as a promising contender for quantum information processing. While the construction of a universal…

One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…

I propose that non-Abelian topological order can emerge from the organization of quantum particles into identical indistinguishable copies of the same quantum many-body state. Quantum indistinguishability (symmetrization) of the…

Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…

This work provides the first experimental elucidation of quantum topological effects in individual hopfions, establishing their potential as building blocks for three-dimensional topological quantum spintronics. The observed Non-Abelian…

Anyons have exotic statistical properties, fractional statistics, differing from Bosons and Fermions. They can be created as excitations of some Hamiltonian models. Here we present an experimental demonstration of anyonic fractional…

We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of a string tension. This competing term induces a nontrivial dynamics of the non-Abelian anyonic quasiparticles and may lead to a breakdown of the…

An important open question for the current generation of highly controllable quantum devices is understanding which phases can be realized as stable steady-states under local quantum dynamics. In this work, we show how robust steady-state…