Related papers: Topological line in frustrated Toric code models
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"…
We investigate the $U(1)$ checkerboard toric code which corresponds to the $U(1)$-symmetry enriched toric code with two distinct star sublattices. One can therefore tune from the limit of isolated stars to the uniform system. The uniform…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
We investigate the impact of an isotropic antiferromagnetic Heisenberg perturbation on the toric code, focusing on the resulting quantum phase transition and the nature of the phase that emerges beyond topological order. Using…
We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…
The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit…
Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider…
We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on read-out. By transforming the system into a 1D transverse Ising model undergoing…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase…
The physical realization of $\mathbb Z_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms…
Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…
Topological phase transitions challenge conventional paradigms in many-body physics by separating phases that are locally indistinguishable yet globally distinct. Using a quantum simulator of interacting erbium atoms in an optical lattice,…
Simulation of quantum systems that provide intrinsically fault-tolerant quantum computation is shown to preserve fault tolerance. Errors committed in the course of simulation are eliminated by the natural error-correcting features of the…