Related papers: Floquet codes with a twist
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example:…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
A topological insulator is regarded as an ideal candidate for information storage and high-speed lossless electrical transmission devices due to robust topological protected boundary modes. Previous studies revealed that symmetry exerts an…
We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach…
We derive the spectral domain properties of two-dimensional (2-D) $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_q$ using the 2-D finite field Fourier transform (FFFT). Based on the spectral nulls of 2-D $(\lambda_1,…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
The recently introduced Floquet codes have already inspired several follow up works in terms of theory and simulation. Here we report the first preliminary results on their experimental implementation, using IBM Quantum hardware.…
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating…
The surface code is a spin-1/2 lattice system that can exhibit non-trivial topological order when defects are punctured in the lattice and thus can be used as a stabiliser code. The protocols developed to create defects in the system have…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…
Spin qubits in semiconductor structures bring the promise of large-scale 2D integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic…
The dynamic engineering of band structures for ultracold atoms in optical lattices represents an innovative approach to understand and explore the fundamental principles of topological matter. In particular, the folded Floquet spectrum…
It has recently been realized that a general class of non-abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductor-ferromagnet domain walls in…
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…
We propose a new physical implementation of spin qubits for quantum information processing, namely defect states in antidot lattices defined in the two-dimensional electron gas at a semiconductor heterostructure. Calculations of the band…
Properties of time-periodic Hamiltonians can be exploited to increase the dephasing time of qubits and to design protected one and two-qubit gates. Recently, Huang et al. [Phys. Rev. Applied 15, 034065 (2021)] have shown that time-dependent…
Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem…
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by…