相关论文: Protocols for Creating Anyons and Defects via Gaug…
One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have…
Circuits can provide a platform to study novel physics and have been used, for example, to explore various topological phases. Gauge fields-particularly, non-Abelian gauge fields-can play a pivotal role in the design and modulation of novel…
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…
We demonstrate the semiclassical nature of symmetry twist defects that differ from quantum deconfined anyons in a true topological phase by examining non-abelian crystalline defects in an abelian lattice model. An underlying non-dynamical…
We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum…
We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are…
For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to…
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…
The macroscopic theory of anyon condensation, rooted in the categorical structure of topological excitations, provides a complete classification of gapped boundaries in topologically ordered systems, where distinct boundaries correspond to…
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to…
We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with…
In this work we present a proposal for realising non-Abelian anyons on a NISQ device. In particular we explore the feasibility of implementing the quantum double model $D(D_4)$. We propose techniques to drastically simplify the circuits for…
We present a new scheme to perform noise resilient universal adiabatic quantum computation using two-body interactions. To achieve this, we introduce a new family of error detecting subsystem codes whose gauge generators and a set of their…
Wire cutting is a technique for partitioning large quantum circuits into smaller subcircuits in such a way that observables for the original circuits can be estimated from measurements on the smaller subcircuits. Such techniques provide…
A new non-Abelian gauge transformation for two-forms is introduced. Construction is based on a fixed map from the spacetime to the loop space which attachs a closed loop to each point of the spacetime. It is argued that this set-up is…
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has…
Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal…