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The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification has been extended to the setting of Adaptive Finite-Depth…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
An accurate description of the low-energy electronic bands in twisted bilayer graphene (tBLG) is of great interest due to their relation to correlated electron phases, such as superconductivity and Mott-insulator behavior at half-filling.…
Anyons are quasiparticles with fractional statistics, bridging between fermions and bosons. We propose an experimental setup to measure the statistical angle of topological anyons emitted from a quantum point contact (QPC) source. The setup…
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…
We describe a method for engineering local $k+1$-body interactions ($k=1,2,3$) from two-body couplings in spin-${1}{2}$ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting…
We propose experimental schemes to create and probe minimum forms of different topologically ordered states in a plaquette of an optical lattice: Resonating Valence Bond, Laughlin and string-net condensed states. We show how to create…
The possibility to engineer artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of…
Fewer-qubit quantum logic gate, serving as a basic unit for constructing universal multiqubit gates, has been widely applied in quantum computing and quantum information. However, traditional constructions for fewer-qubit gates often…
The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained…
Quantum simulations of non-Abelian gauge theories require efficient mappings onto quantum computers and practical state preparation and measurement procedures. A truncation of the Hilbert space of non-Abelian lattice gauge theories with…
We recently proposed quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions [Phys. Rev. Lett. 125, 030504 (2020)]. Conceptually, the scheme is based on the idea that aphysical monolayer optical…
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not…
Non-Abelian anyons, which correspond to collective excitations possessing multiple fusion channels and noncommuting braiding statistics, serve as the fundamental constituents for topological quantum computation. Here, we reveal the exotic…
We propose to realize Majorana edge and corner states in electric circuits. First, we simulate the Kitaev model by an LC electric circuit and the $p_{x}+ip_{y}$ model by an LC circuit together with operational amplifiers. Zero-energy edge…
Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of…
We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one…
A defining feature of topologically ordered states of matter is the existence of locally indistinguishable states on spaces with non-trivial topology. These degenerate states form a representation of the mapping class group (MCG) of the…
Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature are topologically protected gates generated through braiding of Majorana bound states. However, braiding…
The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a…