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The direct compilation of algorithm-specific graph states in measurement-based quantum computation (MBQC) can lead to resource reductions in terms of circuit depth, entangling gates, and even the number of physical qubits. In this work, we…
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…
Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…
Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing…
We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically…
The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However the question of how to obtain and process information about what errors have occurred in order to negate their effects has not…
We consider a lattice of $d=6$ qudits that supports $\mathbf{D}(\mathbf{S}_3)$ non-Abelian anyons. We present a method for implementing both braiding and fusion evolutions using only the operators that create and measure anyons, without…
The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in…
A theoretical spin-based scheme for performing a variety of quantum computations is presented. It makes use of an array of multiple identical computer vectors of phosphorus-doped silicon where the nuclei serve as logical qubits and the…
Color-code quantum computation seamlessly combines Majorana-based hardware with topological error correction. Specifically, as Clifford gates are transversal in two-dimensional color codes, they enable the use of the Majoranas' nonabelian…
Braiding of Majorana fermions gives accurate topological quantum operations that are intrinsically robust to noise and imperfection, providing a natural method to realize fault-tolerant quantum information processing. Unfortunately, it is…
Recent advances in quantum hardware and quantum error correction (QEC) have set the stage for early demonstrations of fault-tolerant quantum computing (FTQC). A key near-term goal is to build a system capable of executing millions of…
This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…
Coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in…
Fast entangling gate operations are a fundamental prerequisite for quantum simulation and computation. We propose an entangling scheme for arbitrary pairs of ions in a linear crystal, harnessing the high electric polarizability of highly…