Related papers: Topological Quantum Programming in TED-K
The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern-Simons theory, which yields the so-called $\rm{SU}(2)_k$ anyon models that often appear in the context of…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation.…
Many quantum systems are being investigated in the hope of building a large-scale quantum computer. All of these systems suffer from decoherence, resulting in errors during the execution of quantum gates. Quantum error correction enables…
Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to infer the topology of a hypothetical manifold from which…
Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…
While the classification of non-interacting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases -- hence to phases with topologically ordered ground…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…
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"…
Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity.…
Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom…
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the…
Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can…
Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a…
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…