Related papers: On Topological Quantum Computing With Mapping Clas…
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…
Ising-type non-Abelian anyons are likely to occur in a number of physical systems, including quantum Hall systems, where recent experiments support their existence. In general, non-Abelian anyons may be utilized to provide a topologically…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to…
We propose a construction of anyon systems associated to quantum tori with real multiplication and the embedding of quantum tori in AF algebras. These systems generalize the Fibonacci anyons, with weaker categorical properties, and are…
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many…
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity.…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
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…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
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…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these…
Superposed orders of quantum channels have already been proved - both theoretically and experimentally - to enable unparalleled opportunities in the quantum communication domain. As a matter of fact, superposition of orders can be exploited…