Related papers: Quantum computing, Seifert surfaces and singular f…

Let $M$ be a connected, closed, oriented three-manifold and $K$, $L$ two rationally null-homologous oriented simple closed curves in $M$. We give an explicit algorithm for computing the linking number between $K$ and $L$ in terms of a…

We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and…

Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key…

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the…

We present here a theory and a computational tool, Silicon-{\sc Qnano}, to describe atomic scale quantum dots in Silicon. The methodology is applied to model dangling bond quantum dots (DBQDs) created on a passivated H:Si-(100)-(2$\times$1)…

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…

We present an economical dynamical control scheme to perform quantum computation on a one dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

We apply Dijkgraaf-Witten invariant over an semiproduct of abelian groups to show that, if the $k/\ell$-surgery along a knot $K$ results in a small Seifert 3-manifold with multiplicities $a_1,a_2,a_3$, then many constraints on…

We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…

In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev…

We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from…

Model calculations of nuclear properties are peformed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified…

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…

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…

The present work studies quantum and classical correlations in three qubits and four qubits general Bell states, produced by operating with braid operators on the computational basis of states. The analogies between the general three qubits…

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored…

We investigate the $\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\Lambda_n$, for every number $n$…

The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation…