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Braiding Operators are Universal Quantum Gates

Louis Hirsch Kauffman, Samuel J. Lomonaco

This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution, R, of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution, R, of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.

Jan 1, 2004183 citations

Quantum teleportation and its applications

Akira Furusawa

I will briefly introduce the concept of quantum entanglement and quantum teleportation.Moreover, I will show their applications.

Journal of the Visualization Society of JapanJan 1, 20070 citations

Braiding operators are universal quantum gates

Louis H Kauffman, Samuel J Lomonaco

This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots and links. Other solutions of the Yang–Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots and links. Other solutions of the Yang–Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.

arXiv:quant-ph/0401090New Journal of PhysicsOct 20, 2004176 citations

Quantum teleportation on generic Hilbert spaces and in optics

Mátyás Koniorczyk

Jan 1, 20031 citation

Онтология на квантовата информация

Васил Пенчев

The article is devoted to quantum information (including its subdomains, namely: quantum communication, quantum computer, quantum cryptography), and its philosophical meaning. Paradox EPR, Bell’s inequality, phenomena of teleportation are discussed of a philosophical point of view. Quantum mechanical nonlocal correlations are interpreted as topological inseparabilities. Information is considered both as a fundamental physical quantity and as a philosophical category.

Jan 1, 20050 citations

Teleportation of Quantum Entanglement(Current Topic)

Akira Furusawa

ButsuriDec 5, 20050 citations

Teleportation topology

Abstract

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Teleportation topology

Abstract

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