# Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation

@article{Alagic2010ApproximatingT3, title={Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation}, author={Gorjan Alagic and Stephen P. Jordan and Robert K{\"o}nig and Ben Reichardt}, journal={Physical Review A}, year={2010} }

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-D topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently… Expand

#### 12 Citations

Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit

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It is shown that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). Expand

Possible universal quantum algorithms for generalized Turaev-Viro invariants

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An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum… Expand

Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups

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It is proved that, for groups which satisfy certain properties, the probability of success of any randomized computation can be approximated to within any $${\varepsilon}$$ε by the plat closure, and the question of simulating anyonic computation in groups uniformly as a function of the group size is made partial progress. Expand

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

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- 2017

A bstractWe apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional… Expand

Algorithms and Complexity for Turaev-Viro Invariants

- Computer Science
- ICALP
- 2015

The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds, but current algorithms to compute them require exponential time. Expand

Ja n 20 17 ( 3 + 1 ) – dimensional topological phases and self – dual quantum geometries encoded on Heegard surfaces

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We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)– dimensional topological quantum field theories to state spaces and operators for a (3 + 1)– dimensional TQFT… Expand

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- Quantum Inf. Comput.
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It is shown how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. Expand

QUANTUM DISCORD AND QUANTUM COMPUTING — AN APPRAISAL

- Computer Science, Physics
- 2011

Emphasis is placed on the "power of one qubit" model, and the boundary between quantum and classical correlations as delineated by quantum discord, and a recent result by Eastin on the role of this boundary in the efficient classical simulation of quantum computation is discussed. Expand

Institute for Quantum Information Findings – 2009-10

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Partial-indistinguishability obfuscation using braids

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A new notion of obfuscation is proposed, which is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions, and can be met by polynomial-time algorithms. Expand

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