A class of anyonic models for universal quantum computation based on weakly-integral anyons has been recently proposed. While universal set of gates cannot be obtained in this context by anyon braiding alone, designing a certain type of sector charge measurement provides universality. In this paper we develop a compilation algorithm to approximate arbitrary $n$ -qutrit unitaries with asymptotically efficient circuits over the metaplectic anyon model. One flavor of our algorithm produces efficient circuits with upper complexity bound asymptotically in $O({3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and entanglement cost that is exponential in $n$ . Another flavor of the algorithm produces efficient circuits with upper complexity bound in $O(n\phantom{\rule{0.16em}{0ex}}{3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and no additional entanglement cost.A class of anyonic models for universal quantum computation based on weakly-integral anyons has been recently proposed. While universal set of gates cannot be obtained in this context by anyon braiding alone, designing a certain type of sector charge measurement provides universality. In this paper we develop a compilation algorithm to approximate arbitrary $n$-qutrit unitaries with asymptotically efficient circuits over the metaplectic anyon model. One flavor of our algorithm produces efficient circuits with upper complexity bound asymptotically in $O({3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and entanglement cost that is exponential in $n$. Another flavor of the algorithm produces efficient circuits with upper complexity bound in $O(n\phantom{\rule{0.16em}{0ex}}{3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and no additional entanglement cost.

arXiv:1504.03383Physical Review AJan 8, 201617 citations

Quantum Computation with Abelian Anyons

Seth Lloyd

arXiv:quant-ph/0004010Quantum Information ProcessingApr 1, 200281 citations

Fault-tolerant quantum computation by anyons

Alexei Kitaev

arXiv:quant-ph/9707021Annals of PhysicsJan 1, 20037,215 citations

Universal quantum computation using Ising anyons from a non-semisimple topological quantum field theory

Filippo Iulianelli, Sung Kim, Joshua Sussan +1 more

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. The conventional theory of Ising anyons, which is believed to describe excitations in the ν = 5/2 fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems. Ising anyons are a promising platform for topological quantum computation, but braiding alone is not universal. Here, authors show that extending to non-semi simple TQFTs introduces new anyon types that enable universal quantum computation with Ising anyons.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. The conventional theory of Ising anyons, which is believed to describe excitations in the ν = 5/2 fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems. Ising anyons are a promising platform for topological quantum computation, but braiding alone is not universal. Here, authors show that extending to non-semi simple TQFTs introduces new anyon types that enable universal quantum computation with Ising anyons.

arXiv:2410.14860Nature CommunicationsAug 5, 20255 citations

Universal Quantum Computation

Junya Kasahara

Jan 1, 20191 citation

Universal quantum computation with metaplectic anyons

Shawn Xingshan Cui, Zhenghan Wang

We show that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p)2 for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.We show that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p)2 for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.

arXiv:1405.7778Journal of Mathematical PhysicsMar 1, 2015121 citations

n

-qutrit unitaries with asymptotically efficient circuits over the metaplectic anyon model. One flavor of our algorithm produces efficient circuits with upper complexity bound asymptotically in $O({3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and entanglement cost that is exponential in

n

. Another flavor of the algorithm produces efficient circuits with upper complexity bound in $O(n\phantom{\rule{0.16em}{0ex}}{3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and no additional entanglement cost.