Demonstrating non-Abelian statistics of Majorana fermions using twist defects

Zheng, Haizhong; Dua, Arpit; Jiang, Liang

doi:10.1103/physrevb.92.245139

Cited by 30 publications

(21 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, 23 23 It becomes apparent that the ancilla parafermions 2 and 3 return to their initialized collective charge state b 23 and an effective braiding exchange is achieved between parafermions 1 and 4 (figure 1(e)) Equation (17) is the central result of our paper and the key insight here is to undo the charge transfers occurred during the measurements to realize the desired braiding operation. Taking N=2, equation (16) is consistent with our previous results of MFs [27] obtained using a wave-function approach.…”

Section: Effective Braiding For Parafermionssupporting

confidence: 89%

See 1 more Smart Citation

Measurement-only topological quantum computation without forced measurements

2017

Self Cite

View full text Add to dashboard Cite

We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501) where the braiding operation is shown to be equivalent to a series of topological charge 'forced measurements' of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons.

show abstract

Section: Effective Braiding For Parafermionssupporting

confidence: 89%

“…The intermediate charge measurement results are implicitly in the short-hand notations, and we can express equations (24)-(27) as…”

mentioning

confidence: 99%

Measurement-only topological quantum computation without forced measurements

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…[47] it was shown that the corners of the planar code where two distinct types of boundary meet can be regarded as a Majorana mode. Throughout the discussion we give here we extend this analogy [45,[85][86][87][88] further.…”

Section: Quantum Computation With the Foliated Surface Codementioning

confidence: 94%

Universal fault-tolerant measurement-based quantum computation

Brown

Roberts

2020

Phys. Rev. Research

View full text Add to dashboard Cite

Certain physical systems that one might consider for fault-tolerant quantum computing where qubits do not readily interact, for instance photons, are better suited for measurement-based quantum-computational protocols. Here we propose a measurement-based model for universal quantum computation that simulates the braiding and fusion of Majorana modes. To derive our model we develop a general framework that maps any scheme of fault-tolerant quantum computation with stabilizer codes into the measurement-based picture. As such, our framework gives an explicit way of producing fault-tolerant models of universal quantum computation with linear optics using any protocol developed using the stabilizer formalism. Given the remarkable fault-tolerant properties that Majorana modes promise, the main example we present offers a robust and resource-efficient proposal for photonic quantum computation.

show abstract

“…For example, they may include increasing or decreasing the number of edges connected to some vertices or changing the number of edges associated with some plaquettes. We refer to such alterations as defects and emphasize that these are local lattice defects as opposed to non-local defects such as lines of dislocations [10,11,12]. We can think of these defects as particles, called genons [13,14].…”

Section: Lattices On Higher Genus Surfacesmentioning

confidence: 99%

The Kitaev honeycomb model on surfaces of genus g ≥ 2

Brennan

Vala

2018

New J. Phys.

View full text Add to dashboard Cite

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan-Wigner fermionization to a surface with genus g=2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled  2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g=6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.To specify a category, we have to identify its objects and morphisms (or arrows) between them. Specifically, objects of the category of n-cobordisms n-Cob are closed oriented (n−1)-dimensional manifolds. These form boundaries of an oriented n-dimensional manifold which then constitutes a morphism between the objects of the category n-Cob. Topological quantum field theory is a rule that associates with (n−1)-manifolds finitedimensional vector spaces and with each n-manifold a map between these vector spaces. Furthermore, this rule OPEN ACCESS RECEIVED

show abstract

Demonstrating non-Abelian statistics of Majorana fermions using twist defects

Cited by 30 publications

References 46 publications

Measurement-only topological quantum computation without forced measurements

Measurement-only topological quantum computation without forced measurements

Universal fault-tolerant measurement-based quantum computation

The Kitaev honeycomb model on surfaces of genus g ≥ 2

Contact Info

Product

Resources

About