Twisted Interferometry

Kevin Walker; Lukasz Fidkowski; Michael Freedman; Parsa Bonderson

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Twisted Interferometry

Parsa Bonderson, Lukasz Fidkowski, Michael Freedman, Kevin Walker

Quantum Physics · Submitted 10 Jun 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.78 · human participants 0.02 · controlled comparison 0.35 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other. These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements. In particular, it enables Ising anyons to generate "magic states," which can be used to implement pi/8-phase gates. We consider the possible implementations of such twisted interferometers in quantum Hall systems, 2D p_x + i p_y superconductors, and 2D Majorana heterostructures, and discuss obstacles and challenges associated with implementation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other.	contribution 1.00	0.78	0.08	asserted 0.84
s1	These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements.	result 0.62	0.90	0.55	hedged possibility 0.82
s2	In particular, it enables Ising anyons to generate "magic states," which can be used to implement pi/8-phase gates.	result 0.91	0.80	0.42	asserted 0.98
s3	We consider the possible implementations of such twisted interferometers in quantum Hall systems, 2D p_x + i p_y superconductors, and 2D Majorana heterostructures, and discuss obstacles and challenges associated with implementation.	contribution 0.64	0.70	0.04	hedged possibility 0.67

What kind of paper the classifier reports this is: method or tool 0.92 · evidence from proof or derivation 0.64.

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The paper

Original abstract

We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other. These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements. In particular, it enables Ising anyons to generate "magic states," which can be used to implement pi/8-phase gates. We consider the possible implementations of such twisted interferometers in quantum Hall systems, 2D p_x + i p_y superconductors, and 2D Majorana heterostructures, and discuss obstacles and challenges associated with implementation.

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How the literature uses it

10 arXiv papers cite this in 16 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Contests it 1 paper

However, proposals to exploit these ideas using topological superconductors in semiconductor-superconductor heterostructures [ref] , or the Moore-Read Pfaffian FQH state with tilted interferometry [ref] , were since found to be insufficient even in principle, as they lack a crucial ingredient: the existence of a finite energy quasiparticle excitation with an appropriate value of topological spin [ref] .

Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires · Introduction · contest 0.71

Builds on it 1 paper

With appropriate assumptions, the analysis also extends to other twisted interferometer designs, such as those described in [ref] .

Twisted Interferometry: the topological perspective · The Double Twisted Interferometer in Ising Systems · 0.85

Uses its method or tool 1 paper

We have used local diagrammatic calculations [ref] as input to topological machinery.

Twisted Interferometry: the topological perspective · Topological Understanding · 0.95

Cites it as background 2 papers

We recall the bare bones of anyonic interferometry in a general anyonic context (as developed in [ref] ; see [ref] for notational clarification and calculational details).

Twisted Interferometry: the topological perspective · What an Anyonic Interferometer Does in Two Different Languages · 0.90
There are several attempts to make universal quantum computation based on Majorana fermions [ref] .

Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions · Introduction · 0.91

What it cites · 31 sentences without a confident label

Builds on 1 paper

This is a convenient place to consider in more detail a modest generalization of this analysis that was mentioned briefly in [ref] , where the complementary anyons $C$ (outside of the interferometry loop) are divided into two groups $C_1$ and $C_2$ located on the two different sides of the interferometer (below and above), as shown in Fig. [ref].

Interferometry of non-Abelian Anyons · Generalized Target System · 0.98

Compares with 2 papers

Thus, this method, which bears a number of similarities to that of Refs. [ref] , can only be viewed as a topologically unprotected method of producing $π/8$-phase gates, which will require error-correction.

Implementing arbitrary phase gates with Ising anyons · Partial Interferometry and Faking the Twist for Ising-type Anyons · 0.92
Thus, this method, which bears a number of similarities to that of Refs. [ref] , can only be viewed as a topologically unprotected method of producing $π/8$-phase gates, which will require error-correction.

Improved phase gate reliability in systems with neutral Ising anyons · Partial Interferometry and Faking the Twist for Ising-type Anyons · 0.92

Cites as support 1 paper

Fortunately, the convergence of the interferometry process is exponentially fast in number of probes sent through an interferometer [ref] , so twisted interferometry is still topologically protected in the sense that the error of the operation will be exponentially suppressed as $N$ is increased.

Interferometry of non-Abelian Anyons · Implementation Issues and Obstacles · 0.98

Cites as background 18 papers

(We refer the reader to [ref] for additional details and background on the UBTC formalism used in the analysis.)

Interferometry of non-Abelian Anyons · Tensor Category Analysis · 0.97
In quantum Hall systems, the Moore-Read (MR) Pfaffian [ref] and anti-Pfaffian [ref] states are the strongest candidates for the $ν=5/2$ quantum Hall state [ref] and the Bonderson-Slingerland (BS) hierarchy states [ref] over these provides a strong candidate for the $ν=12/5$ state [ref] .

Particle-hole symmetry and the Pfaffian state · Twisted Interferometry with Ising Anyons · 0.91
In quantum Hall systems, the Moore-Read (MR) Pfaffian [ref] and anti-Pfaffian [ref] states are the strongest candidates for the $ν=5/2$ quantum Hall state [ref] and the Bonderson-Slingerland (BS) hierarchy states [ref] over these provides a strong candidate for the $ν=12/5$ state [ref] .

Nonconventional odd denominator fractional quantum Hall states in the second Landau level · Twisted Interferometry with Ising Anyons · 0.91

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