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Questions tagged [topological-quantum-computing]

Topological quantum computing is a theoretical quantum computing model that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions).

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How to get the surviving stabilisers of a fusion network

In Fig. 5 of PsiQuantum's Fusion-based quantum computation paper, it's clear to me how to get R, F, and C. How do I get S? Just by looking at (a), I could obviously tell you that we end up with <...
compp's user avatar
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2 votes
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How can I obtain the rotated surface code from the original unrotated one?

I am trying to understand the equivalence between the original planar surface code and the rotated version. Looking at Tomita and Svore's paper (2014), they say "The number of qubits [from ...
Ezequiel Rodriguez Chiacchio's user avatar
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1 answer
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Are there logical operations unique to topological quantum computing?

Are there any algorithms or logical operations which are only unique to topological quantum computing architecture ?
Chetan Waghela's user avatar
2 votes
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MWPM / Union Find Implementations for 3D Toric Code

I am currently looking into 3D surface codes and was wondering if there are open-source implementations for decoders like MWPM or the Union Find decoder. I found quite a lot of different GitHub repos ...
Oliver's user avatar
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How to account for a partial derivative term in an Operator, in Qiskit?

The crystal momentum p1 = h bar * k and this is defined in the reciprocal momentum, I am guessing this p1 is not a real momentum since the reciprocal space is an imaginary space which we use for ...
CuriousMind's user avatar
2 votes
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The planar surface code vs the toric code

Where can I find a numerical or analytical comparison of the effect of open and closed boundaries on surface code error correction power, such as the logical error rate at the threshold, logical error ...
Yaron Jarach's user avatar
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Prospects of topological/anyon approach to QC

Given the recent articles/preprints by Google and Quantinuum claiming implementation of braiding of non-Abelian anyons on a quantum processor, what is the likely impact of these findings, and ...
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3 votes
2 answers
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Is the honeycomb code a subsystem code?

The paper https://arxiv.org/abs/2110.09545.pdf claims that the honeycomb code falls outside the definition of a subsystem code. But here: https://errorcorrectionzoo.org/list/subsystem, here: https://...
Yaron Jarach's user avatar
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Capping in topological cluster state error correction simulation

In this paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.052316, section IX., it is written: "...The logical error rate (p_L) of a given error model is determined by a continuous ...
Yaron Jarach's user avatar
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1 answer
93 views

Surface code expansion in the lattice surgery context

In this paper: https://iopscience.iop.org/article/10.1088/1367-2630/14/12/123011, the authors describes how to inject a magic state into a small planar surface code, and then how to expand the code (...
Yaron Jarach's user avatar
2 votes
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How are the twist defects and domain walls on topological color code of pratical use?

I found an article that talks about the twist and domain walls on topological color codes, but I fail to understand how they are of practical use? Similarly, we can change the type of path and stuff ...
LittleBlue's user avatar
1 vote
1 answer
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Quantum dimension of an anyon

In the book Introduction to Topological Quantum Computation Jiannis K. Pachos page 60 Equ.(4.16) $\text{dim}(M_{(n)}) \propto d_a^n$, two lines after (4.16) said that, The dimension of $M_{(n)}$ is ...
Embra_QN's user avatar
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0 answers
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Need help to understand topological color codes

I am doing work on topological color codes, but after searching a lot of papers I could not find one that explained some points. Why do we need the colors for? Why do we have different types of color ...
LittleBlue's user avatar
2 votes
1 answer
218 views

Is there a way to perform a defect-free logical CNOT on the toric code?

I was curious to whether the two logical qubits on the toric code can be entangled through, for instance, a logical CNOT operation. However, I cannot find any information on this, only how you can do ...
JoJo's user avatar
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3 answers
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Are there open source implementations of quantum error correction decoders?

To detect and correct for errors in a topological quantum memory (toric code for example) one needs a quantum error correction algorithm also known as decoder. The minimum weight perfect matching (...
francois-marie's user avatar
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Quantum entanglement as topological entanglement

According with Aravind: the Hopf link, L2a1, corresponds to the Bell state $\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$, the Borromean link (L6a4) can be considered as GHZ state $\frac{1}{\...
Juan Ospina's user avatar
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Is there a code version for the Quantum Mean Approximation algorithm?

I found this paper https://arxiv.org/pdf/1106.4267.pdf which describes a method to find the mean of all numbers in a list using a quantum algorithm. However, all it gives is the math behind it. Is ...
AadiTiwari's user avatar
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What is a diference between solitons and anyons?

In the article Creation and annihilation of mobile fractional solitons in atomic chains the authors claim that they prepared 1D solitons which can be used in topological quantum computing. Based on ...
Martin Vesely's user avatar
2 votes
1 answer
398 views

Why Is This the Ground State of a Toric Code?

I am currently trying to study the ground state of the Toric Code. I am currently reading this paper. The Hamiltonian is given by the following, where $A_s$'s are the star operators made out a tensor ...
Debbie's user avatar
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Origin of braiding in measurement-only TQC

I have a technical question on the "measurement-only"-proposal for topological quantum computation on anyons. First some background: Background. While it has become a common idea that ...
Urs Schreiber's user avatar
1 vote
1 answer
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extracting the Pauli error on the data qubits at the end of circuit in stim

Let's say one implements the following circuit in stim from the stim tutorial: ...
user111's user avatar
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1 answer
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What is the Stabilizer of a Code?

I am currently reading the beginning of the paper Topological Quantum Memory and I am confused about one part: The check operators generate an Abelian group, the code’s stabilizer. When I learned ...
Debbie's user avatar
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3 answers
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Simulate Surface /Topological Code with Majorana - Huge Complexity Saving

This article "Correcting coherent errors with surface codes" is talking in the methods section, about simulating topological codes / surface codes, using Majorana equivalent. It is also ...
Ron Cohen's user avatar
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What do Z logical errors look like in 3d color codes?

I am trying to better understand (standard, not gauge) 3d color codes. In particular, I am working with the lattice proposed in 1. I understand how X error works, forming strings of the kind Vertex -&...
Pablo's user avatar
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2 answers
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Can you make anyons in 3 dimensions using rings?

I heard that anyons can only be made in 2 dimensions because when you visualize the spacetime diagram of a 2-dimensional system with point particles, you can get braids, but if you do the same with a ...
MaudPieTheRocktorate's user avatar
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1 answer
178 views

Why is this topological gate mentioned in Raussendorf et al. 2007 a CNOT?

I read a Paper about quantum error corrections. I don't know why this is a CNOT gate. How to calculate this kind of CNOT gate as a topology form?
QuantumDots's user avatar
4 votes
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54 views

How to do the counting when computing the fault tolerant threshold of quantum codes?

Here, I want to ask a basic question about how to compute the fault tolerance threshold of quantum codes. As I know, maybe, the most usual way is to do some simulations. Howvever, I am more intersted ...
Bruce Fang's user avatar
6 votes
1 answer
285 views

Does this experimental discovery of anyons enables the topological quantum computer (e.g. Microsoft) to become a reality?

Microsoft has its own agenda regarding quantum computer - it is topological quantum computer being invented by the team lead by Michael Freedman https://www.microsoft.com/en-us/research/project/...
TomR's user avatar
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314 views

Topological quantum computer and two dimensional materials

Recently I read thread on topological quantum computers. If I understood correctly, gates in such computers are based on "effects" in two dimensional spaces. Since our space is three dimensional, such ...
Martin Vesely's user avatar
2 votes
0 answers
25 views

Why does non-locality and the particle-hole symmetry not contradict each other?

Currently, I'm learning about topological quantum computers. In one of the explained techniques, cooper pairs in superconductors are considered, where a cooper pair with a hole form a Majorana bound ...
nippon's user avatar
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History of anyon theory, braidings and tensor categories

What was the first paper/who was the first person to phrase anyon theory in terms of tensor categories? Going through Wilczek's book on fractional statistics, some of the reprinted papers anticipate ...
Oliver's user avatar
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1 answer
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Simulating quantum computers using anyon braiding

I am new to the concept of topological quantum computation (TQC). Recently I have been thinking about simulating a quantum computer on a classical computer. I know that if I use merely the unitary ...
wooohooo's user avatar
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4 votes
1 answer
201 views

Measuring Ising anyons: What is a fusion measurement?

I have several doubts about measuring Ising anyons. Measurement is crucial for quantum computation and even more so for magic state distillation which is necessary to make Ising anyons universal. ...
Marsl's user avatar
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3 votes
1 answer
140 views

Topological anyonic molecule statistics

In the last chapter of John Preskill's Lecture Notes for Physics 219: Quantum Computation (PDF), he mentions the following on pg.12. This behavior is compatible with the spin-statistics connection: ...
Siddhant Singh's user avatar
17 votes
1 answer
559 views

Reference that explains how to read 3d topological diagrams for surface code computations

I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white ...
Craig Gidney's user avatar
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5 votes
2 answers
321 views

What is the correspondence between adiabatic phase and a topological phase?

In the adiabatic model, we have a system acquiring a Berry phase due to cyclic slow periodic evolution under a Hamiltonian. While in the topological phases, we talk about systems such as anyons which ...
Siddhant Singh's user avatar
8 votes
1 answer
120 views

Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems ...
user avatar
2 votes
1 answer
125 views

Is there any tool or simulator for Topological quantum gates and circuits? [duplicate]

I am starting to step into the field of Topological Quantum Information and Computation and am in search of tools which I can use to directly simulate or realize these transformations in a textual or ...
Siddhant Singh's user avatar
8 votes
2 answers
612 views

Are there any other companies besides Microsoft pursuing topological QC?

Also, why is Microsoft placing such an emphasis on topological qubits when most other companies seem to be focusing on other qubit technologies? I know topological qubits could handle noise far ...
jman's user avatar
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9 votes
2 answers
280 views

Topological Circuit Simulator

Does something like Quirk exist for topological (eg. braided) circuits? Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
user820789's user avatar
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6 votes
2 answers
292 views

Anyon alternatives in topological quantum computing

A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons. -Wikipedia Are there other instances of topological quantum computing ...
user820789's user avatar
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9 votes
2 answers
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How does the size of a toric code torus affect its ability to protect qubits?

The Toric code Hamiltonian is: $\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$ where the $v$ and $p$ are defined according to this picture (courtesy of James ...
user1271772 No more free time's user avatar
10 votes
1 answer
647 views

Are there connections between long-range entanglement and topological quantum computation?

Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot ...
Yupan Liu's user avatar
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25 votes
2 answers
708 views

What is the status of confirming the existence of anyons?

In a comment on my answer to the question: What exactly are anyons and how are they relevant to topological quantum computing? I was asked to give specific examples of occurrence of anyons in nature. ...
user1271772 No more free time's user avatar
26 votes
3 answers
6k views

What exactly are anyons and how are they relevant to topological quantum computing?

I have been trying to get a basic idea of what anyons are for the past couple of days. However, the online articles (including Wikipedia) seem unusually vague and impenetrable as far as explaining ...
Sanchayan Dutta's user avatar
15 votes
1 answer
2k views

Is Gil Kalai's argument against topological quantum computers sound?

In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the ...
Discrete lizard's user avatar
3 votes
2 answers
564 views

What is the most economical and preferred basis for the qudit?

In Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code, the authors state on page 2 in section I. Background, A. Topological model: We consider a system supporting nonabelian ...
Rob's user avatar
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19 votes
2 answers
2k views

How does topological quantum computing differ from other models of quantum computing?

I've heard the term Topological Quantum Computer a few times now and know that it is equivalent to quantum computers using circuits with respect to some polynomial-time reduction. However, it is ...
dtell's user avatar
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