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).
52 questions
3
votes
0
answers
67
views
How does the surface code have four twist defects, one at each corner?
In Craig Gidney’s Y Basis paper he states “Recall that a surface code patch has four twist defects, one at each corner” and cites Ben Brown et al.’s ‘Poking’ paper. I do not understand how to ...
- 125
1
vote
0
answers
41
views
Is there an upper bound on two-qubit fidelity improvements?
The higher the two-qubit fidelity, the lower the overhead for quantum error correction. This is especially preferable due to the fact that cheap QRAM would be useful for practical applications, QRAM ...
- 1,993
3
votes
1
answer
250
views
Finding Fusion Matrix for simple non-abelian anyon model
Given the anyon particles: $\{1, \Lambda, \Phi\}$ and fusion rules:
$$\Lambda \times \Lambda = 1, \quad \Lambda \times \Phi = \Phi \times \Lambda = \Phi, \quad \Phi \times \Phi = 1 + \Lambda + \Phi$$
...
3
votes
1
answer
69
views
How does one identify Pauli logicals in a hyperbolic surface code?
I understand how the Pauli X and Z logicals on the planar surface code work - they are stringlike operators between either the rough boundaries (in case of the Z logical) or between smooth boundaries (...
- 31
2
votes
1
answer
101
views
How do Union-Find Decoders deal with Measurement errors through multiple measurement rounds?
I've read a few papers regarding to Surface Code and its decoding algorithms. I've learned that a Union-Find decoder need up to $d$ measurement rounds to deal with measurement errors.
These ...
- 25
0
votes
0
answers
35
views
Toric Code with stim?
Is there any way to encode toric code with stim with desired error such as erasure error and z error? I have seen their documentation on surface code but that is already encoded. Is there any good ...
- 1
3
votes
1
answer
118
views
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 <...
- 143
2
votes
0
answers
70
views
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 ...
0
votes
1
answer
113
views
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 ?
- 408
2
votes
0
answers
66
views
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 ...
- 21
2
votes
0
answers
351
views
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 ...
- 764
4
votes
0
answers
68
views
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 ...
user4824
3
votes
2
answers
324
views
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://...
- 764
0
votes
1
answer
208
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 (...
- 764
2
votes
0
answers
50
views
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 ...
- 71
1
vote
1
answer
150
views
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 ...
- 11
2
votes
0
answers
49
views
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 ...
- 71
2
votes
1
answer
321
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 ...
- 99
5
votes
3
answers
477
views
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 (...
- 309
4
votes
0
answers
88
views
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}{\...
- 141
2
votes
0
answers
17
views
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 ...
- 21
4
votes
0
answers
75
views
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 ...
- 14.9k
2
votes
1
answer
537
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 ...
- 199
8
votes
0
answers
311
views
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 ...
- 281
1
vote
1
answer
250
views
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:
...
- 173
2
votes
1
answer
445
views
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 ...
- 199
5
votes
3
answers
165
views
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 ...
- 1,502
4
votes
0
answers
141
views
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 -&...
- 583
6
votes
2
answers
257
views
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 ...
5
votes
1
answer
200
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?
- 167
4
votes
0
answers
59
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 ...
- 61
6
votes
1
answer
294
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/...
- 413
3
votes
2
answers
333
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 ...
- 14.9k
2
votes
0
answers
26
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 ...
- 1,567
5
votes
0
answers
83
views
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 ...
- 51
5
votes
1
answer
225
views
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 ...
- 181
4
votes
1
answer
240
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.
...
- 959
3
votes
1
answer
148
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: ...
- 1,795
17
votes
2
answers
672
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 ...
- 42k
6
votes
2
answers
348
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 ...
- 1,795
8
votes
1
answer
138
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 ...
user5438
2
votes
1
answer
129
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 ...
- 1,795
8
votes
2
answers
697
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 ...
- 443
9
votes
2
answers
286
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)?
- 3,342
6
votes
2
answers
315
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 ...
- 3,342
9
votes
2
answers
644
views
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 ...
10
votes
1
answer
724
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 ...
- 498
25
votes
2
answers
762
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. ...
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 ...
- 17.8k
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 ...
- 3,134