All Questions
Tagged with error-correction topological-quantum-computing
15
questions
2
votes
1
answer
65
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
3
votes
1
answer
107
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 <...
- 113
2
votes
0
answers
49
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 ...
2
votes
0
answers
252
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 ...
- 724
3
votes
2
answers
275
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://...
- 724
2
votes
1
answer
253
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
4
votes
3
answers
398
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 (...
- 199
1
vote
1
answer
208
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
5
votes
3
answers
156
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 ...
- 1,482
4
votes
0
answers
128
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 -&...
- 521
5
votes
1
answer
182
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?
- 157
4
votes
0
answers
55
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
17
votes
1
answer
587
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 ...
- 39.6k
9
votes
2
answers
602
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 ...
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 ...
- 3,124