As of May 31, 2023, we have updated our Code of Conduct.

Questions tagged [toric-code]

The toric code is a topological quantum error correcting code, and an example of a stabilizer code defined on a two-dimensional spin-lattice. It is the simplest and most well studied of the quantum double models (first studied in the context of Z2 spin liquid in 1991). It is also the simplest example of topological order—Z2 topological order. The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. (Wikipedia)

Filter by
Sorted by
Tagged with
0 votes
1 answer
23 views

How horizontal loops on the toric code are all undetectable?

I understand that if we have, for example, the blue path doesn't make any check operator detect any error, but what about the red path? We have the check operator detecting since there is just one ...
LittleBlue's user avatar
2 votes
1 answer
57 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
  • 89
1 vote
2 answers
78 views

How to Switch Toric Code to Surface Code (no using STIM!)

Here is the toric code example which I found from :https://pymatching.readthedocs.io/en/latest/toric-code-example.html ...
quest's user avatar
  • 560
1 vote
1 answer
117 views

Pymatching Toric Code vs Surface Code

I am looking the example of toric code in Pymatching. Here is the code: ...
quest's user avatar
  • 560
1 vote
1 answer
72 views

How to get the matched nodes using Matching.decode() in PyMatching?

In the module matching.py of PyMatching, it is possible to construct Matching objects to decode matching graphs using the minimum-weight perfect matching decoder. The ...
francois-marie's user avatar
4 votes
0 answers
49 views

Why are all the error cosets $Q.S$ given the erasure chain $\mathcal E$ and a syndrome $\sigma$ equiprobable? (Delfosse-Zémor)

In arXiv 1703.01517 (published here), a maximum likelihood decoding for qubit loss is explained. A quantum erasure channel erases each qubit independently with some probability $p$ and replaces it ...
Sanchayan Dutta's user avatar
0 votes
1 answer
105 views

Energy and degeneracy of the ground state and excitations of the toric code

Recall the hamiltonian of the toric code: (information mainly extracted from https://arxiv.org/pdf/1610.09260.pdf) Consider Je=Jm=1. I've been trying to get the exact energies and degeneracies of the ...
MarcPN's user avatar
  • 3
2 votes
1 answer
179 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
  • 199
2 votes
1 answer
376 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 ...
Debbie's user avatar
  • 199
2 votes
1 answer
37 views

Questions on Definitions and Concepts Regarding Toric Codes

Currently, I reading the toric code section in the beginning of the paper Topological Quantum Memory. Here are a couple of sections that are somewhat confusing to me. (1) This quote below is under a ...
Debbie's user avatar
  • 199
4 votes
2 answers
553 views

is the minimum weight perfect matching decoder optimal

The toric code and other popular codes can be decoded using minimum weight perfect matching. Is this an optimal decoder? Here by optimal, I mean it gives the best logical error rate vs physical error ...
unknown's user avatar
  • 1,742
1 vote
1 answer
453 views

how to simulate toric and surface codes with stim + PyMatching

According to PyMatching's github page the package can be decode toric and surface codes. Stim's example uses stim + PyMatching combination to get logical error rate vs physical error rate curves for ...
unknown's user avatar
  • 1,742
4 votes
0 answers
101 views

Is the quantum Singleton bound compatible with the Toric Code?

Note: Cross-posted on Physics SE. The quantum Singleton bound states that for an error-correcting code with $n$ physical qubits and $k$ encoded qubits, and some subsystem $R$ of $m$ qubits that can '...
Joe's user avatar
  • 141
9 votes
2 answers
451 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 ...
user1271772's user avatar
  • 12.8k