New answers tagged error-correction
1
vote
Using PyMatching for CSS code with more than two Stabilizers per qubit
PyMatching is a decoder based on matching. It fundamentally relies on an assumption that errors produce pairs of detection events (or a single detection event next to a boundary), and decoding is done ...
- 26.2k
2
votes
Accepted
Why can a distance $d =2t+1$ code correct $2t$ errors of known locations?
Let's assume your error correcting code stores 1 logical qubit. It has logical states $|0_L\rangle$ and $|1_L\rangle$. Now, for any $\sigma$ which is a tensor product of Pauli operators on no more ...
- 49.3k
1
vote
Accepted
Necessity for discarding errored magic state distillation
The reason you discard them is because this makes distillation much more efficient.
For example, consider 15-to-1 T state distillation using the Reed-Solomon code. This code has distance 3, so you can ...
- 26.2k
4
votes
What does it mean for a stabilizer to commute with an error?
Try writing out each stabilizer as a binary string. In this case, you'll have strings of length 10, the first 5 corresponding to X positions, and the second 5 corresponding to Z positions. Hence, for ...
- 49.3k
3
votes
Accepted
Code whose only transversal gate is phase gate $ P $
TL;DR: Such codes may be obtained by concatenating the repetition code with a code whose only transversal $Z$ rotations are generated by the $P$ gate.
Preliminaries: Repetition code
Repetition code ...
- 15.4k
3
votes
Accepted
How the real IBM quantum computers apply arbitrary Rz(θ) gate rotation?
Answering question (1): Z rotations are implemented purely in software by changing the relative phase between the projection of the qubit vector on the Bloch sphere and the microwave control tone.
...
- 1,128
1
vote
Accepted
Are $[[n,k,d]]$ quantum error correction codes linear?
the website has tables for both classical and quantum codes; look more carefully (QECC in left column). $[[n,k,d]]$ is notation for linear codes.
You can put the generators in many forms; there are ...
- 1,400
3
votes
How to implement the Circuit of Steane's code for Quantum Error Correction?
I will do some of the work using a small python library I am writing to play with quantum stabilizer codes. It's called stac.
Let's load up the Steane code.
...
3
votes
Stabilizer Code with small support
Let's think for a moment why the Steane code basis state have a support of 8. The Steane code is a CSS code with generators,
$$g_0 = X_0X_1X_2X_3$$
$$g_1 = X_0X_1X_4X_5$$
$$g_2 = X_0X_2X_4X_6$$
$$g_3 =...
1
vote
Accepted
$ [[n,1,d]] $ codes with $ n $ even
Here's the $[[24,1,8]]$ code and its logicals :
stabilizers : [
...
- 1,400
1
vote
Accepted
High-weight errors from ion trap crosstalk
Before going further, I think it is worth pointing out that trapped ions have any-to-any rather than all-to-all coupling. With maybe a few exceptions, no one is doing anything more than two qubit ...
- 381
2
votes
Accepted
Does Stim work if some syndromes are only measured every 2 rounds?
Yes, Stim can handle this case. If you declare a DETECTOR over measurements that are two rounds apart, it will be handled just like any other detector.
To be honest,...
- 26.2k
Top 50 recent answers are included