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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 ...
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2 votes
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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 ...
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1 vote
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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 ...
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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 ...
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3 votes
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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 ...
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3 votes
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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. ...
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1 vote
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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 ...
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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 : [ ...
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1 vote
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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 ...
2 votes
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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,...
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