Talk:Quantum error correction

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Talk

Would be nice if someone put a more detailed description of Shor's, Steane's, and the 5-qubit codes, as well as possibly Gottesman's stabilizer trickery, together with pretty pictures of quantum circuits. I will try to do that, provided I have enough time. —The preceding unsigned comment was added by 69.156.154.50 (talk • contribs) 03:19, 14 January 2005.

Theoretically, I could add a lot of information here and on the articles for the more important codes. I'm not promising anything, though! Melchoir 02:10, 1 January 2006 (UTC)[reply]

It has been almost six years since your request and I just added some "pretty pictures of quantum circuits". Bender2k14 (talk) 01:27, 21 December 2010 (UTC)[reply]

Shor's code should have its own Wikipedia article, as should have the Bacon-Shor code. — Preceding unsigned comment added by 129.97.120.172 (talk) 18:23, 16 August 2011 (UTC)[reply]

General Question

Can a quantum error code of any variety correct the error in a and b of a qubit a |0> + b |1> ? It doesn't appear that any projective measurement will be able to correct an unknown error in "a". For clarity of the subject, this question ought to be addressed in the article by some expert. Cryptonaut 03:39, 17 April 2006 (UTC)[reply]

Think of the error as a quantum operation on the original state. Measuring the syndrome collapses this operation into a correctible error. The article actually does, in my opinion, a very good job of explaining this. 71.77.1.215 06:26, 27 June 2007 (UTC)[reply]

Approaches Other Than the Stabilizer Formalism?

Right now this topic only seems to mention the stabilizer formalism for correcting quantum errors, which can be a bit misleading. Even if the other approaches to quantum error correction aren't delved into in-depth, it should at least be mentioned that the stabilizer formalism misses some correctable quantum errors that other approaches catch. (As a perfect example, the 3-qubit channel with 3 Kraus Operators Z1, Z2 and Z3 would not give even a single-qubit correctable code under the stabilizer formalism (I think), but actually admits a 2-qubit perfectly correctable code). 131.104.9.166 18:19, 28 June 2007 (UTC)[reply]

I have started a section titled "General codes" which will hopefully expand to address this issue. I have only put the definition of a correctable subspace for now, but things like correctable subsystems and the Knill-Laflamme conditions would fit naturally into this section. JokeySmurf (talk) 15:55, 27 February 2009 (UTC)[reply]

The figure about the bit flip code

The right most CNOT gate has two inputs. But the vertical input comes from the outputs of two previous CNOT gates. What if the two CNOT gates output different values?

In the example, there are 4 projectors. If we apply P0, the outcome will be zero. Doesn't that collapse the state of three qubits? I understand that P1 doesn't for the error scenario (the first qubit is flipped). — Preceding unsigned comment added by 24.43.92.66 (talk) 00:33, 22 November 2017 (UTC)[reply]

The CNOT-like symbol on the right is actually a Toffoli gate, or CCNOT gate. As an aside, a CNOT has two inputs---the target bit and the control bit. A Toffoli gate has three inputs---two controls and a target. Salelder (talk) 02:35, 20 June 2018 (UTC)[reply]

Maybe it would be helpful to put links to the list of gates on https://en.wikipedia.org/wiki/Quantum_logic_gate as part of the figure captions? User:jqt (Feb 2022) — Preceding undated comment added 11:56, 28 February 2022 (UTC)[reply]

Standarize Pauli matrices

Either use $X,Y,Z$ or $\sigma _{x},\sigma _{y},\sigma _{z}$ but not both.--ReyHahn (talk) 16:34, 5 May 2021 (UTC)[reply]

Also these matrices should be defined at the beggining and not in some intermediate section.--ReyHahn (talk) 09:50, 1 June 2021 (UTC)[reply]

Done Punk physicist (talk) 17:32, 5 October 2021 (UTC)[reply]

New equation for quantum feedback error correction

Now, physicists have developed a "master equation" that will help engineers understand feedback at the quantum scale. Their results are published in the journal Physical Review Letters.(source:Phys.org) — Preceding unsigned comment added by 151.34.110.31 (talk) 16:39, 28 August 2022 (UTC)[reply]