A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect. A unitary encoding circuit rotates the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects for local noisy errors.
Questions tagged [stabilizer-code]
369 questions
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What is a Bacon-Shor code and what is its significance?
I'm at the AQC conference at NASA and everybody seems to suddenly be talking about the Bacon-Shor code but there is no Wikipedia page and the pdf that I gave a link to does not really explain what it is and how it works.
How does it compare to the…
user1271772 No more free time
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Connection between stabilizer generators and parity check matrices in the Steane code
I'm working through Mike and Ike (Nielsen and Chuang) for self-study, and I'm reading about stabilizer codes in Chapter 10. I'm an electrical engineer with somewhat of a background in classical information theory, but I'm by no means an expert in…
Travis C Cuvelier
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What is the difference between "code space", "code word" and "stabilizer code"?
I keep reading (e.g. Nielsen and Chuang, 2010; pg. 456 and 465) the following three phases; "code space", "code word" and "stabilizer code" - but am having a difficult time finding definitions of them and more importantly how they differ from one…
Quantum spaghettification
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How to calculate the distance of stabilizer code?
How to calculate the distance of the stabilizer code [[n,k,d]]? It's better if you can make a 3-qubit example. And what's the relationship between d and Pauli group?
Zeo
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Significance of Clifford operations from quantum error correction perspective
In the literature on QECC, Clifford gates occupy an elevated status.
Consider the following examples which attest to this:
When you study stabilizer codes, you separately study how to perform encoded Clifford gates (even if these aren't applicable…
Tanmay Singal
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Degeneracy of Quantum Error Correction Codes
The feature of quantum error correcting codes called degeneracy is that they can sometimes be used to correct more errors than they can uniquely identify. It seems that codes exhibiting such characteristic are able to overcome the performance of…
Josu Etxezarreta Martinez
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Why is the Pauli group used for stabilizers?
When it comes to error correction, we take our stabilizers to be members of the Pauli group. Why is the Pauli group used for this and not, say, the group of all unitary matrices?
Quantum spaghettification
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Are all $[[n, k, d]]$ quantum codes equivalent to additive self-orthogonal $GF(4)^n$ classical codes?
Theorem 2 of [1] states:
Suppose $C$ is an additive self-orthogonal sub-code of $\textrm{GF}(4)^n$, containing $2^{n-k}$ vectors, such that there are no vectors of weight $
SLesslyTall
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Transversal logical gate for Stabilizer (or at least Steane code)
I know that for Steane code, we can implement transversally some gates like cNOT, Hadamard and Pauli.
What I am looking for is a resource in which it is explained why implementing those gate give rise to the good logical operation.
If this is a…
Marco Fellous-Asiani
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CSS codes are the only stabilizer codes with transversal CNOT?
Given a stabilizer code $\mathcal{C}$ then
$$
\mathcal{C} \text{ is CSS} \iff \text{CNOT} \text{ is transversal}.
$$
The forward implication is well known, see for example Transversal logical gate for Stabilizer (or at least Steane code). On the…
Eric Kubischta
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CSS Code in disguise
Suppose I have a quantum error correcting code described by a set of stabilizers. Is there any easy way of checking whether or not it is equivalent to a code constructed using the CSS construction, using local Clifford transformations?
guest-20
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How to implement controlled multiqubit gates in qiskit?
To implement a stabilizer code I need to measure stabilizer generators, as shown in Fig. 10.16 in Nielsen & Chuang. Is there a way for controlled multiqubit gates in qiskit?
Jacey Li
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9
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What exactly is a subsystem code?
I'm sure I'm just tripping up on terminology here. I'm new to the wonderful field of QEC, and so far am familiar with the stabiliser formalism and basic codes such as the generic surface code. I keep seeing references in the [vast] literature to…
user23402
9
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What does "lift" mean in the Lifted Product (LP) Code?
I am watching this talk about Lifted Product Code (LP). For me, it's quite straightforward to see how to construct a HyperGraph Product Code (HGP) using two separate classical codes. However, I failed to grasp the idea of lifting and how this could…
Yunzhe
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Allowed CNOT gates for IBM Q 5 quantum computer
I trying to do some tests in the IBM Q5 computer of IBM quantm experience for some simple error correction protocols, but as I can see, some operations between the qubits are not allowed.
For example, it is not possible to perform a CNOT operation…
Josu Etxezarreta Martinez
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