Questions tagged [error-correction]
Quantum error correction (QEC) is a collection of techniques to protect quantum information from decoherence and other quantum noise, to realise fault-tolerant quantum computation. Quantum error correction is expected to be essential for practical quantum computation in the face of noise on stored quantum information, faulty quantum gates, faulty state preparations, and faulty measurements. (Wikipedia)
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Extracting syndromes by measuring gauge operators in subsystem codes
In subsystem codes, it is well-known that we can extract syndromes by measuring some gauge operators, instead of measuring stabilizers. For example, if a stabilizer $s$ is a product of gauge operators ...
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A question on dimensions of the basis vectors for the $[[6,4]]$ code
I am working from page $8$ of this paper.
The generator for the coset representatives of $C^{\perp}$ in $C$ for the $[6,5,2]$ classical code is given by $$G_{C/C^{\perp}} = \begin{bmatrix} 1 & 1 &...
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Code distance and existence of isometry in tensor networks
Recently, I've been looking into quantum error correction codes as tensor networks. I collected the following "facts" (which may be wrong, if so, please feel free to correct me on them).
A $[...
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The definition of Hastings and Haah honeycomb code
In the original paper of the honeycomb code, the edges are classified by the numbers 0, 1, 2 based on which faces they are connected to, and the types of Pauli of each edge are defined based on the ...
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What is the syndrome in Hastings and Haah honeycomb code?
In the honeycomb code proposed by Hastings and Haah, by measuring 2-body checks and multiplying these values, they obtain the values of plaquette stabilizers. In the decoding, do they use only the ...
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Intuitions for magic quantification in a particular state
Suppose we define a magic state on $2n + 1$ qubits as:
\begin{equation}
\prod_{i = 1}^{n} CCZ(0, i, i+n) |+\rangle^{\otimes 2n + 1}.
\end{equation}
Does anyone have an intuition for the scaling of the ...
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`predictions` and `fault_ids` in Stim and PyMatching for surface code decoding
When I tried to use Stim and PyMatching to decode errors in a Rotated Planar code, I noticed that, Regardedless of the code distance, predictions.shape, as well as ...
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Shadow weight enumerators
Is there any physical intuition or motivation behind the "shadow weight enumerator" of a quantum error correcting code?
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Effect of rounds in surface-code simulation with Stim
I'm learning Stim with the official tutorial and have a question.
I made a small program:
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How exactly does measuring a syndrome operator work for 'non-discrete' errors?
I am reading a summary of the stabilizer formalism in this paper, which considers the following encoding of a single qubit in three qubits:
$$
|\overline{0}\rangle=\frac{1}{\sqrt{2}}(|000\rangle+|111\...
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Can IBM Quantum hardware handle any CSWAP at all?
I am designing quantum algorithms where the quantum circuit uses CSWAP gates a lot. The result is very noisy on the quantum hardwares. So I designed really simple circuits to test whether it is indeed ...
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Deriving |𝐶𝐶𝑍⟩ magic states from |𝐶𝐶𝐶𝑍⟩?
Analogous to the $|T\rangle$ and $|CCZ\rangle$ magic states, one can define a $|C^n Z\rangle$ magic state. Is there any known quantification of the amount of magic of this state, and is there a way to ...
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Does one have multiple degrees of freedom in defining logical states and logical operators of a QEC?
Consider a rotated surface code. Let the surface code have $Z$ stabilizers along the top and bottom boundary and $X$ stabilizers along the left and right boundary.
If I initialize all the physical ...
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Obtaining the stabilizer outcome by small operators
Suppose we want to obtain the measurement outcome of the stabilizer $X_1X_2X_3X_4X_5X_6$. Of course, by measuring $X_1X_2$, $X_3X_4$, $X_5X_6$ in this order and combining these three outcomes, we can ...
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The understandings of logical operator
In quantum error correcting code, such as shor 3-qubit code, code space is spanned by the basis {|000>, |111>}. The logical X operator is XXX and the logical Z operator is IIZ. When the code ...
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