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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Are transversal entangling gates possible for stabilizer codes other than CSS?
It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304....
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Is working with the |+> , |-> basis any harder than the |0>, |1> basis?
Say I have a code, for example the $ [[5,1,3]] $ code, and I want to (fault tolerantly) prepare the logical $ |+ \rangle $ state. Is that any harder than preparing the logical $ | 0 \rangle $ state? ...
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Highest theoretical threshold to fight single-qubit depolarizing noise for noiseless error-correction
Let's consider that each qubit in the lab faces a single-qubit depolarizing channel $\mathcal{N}(\rho)=(1-p) \rho + p \mathbb{I}/2$.
Is there a theoretical result indicating the largest value of $p$ ...
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Is it sufficient to assume a constant coherent error?
I've recently started working with quantum errors and noise and came across an intriguing but simple question. When we consider coherent errors in quantum gate operations, it's common to model them as ...
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Boundary conditions for surface code
I have a question about boundary conditions for surface codes. Do any surface codes have torus-like boundary conditions? Are there any surface codes that don't actually have boundary conditions, i.e. ...
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How is $(\langle \psi| E_{a}^\dagger E_{b} | \psi \rangle)^\dagger = C_{ba}^*\langle \psi| \psi \rangle $
I am reading through Daniel Gottesmans surviving as a quantum computer in a classical world. On page 36, he presents the following theorem:
Theorem 2.7 (QECC Conditions). $(Q, \mathcal{E})$ is a $Q E ...
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Is every code with a universal set of transversal gates trivial?
The quantum repetition code is an $ [[n,1,1]] $ stabilizer code with stabilizer generators $ Z_iZ_{i+1} $ for $ i=1, \dots, n-1 $.
The Eastin-Knill theorem states that a $ d >1 $ code cannot have a ...
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What does DETECTORs mean in the example circuit for rotated surface code in Stim?
In Stim, an example circuit for rotated surface code is provided:
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Advantages and disadvantages of rotated surface code
I think one of the advantages of rotated surface code is that it can express surface code with fewer physical bits. Are there any other advantages?
Also, are there any disadvantages compared to ...
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What is the easiest way to get path graph from Stim?
In Stim, we can get a detector graph with the probability of each error mechanism occurring. Now I want to construct a path graph from the detector graph, which is usually done by Dijkstra's algorithm....
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How does measurement based quantum computing (MBQC) behave under error propagation?
In the quantum circuit model, we know how to handle error propagation if we implement a unitary $U'$, which is $\varepsilon$-close to the ideal unitary $U$ and a state $|\psi'\rangle$, which is also $\...
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Are close states still close after measurement (regarding trace distance)?
We are given two states $|\psi_1\rangle, |\psi_2\rangle \in \mathbb{C}^2 \otimes \mathbb{C}^2$ with trace distance $\leq \varepsilon$, so they are very close to each other.
Now, assume we measure the ...
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Necessary condition for transversal Hadamard by family of stabilizer codes
A necessary and sufficient condition for a stabilizer code having transversal $CNOT$ is that the code is a CSS code (see Theorem 11.5 here or the question here).
I know that a sufficient condition for ...
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Define the $k$-local transversal logical operation
For a $[[n, 1]]$ QEC code $\mathcal{Q}$, we say single logical gate $R$ is transversal if the logical $\bar{R}$ can be implemented with $R^{\otimes n}$.
I am wondering if we could expand the ...
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Why can Pauli errors $E$ be decomposed as $E=T(S)LG$ with $T(S)$ "pure errors"?
I have a question about the decomposition of Pauli errors.
Pauli error $E \in \{I,X,Y,Z\}^{{\bigotimes}n}$ that satisfies the syndrome $S$ can be decomposed into a product of pure error $T(S)$, ...
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