Questions tagged [quantum-error-correction]

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Sufficient Existence of a CPTP map based on piecewise state mappings

Suppose I want to determine whether there exists a CPTP map, $\mathcal{E}$, such that $\mathcal{E}(\rho_i) \rightarrow \rho_i^{'}$ for $i \in S$. I'm specifically interested in the case where $|S| = 2$...
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How to check that an element belongs to a stabilizer group?

My direct Question: For a given stabilizer $S=\langle g_1,...,g_n\rangle$ (only represented by the generator) and an operator $g$, how can we check that $g\in S$? A wrong answer is to check that "...
• 181
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Is it enough to recovery density matrix for error correction in quantum computing?

When we discuss error correction, we always talk about the recovery of the density matrix of a single qubit. But somehow I feel that this is not enough. Consider a circuit that contains more than 1 ...
• 181
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Well-definedness of commutation relation in commuting local Hamiltonians

I'm reading the famous paper by Haah: Local stabilizer codes in three dimensions without string logical operators. In the last sentence of the introduction, he wrote: A logical operator is a Pauli ...
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Photon loss errors versus photon subtraction errors

Cat codes, $|0_L\rangle\approx|\alpha\rangle + |-\alpha\rangle$ and $|1_L\rangle\approx|i\alpha\rangle + |-i\alpha\rangle$, are said correct single-photon loss errors in the literature. Similarly, ...
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On the optimality of Stabilizer codes

I have been studying about quantum error correction codes, specifically aobut the so-called stabilzer codes, and I wonder if are this class of quantum codes the best codes known (in terms of capacity ...
10 votes
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Topological quantum error correcting codes which are not CSS codes

The most promising-seeming quantum error correction codes for the medium-to-long term are the topological codes, of which the toric code (and variants such as planar surface codes) and colour codes ...
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5 votes
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What are the quiescent states of the surface code?

Notation $$X \equiv \sigma_x \qquad Z \equiv \sigma_z$$ Introduction The surface code is a quantum error correction code. In the surface code, we have a two-dimensional grid of qubits each coupled ...
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Quantum Error Correction: Surface code vs. color code

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit ...
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