Questions tagged [toric-code]

The toric code is a topological quantum error correcting code, and an example of a stabilizer code defined on a two-dimensional spin-lattice. It is the simplest and most well studied of the quantum double models (first studied in the context of Z2 spin liquid in 1991). It is also the simplest example of topological order—Z2 topological order. The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. (Wikipedia)

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is the minimum weight perfect matching decoder optimal

The toric code and other popular codes can be decoded using minimum weight perfect matching. Is this an optimal decoder? Here by optimal, I mean it gives the best logical error rate vs physical error ...
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how to simulate toric and surface codes with stim + PyMatching

According to PyMatching's github page the package can be decode toric and surface codes. Stim's example uses stim + PyMatching combination to get logical error rate vs physical error rate curves for ...
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Is the quantum Singleton bound compatible with the Toric Code?

Note: Cross-posted on Physics SE. The quantum Singleton bound states that for an error-correcting code with $n$ physical qubits and $k$ encoded qubits, and some subsystem $R$ of $m$ qubits that can '...
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How does the size of a toric code torus affect its ability to protect qubits?

The Toric code Hamiltonian is: $\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$ where the $v$ and $p$ are defined according to this picture (courtesy of James ...