Additionally, we also show that the advantage in the pseudo‐threshold rates begins to saturate for any possible degree of asymmetry in the error channel as the surface code asymmetry is continued to be increased. Quantum error correction protocols will play a central role in the realisation of quantum computing the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. However, as the asymmetry of the channel increases, higher pseudo‐threshold is obtained with increasing dz when dx is kept constant at a low value. Our results show that for low degree of asymmetry, it is advantageous to increase dx along with dz. We demonstrate that compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo‐threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. \cite$ errors in a depolarisation channel. The algebraic approach of the proof yields a new, less technical proof for the OQEC case. (we use 1d to denote identity operator on a d-dimensional Hilbert space) with. Then we extend one of the basic results for subsystem codes in operator quantum error correction (OQEC) to the OAQEC setting: Every hybrid classical-quantum code is shown to be unitarily recoverable in an appropriate sense. CSS QECCs are known to have simple circuits. Quantum error correction (QEC), as a standard tool in quantum information. This approach does not work for a quantum channel in which, due to the no-cloning theorem, it is not possible to repeat a single qubit three times. A requisition for a quantum error correcting code (QECC) is that its encoding and decoding circuits need to have low gate count. The repetition code works in a classical channel, because classical bits are easy to measure and to repeat.
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