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While such algebraically defined noise models are attractive from a theoretical viewpoint, they often do not correspond to noise encountered in real-world setups. 14 The efficient simulability property has recently been extended beyond Pauli noise to random Cliffords and Pauli-type projectors. 13 The effect of Pauli noise also is efficiently simulable thanks to the Gottesman-Knill theorem, providing numerical evidence for high error thresholds of topological codes. 9 exploited this algebraic structure to establish the first analytical threshold estimates, see also. This kind of noise can be fully described by the stabilizer formalism.
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With suitable probabilities \(\varepsilon _j^x,\varepsilon _j^y,\varepsilon _j^z\) and \(\varepsilon _j = 1 - \varepsilon _j^x - \varepsilon _j^y - \varepsilon _j^z\). This gives more confidence in the viability of the fault-tolerance architecture pursued by several experimental groups. Our work demonstrates that coherent effects do not significantly change the error correcting threshold of surface codes.
Thresholds of quantum error correction codes code#
We find that for large code size the logical-level noise is well approximated by random Pauli errors even though the physical-level noise is coherent. We observe that the standard Pauli approximation provides an accurate estimate of the error threshold but underestimates the logical error rate in the sub-threshold regime. Here we report the first large-scale simulation of quantum error correction protocols based on the surface code in the presence of coherent noise. However, Pauli noise models fail to capture coherent processes such as systematic unitary errors caused by imperfect control pulses. The error suppression achieved by the surface code is usually estimated by simulating toy noise models describing random Pauli errors. Surface codes are building blocks of quantum computing platforms based on 2D arrays of qubits responsible for detecting and correcting errors.