A fault-tolerance record for comparing physical error, syndrome extraction, decoder choice, and logical failure.
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Surface-code families are central to scalable fault tolerance because they use local stabilizer checks and planar connectivity. The XZZX variant illustrates why matching a code to biased noise can matter as much as the code name.
No input port, deliberately. You measure a state with this entry; you do not apply it and pass a register on.
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No output port, deliberately. An observable is measured with, never applied, so there is no register to hand on.
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Not a stage. You measure a state with this; you do not apply it and pass a register on. It has a width and deliberately no ports. See all 60 →
Surface codes protect a logical qubit using only local stabilizer checks on a 2D lattice: data qubits sit on edges or vertices, and repeated measurement of local -type and -type stabilizer operators produces a syndrome without ever measuring the encoded logical state directly. Stacking syndrome rounds over time traces out a space-time syndrome graph; a decoder (typically minimum-weight perfect matching or a neural/tensor-network decoder) infers the most likely error chain consistent with that graph, and the logical observable fails only when the true error and the inferred correction differ by a nontrivial logical operator — an event whose rate drops super-linearly below the physical error rate once the code operates below its threshold. The XZZX variant this record cites reshapes the stabilizers so that a biased (e.g. dephasing-dominated) physical noise channel is matched more efficiently than the standard surface code, without needing a higher weight. This record documents the syndrome-round and logical-observable workflow as an architecture reference; it makes no hardware threshold claim of its own, and — per its caveat — decoder quality, leakage, measurement error, and connectivity determine the useful operating point.
OPENQASM 3.0;
include "stdgates.inc";
// A stabilizer round is layout- and decoder-specific.
qubit[5] data;
qubit[4] ancilla;
// Prepare, entangle, measure ancilla, then decode.The reference keeps syndrome and decoder boundaries visible rather than pretending a universal hardware layout.
Classical parity-check codes and decoders provide an intuition for syndrome processing, but they do not preserve an unknown quantum phase.
A local quantum code can suppress logical errors below physical errors when the full architecture operates below its threshold.
Benchmark physical-versus-logical error rates, qubit and gate overhead, measurement rounds, decoder latency, and noise bias.
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Shows how a surface-code variant can exploit structure in biased Pauli noise and decoder design.
arxiv.org/abs/2009.07851 ↗Provides a foundational contrast between early block-code protection and scalable local-check architectures.
doi.org/10.1103/physreva.52.r2493 ↗