|ψ⟩
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|ψ⟩ = α|0⟩ + β|1⟩  •  iℏ ∂|ψ⟩/∂t = Ĥ|ψ⟩
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Surface-17 QEC Lattice | Distance-3 Fault-Tolerant Benchmark

Quick Technical Answer: Surface-17 is a distance-3 (d=3) rotated surface code comprising 9 data qubits and 8 syndrome ancilla qubits (4 X-plaquettes and 4 Z-plaquettes) capable of correcting any single arbitrary physical qubit error (bit-flip or phase-flip).
Formula / Unitary: [[n, k, d]] = [[9, 1, 3]], \quad t = \lfloor (3-1)/2 \rfloor = 1 \text{ correctable error}
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Syndrome Measurement Cycle in Itachi Studio

In each QEC cycle, ancilla qubits measure the parity of surrounding data qubits without reading their state. Non-trivial syndrome values (eigenvalue -1) indicate error endpoints, which are matched and neutralized by the Minimum-Weight Perfect Matching (MWPM) decoder.

Frequently Asked Questions

What physical errors can Surface-17 correct?

Surface-17 can correct any single X (bit-flip), Z (phase-flip), or Y = iXZ (combined bit-phase flip) error occurring on any of the 9 data qubits during a cycle.

Related Topics & Quantum Guides:

Surface CodeMinimum-Weight Perfect Matching (MWPM)Steane [[7,1,3]] Code