A two-dimensional topological code needing only nearest-neighbour connectivity, with a relatively forgiving error threshold near 1% — the leading candidate for real fault-tolerant hardware.
Why it matters
Almost every superconducting-qubit roadmap in the industry is built on the surface code, so its overheads set the qubit counts everyone quotes for useful machines.
After this you will be able to
Hand-picked and ordered. If you only have time for one, take the first.
The standard reference on surface codes, written as a tutorial rather than a terse paper. Where every industrial fault-tolerance roadmap ultimately points.
A cross-referenced encyclopedia of classical and quantum error-correcting codes, each with properties, decoders and references. Indispensable once you are past the textbook codes.
Simulates million-qubit stabiliser circuits in seconds, which is what makes modern error-correction research computationally possible. The tutorial notebooks double as a surface-code course.
The standard fast decoder for surface codes, and the natural companion to Stim. Together they let you run realistic threshold simulations on a laptop.
The first convincing demonstration that adding more physical qubits made the logical qubit better rather than worse. Arguably the most important experimental result of the decade so far.
Topics that list Surface codes as a prerequisite.