A fault-tolerant pairwise measurement-based code on eight qubits

Understand

We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3.

• The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28.
• We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group.
• We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement.