Arbitrary error detection in a planar lattice of the surface code

We detect arbitrary single-qubit errors on a system of four superconducting qubits arranged in a planar lattice, amenable to the surface code. The error detection protocol is based on the stabilizer formalism and protects a codeword encoded on an entangled two-qubit state by quantum non-demolition parity measurements, ZZ and XX. These parity measurements are performed using the other two qubits acting as syndromes. We introduce a bit- or phase-flip single-qubit error applied to the codeword and show that this error can be revealed uniquely in the syndromes. The -non-trivial- geometric arrangement of the qubits is essential to the surface code algorithm and is therefore extendable throughout the two-dimensional plane, encoding progressively larger logical Hilbert spaces towards a fully scaled fault-tolerant quantum computer.