  To build a fault-tolerant quantum computer, it is necessary to implement a
quantum error correcting code. Such codes rely on the ability to extract
information about the quantum error syndrome while not destroying the quantum
information encoded in the system. Stabilizer codes are attractive solutions to
this problem, as they are analogous to classical linear codes, have simple and
easily computed encoding networks, and allow efficient syndrome extraction. In
these codes, syndrome extraction is performed via multi-qubit stabilizer
measurements, which are bit and phase parity checks up to local operations.
Previously, stabilizer codes have been realized in nuclei, trapped-ions, and
superconducting qubits. However these implementations lack the ability to
perform fault-tolerant syndrome extraction which continues to be a challenge
for all physical quantum computing systems. Here we experimentally demonstrate
a key step towards this problem by using a two-by-two lattice of
superconducting qubits to perform syndrome extraction and arbitrary error
detection via simultaneous quantum non-demolition stabilizer measurements. This
lattice represents a primitive tile for the surface code, which is a promising
stabilizer code for scalable quantum computing. Furthermore, we successfully
show the preservation of an entangled state in the presence of an arbitrary
applied error through high-fidelity syndrome measurement. Our results bolster
the promise of employing lattices of superconducting qubits for larger-scale
fault-tolerant quantum computing.
