Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code

Abstract: 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.