Demonstration of Shor encoding on a trapped-ion quantum computer

Quantum error correction is crucial for constructing a fault-tolerant quantum computer. By employing redundancy, error-correcting codes protect logical qubits against errors at the physical-qubit-level during state preparation, operations and measurement. Here we demonstrate an encoding of a logical qubit with the Shor code, which detects and corrects single-qubit bit-flip and phase-flip errors, on a trapped ion system. Using nine physical qubits, we prepare a logical state $\ket{0}$ with $98.75\%$ fidelity and a logical state $\ket{1}$ with $98.51\%$ fidelity after correction with majority voting. We further investigate the robustness of the logical qubit and shows data extrapolating its performance to deeper encodings.