Fault-Tolerant Operation of a Quantum Error-Correction Code

Quantum error-correction remains a critical component to realizing the full promise of quantum algorithms.  In this talk, I will discuss experimental progress towards creating and controlling logical qubits on a trapped ion quantum computer. Our code of choice is the Bacon-Shor [[9,1,3]] subsystem code, which consists of 9 data qubits, encoding 1 logical qubit, with stabilizer measurements mapped to 4 ancilla qubits capable of correcting any single qubit error. Recently, we have experimentally demonstrated fault-tolerant preparation, rotation, syndrome extraction, and measurement of a logical qubit.  Remarkably, the logical qubit exceeds the fidelity of the entangling operations used to create it.  Additionally, we measure the four Bacon-Shor stabilizer generators directly and are able to detect single qubit Pauli errors. Looking forward, we will lay out the near-term path for achieving multiple rounds of error correction and logical CNOT gates. (https://arxiv.org/abs/2009.11482)