Preservation of Quantum States by Local Error Correction on a Two-dimensional Toric Code in a Rydberg Atom Array*

To build a reliable quantum computer, errors occurring in quantum hardware and corrupting the information being processed must be identified and corrected systematically by quantum error correcting codes (QECC). This research project focuses on the toric code—a canonical example of a topological error correcting code. Traditionally, decoding in the toric code is done with global error syndrome information, which are the measured values of all stabilizer operators. However, in the Rydberg atom array setup that is one of the platforms for experimentally prepared toric code state, mid-circuit measurements are more costly than than coherent local quantum operations, including multi-qubit gates and dynamical rearrangement.

In this project, we develop a hybrid decoding protocol that performs local error correction with a sequence of local quantum gates before applying traditional global error correction. Based on extensive circuit-level simulations, we show that this hybrid decoding protocol is effective in extending the logical qubit lifetime under the realistic faulty quantum gates with small gate error. Using reinforcement learning, we further optimize the protocol tailored to the Rydberg atom array, and provide estimates on gate fidelities necessary for our scheme to be useful for improving the lifetime of logical qubits and enabling more reliable quantum computation.