ERASER: Towards Adaptive Leakage Suppression for Fault-Tolerant Quantum Computing

Quantum error correction (QEC) codes can tolerate hardware errors by encoding fault-tolerant logical qubits using redundant physical qubits and detecting errors using parity checks. Leakage errors occur in quantum systems when a qubit leaves its computational basis and enters higher energy states. These errors severely limit the performance of QEC due to two reasons. First, they lead to erroneous parity checks that obfuscate the accurate detection of errors. Second, the leakage spreads to other qubits and creates a pathway for more errors over time. Prior works tolerate leakage errors by using leakage reduction circuits (LRCs) that modify the parity check circuitry of QEC codes. Unfortunately, naively using LRCs always throughout a program is sub-optimal because LRCs incur additional two-qubit operations that (1) facilitate leakage transport, and (2) serve as new sources of errors. Ideally, LRCs should only be used if leakage occurs, so that errors from both leakage as well as additional LRC operations are simultaneously minimized. However, identifying leakage errors in real-time is challenging. To enable the robust and efficient usage of LRCs, we propose ERASER that speculates the subset of qubits that may have leaked and only uses LRCs for those qubits. Our studies show that the majority of leakage errors typically impact the parity checks. We leverage this insight to identify the leaked qubits by analyzing the patterns in the failed parity checks. We propose ERASER+M that enhances ERASER by detecting leakage more accurately using qubit measurement protocols that can classify qubits into $|0\rangle, |1\rangle$ and $|L\rangle$ states. ERASER and ERASER+M improve the logical error rate by up to $4.3\times$ and $23\times$ respectively compared to always using LRC.