Improved error correction with leakage reduction units built into qubit measurement in a superconducting quantum processor

Technical Summary: Improved Error Correction with Leakage Reduction Units in Superconducting Quantum Processors

Problem Statement
Leakage of population out of the computational subspace (e.g., from the $|e\rangle$ state to the $|f\rangle$ state in transmon qubits) is a critical error source in superconducting quantum circuits. Unlike standard Pauli errors, leakage events violate the core assumptions of stabilizer codes like the surface code, as they cannot be mapped to the Pauli framework. Furthermore, leakage is damaging because it can persist for multiple Quantum Error Correction (QEC) cycles, creating temporally correlated errors, and can propagate through two-qubit gates to create spatially correlated errors. While hardware design and leakage-tolerant codes offer partial solutions, active mitigation via Leakage Reduction Units (LRUs) is often hindered by the requirement for dedicated time steps within the QEC cycle, which introduces idle time and increases the overall physical error rate.

Methodology
The authors experimentally demonstrate a high-fidelity, time-efficient LRU that operates concurrently with transmon measurement, incurring no time overhead. The protocol is adapted from the Double-Drive Reset of Population (DDROP) technique and is implemented on a superconducting processor with a circuit quantum electrodynamics (cQED) architecture.

• Mechanism: The LRU utilizes simultaneous microwave drives on the transmon and its readout resonator.
  • A transmon drive is applied at the $|e\rangle \leftrightarrow |f\rangle$ transition frequency ($\omega_{ef,0}$) when the resonator is empty.
  • A resonator drive is applied at the resonator frequency when the transmon is in $|e\rangle$ ($\omega_{r,e}$).
  • The process relies on the dispersive shift ($2\chi$). As the resonator drive populates the resonator with photons, the transmon transition frequency shifts. This shift detunes the transmon drive from the $|e\rangle \leftrightarrow |f\rangle$ transition, effectively locking the system in the computational subspace and preventing re-excitation to $|f\rangle$.
• Concurrent Operation: The LRU is integrated directly into the measurement pulse sequence. A delay ($t_{delay}$) is introduced between the resonator and transmon drives to allow for a distinct readout window before the leakage removal begins. This enables a three-level readout (3RO) that distinguishes $|g\rangle$, $|e\rangle$, and $|f\rangle$ without extending the measurement duration.
• Calibration: Parameters (drive frequencies, amplitudes, and $t_{delay}$) were optimized using a Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to maximize the geometric mean of assignment fidelity and leakage removal efficiency.

Key Results

• Leakage Removal Efficiency: The LRU achieves a leakage removal fraction of 98.4% (returning population from $|f\rangle$ to $|e\rangle$) without compromising the assignment fidelity between computational states $|g\rangle$ and $|e\rangle$ (99.2%).
• Readout Fidelity: The average 3RO assignment fidelity for the LRU-enhanced measurement is 98.2%, nearly identical to the standard measurement (98.3%). The protocol successfully distinguishes the $|f\rangle$ state, transforming a non-Pauli error into a heralded error for the decoder.
• QEC Benchmarks: The LRU-enhanced measurement was integrated into two QEC experiments:
  1. Memory Experiment (Repetition-5): A distance-3 bit-flip repetition code. Combining LRU with 3RO yielded the lowest logical error rate across all leakage levels. At a baseline leakage rate of 1.0%, 3RO alone reduced the logical error rate by 11.1%; adding LRU provided further improvements at higher leakage rates.
  2. Stability Experiment (Stability-7): A 7-qubit experiment testing logical observable movement (analogous to lattice surgery). The LRU successfully mitigated the propagation of leakage-induced correlated errors. The error suppression factor ($\gamma$) remained stable against increasing leakage rates when LRU was used, whereas it degraded significantly without it. The combination of LRU and 3RO provided the best performance, increasing $\gamma$ by up to 90% at intermediate leakage levels compared to standard 2RO without LRU.

Significance and Claims
The paper claims that this work provides a practical, zero-overhead method for combating leakage, one of the most detrimental error channels in superconducting processors. By integrating the reset mechanism directly into the measurement pulse, the authors demonstrate that active error removal can be combined with richer syndrome information (3RO) to significantly improve logical performance.

The authors emphasize that their results show QEC without post-selection performs best when combining the LRU with 3RO. This approach transforms leakage from a persistent, correlated error into a tractable, heralded error, allowing decoders (specifically neural networks in this work) to correct for it more effectively. The technique is broadly applicable to current superconducting processors as it only requires a dispersively coupled readout resonator. The authors conclude that this method is a valuable tool for improving the performance and scalability of near-term QEC implementations, though they note that future work is needed to characterize microwave crosstalk in parallel LRU deployments and to optimize system parameters for even lower physical error rates.