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

TL;DR

Leakage to non-computational states poses a major challenge for superconducting QEC. The authors introduce a leakage reduction unit (LRU) that runs concurrently with qubit measurement, resetting leakage without adding time cost, and achieve $98.4\%$ leakage removal with $3$-level readout (3RO) readout improving decoding. They demonstrate the approach in two QEC benchmarks—a distance-3 memory code (Repetition-5) and a stability code (Stability-7)—showing that LRU combined with 3RO provides the best logical performance across controlled leakage, including in the presence of neural-network decoding. The zero-overhead nature and compatibility with standard cQED hardware suggest a practical path toward mitigating leakage in scalable quantum processors and near-term QEC implementations.

Abstract

Leakage to non-computational states is a source of correlated errors in both time and space that limits the effectiveness of quantum error correction (QEC) with superconducting circuits. We present and experimentally demonstrate a high-fidelity, leakage reduction unit (LRU) operating concurrently with transmon measurement without incurring time overhead. Adapted from double-drive reset of population (DDROP), the protocol utilizes simultaneous drives on the transmon and its readout resonator, leveraging the dispersive shift to create a directional process that returns the transmon to the computational subspace. The LRU achieves a 98.4% leakage removal fraction without compromising the computational-state assignment fidelity (99.2%). We combine LRU-enhanced measurement and neural-network decoding to successfully suppress logical error rates in both memory and stability QEC experiments without any post-selection.

Figures (13)

• Figure 1: Simplified schematic of the leakage reduction unit (LRU) protocol. The energy levels of the coupled transmon-resonator system are shown, with states labeled as $|$Transmon, Resonator$\rangle$. The protocol utilizes two simultaneous drives: a transmon drive at the frequency of the $\left| e \right\rangle\leftrightarrow\left| f \right\rangle$ transition when there is no photon in the resonator, $\omega_{ef,0}$, and a resonator drive at the resonator frequency when the transmon is in $\left| e \right\rangle$, $\omega_{r,e}$. The process begins with the system in an arbitrary leakage state $\left| f, n \right\rangle$. The resonator population quickly decays to zero at a rate $\kappa$, resulting in the state $\left| f, 0 \right\rangle$. The transmon drive, which is resonant with the $\left| f, 0 \right\rangle\leftrightarrow\left| e, 0 \right\rangle$ transition, then transfers the population to $\left| e, 0 \right\rangle$. Subsequently, the resonator drive populates the resonator, moving the system to a final steady state, $\left| e, m \right\rangle$. The directionality of this process is ensured by the dispersive shift, 2$\chi$. As photons accumulate in the resonator, the transmon transition frequency shifts. The original transmon drive at $\omega_{ef,0}$ becomes off-resonant with the $\left| e, m \right\rangle\leftrightarrow\left| f, m \right\rangle$ transition by an amount 2$m\chi$, preventing the system from being re-excited to the $\left| f \right\rangle$ state manifold. Likewise, the resonator drive is off-resonant when the transmon is in $\left| f \right\rangle$, preventing photon accumulation. Once the drives are removed, the system quickly decays to $\left| e, 0 \right\rangle$, effectively removing leakage from $\left| f \right\rangle$.
• Figure 2: Calibration of the LRU pulse. (a) The experimental pulse sequence used for calibration. The transmon is first prepared in the $\left| g \right\rangle$, $\left| e \right\rangle$, or $\left| f \right\rangle$, followed by the LRU-enhanced measurement. A delay, $t_{\mathrm{delay}}$, is introduced between the resonator and transmon drives to enable three-level readout. Finally, population tomography is performed using a standard measurement with readout errors corrected. (b--e) Performance versus drive parameters. Each point averages over 4,000 shots. In (c), three distinct behaviors are observed: a coherent region at low resonator power where Rabi oscillations dominate; a central working region where balanced drives enable the intended LRU process; and a high power region where the strong resonator drive populates the resonator with photons exceeding the critical photon number of the dispersive regime. In (d, e), the trade-off between assignment fidelity and leakage removal is explored. In (d), the assignment fidelity increases with $t_{\mathrm{delay}}$ before being limited due to transmon relaxation. In (e), the residual $\left| f \right\rangle$ population increases as $t_{\mathrm{delay}}$ gets longer; it rises slowly at first while photons build up in the resonator, then rises more quickly as the reduced time for the removal process becomes the dominant factor. The white dashed lines indicate contours for infidelity (0.07) and residual population (0.02). The yellow star marks the final choice of parameters.
• Figure 3: Performance comparison of LRU-enhanced and standard measurements. The LRU-enhanced measurement (left column) is compared to a standard measurement (right column), which is implemented by turning off the transmon drive while keeping all other parameters identical. (a, b) Single-shot I-Q data with 4,000 shots for each state. (c, d) Readout assignment matrices, showing the probability of assigning a measurement outcome given a prepared state. The average assignment fidelities are 98.2% (LRU) and 98.3% (standard). (e, f) Population transfer matrices, showing the probability of the transmon being in a final state given its initial state. The matrix in (e) demonstrates a leakage removal fraction of 98.4%.
• Figure 4: Memory experiment of a distance-3 bit-flip repetition code. (a) Schematic showing the five qubits used, with data qubits in red and measure qubits in green. Quantum circuit consisting of qubit initialization, $R$ rounds of stabilizer measurements, and final measurement. (b, c) Logical error probability ($p_L$) as a function of the number of QEC rounds ($R$) at baseline leakage ($\widetilde{L_1}=1.0\%$) and intermediate leakage ($\widetilde{L_1}=3.6\%$). Performance is compared for protocols with LRU (orange) and without (No LRU, blue), using either a three-level (3RO, solid lines, circles) or two-level (2RO, dashed lines, triangles) readout on the measure qubits. Results are averaged over all basis states $|i, j, k\rangle$. (d) Extracted logical error rate per round ($\varepsilon_L$) as a function of the estimated leakage rate ($\widetilde{L_1}$). The combination of LRU with 3RO consistently provides the lowest error rate, with the advantage growing as leakage increases.
• Figure 5: Stability-7 experiment. (a) Schematic of the seven qubits used and quantum circuit. Device and conventions are the same as in Fig. 4. CZ gates with narrower horizontal spacing between them are executed simultaneously. (b, c) Logical error probability ($p_L$) versus QEC rounds ($R$) at baseline leakage ($\widetilde{L_1}=1.2\%$) and intermediate leakage ($\widetilde{L_1}=3.7\%$). The legend is the same as in Fig. 4. The data (scatters) is fit to $p_L = A e^{-\gamma R}$ starting from round 10 (solid lines). (d, e) Extracted fitting parameters $\gamma$ (higher is better) and $A$ (lower is better) as a function of the leakage estimate $\widetilde{L_1}$. With the LRU, the error suppression factor $\gamma$ remains stable against increasing leakage. The combination of LRU with 3RO consistently provides the best performance for both $\gamma$ and $A$.