Syndrome-Resolved Decoding of Qubit Readout Errors

The gist The Readout Error Decoder (RED) converts repeated thresholded binary records into a channel-resolved error budget, identifying limiting readout error channels without requiring dedicated discrimination of non-computational states.

Introduction and Motivation

Conventional benchmarks like measurement fidelity and repeatability metrics fail to resolve the individual contributions of different readout error mechanisms, such as assignment errors, bit flips within the computational subspace, and leakage to non-computational states The paper introduces RED, which converts repeated thresholded binary records into a channel-resolved error budget This approach is inspired by fault-tolerant quantum error correction where syndrome histories are decoded to infer underlying errors.

RED Protocol and Syndrome Classification

The RED protocol interleaves repeated readouts with a fixed operation G ∈ I, X, X-τ-X to compare the expected logical record li with the measured record mi. The correlation record is defined as Ci = 1 − 2 [(li−1 ⊕ li) ⊕ (mi−1 ⊕ mi)]. Consecutive broken correlations are grouped by run length into syndromes S1, S2, and S3+, corresponding to one, two, and three or more broken correlations respectively. The decoder dictionary maps these syndromes to error channels: Assignment error is associated with S2, Bit-flip error with S1, and Leakage error with S3+.

Error Channel Validation and Characterization

The RED protocol is validated using controlled error injections, such as a π01 pulse for bit-flip injection, which shows the extracted bit-flip rate increases approximately linearly with Pb with a slope close to unity. Similarly, leakage injection via a π12 pulse demonstrates that the extracted leakage error from the X-τ-X sequence increases linearly with Pf with a fitted slope of 0.887. Furthermore, varying readout duration (tRO) reveals error dependencies; assignment-error rates decrease rapidly with increasing tRO as SNR improves, while bit-flip errors increase approximately linearly over the fitted range.

Leakage Detection Regimes

The paper distinguishes between long-lived and short-lived leakage based on their persistence relative to the readout cycle. Long-lived leakage is identified as S3+ from the X sequence, which occurs when τleak ≫ tcycle. Short-lived leakage is probed with an inter-readout gate sequence like X-τ-X, which detects the excess S1 under this sequence. The delay τ between two π01 pulses is essential for detecting short-lived leakage, as it must be several times the leakage lifetime to fully capture it.

Device Specific Results and Limitations

The RED protocol was demonstrated on fluxonium and transmon qubits across distinct leakage-lifetime regimes. The resulting channel-resolved error budget identifies the limiting readout error channel, showing that similar total error rates can arise from distinct underlying mechanisms. The syndrome-to-channel mapping has limitations because different error processes can produce the same syndrome, and overlapping errors introduce higher-order contamination. However, the leading error channel and qualitative error hierarchy remain informative even in this regime. The framework is suggested to be adaptable to other platforms with repetitive QND measurement.

Conclusion

RED decodes repeated binary readout records into a channel-resolved error budget for assignment, bit-flip, and leakage errors, resolved by the g⟩ and e⟩ branches. The protocol successfully separates assignment from bit-flip errors and recovers both rates. By separating the total error into physical error channels, RED reveals the dominant readout-error mechanism on each device, information not available from Measurement infidelity or QNDness alone. The protocol covers both lifetime regimes with the same decoder. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium. The excess S3+ rates from both branches also remain at the noise floor, showing that this short-lived leakage is revealed by the excess S1 but not by S3+. The excess-S1 values provide the fluxonium short-lived leakage entry in Table III. The two devices discussed show these two lifetime regimes: long-lived leakage on the transmon and short-lived leakage on the fluxonium.

1. Bold channel-resolved error budgeting: The improved AI system can move beyond conventional measurement fidelity and repeatability metrics by using RED to identify the limiting readout error channel, providing a channel-resolved error budget.

2. Targeted readout optimization: This capability allows the AI to guide hardware improvements by identifying which specific mechanisms limit performance, as the paper states this provides a basis for targeted readout optimization across different qubit modalities.

3. Cross-platform error characterization: The system can apply the same decoding principle to new architectures, as RED can be adapted to other quantum platforms with repeated state detection and leakage outside a chosen computational subspace, including semiconductor spin qubits, trapped ions, and neutralatom arrays.

4. Leakage regime identification: The AI can distinguish between different physical error dynamics by classifying leakage into long-lived leakage (S3+) versus short-lived leakage (excess S1 under X-τ-X sequence), allowing it to probe the underlying physics relevant to specific qubit types.

5. Dynamic readout parameter tuning: By using the extracted error rates dependent on readout duration, tRO, the system can determine optimal measurement times to minimize total error, as shown in Table III where devices are characterized at the readout duration that minimizes the total RED error for each device.

Readout errors in superconducting qubits include incorrect state assignment, bit flips within the computational subspace, and leakage to non-computational states. These errors require different mitigation strategies, yet conventional measurement fidelity and repeatability metrics do not resolve their individual contributions. Previous repeated-readout studies have shown that temporal correlations reveal additional information about readout errors. Here we introduce the Readout Error Decoder (RED), which converts repeated thresholded binary records into a channel-resolved error budget. Controlled error injections validate the channel-specific response of the decoder. We demonstrate RED on both fluxonium and transmon qubits and across distinct leakage-lifetime regimes. RED identifies the error channels limiting readout performance without requiring dedicated discrimination of non-computational states, providing a basis for targeted readout optimization across different qubit modalities.