ReloQate: Transient Drift Detection and In-Situ Recalibration in Surface Code Quantum Error Correction

TL;DR

DFR-based prediction is demonstrated to be an effective LER predictor, and remapping as a spatially efficient and timely mitigation response for small code distances is demonstrated, both of which are significant steps in furthering practical QEC.

Abstract

Quantum error correction (QEC) promises to exponentially suppress qubit noise, but typically assumes spatially-uniform and temporally-constant noise rates. However, real quantum hardware exhibits variation in noise levels over time, which will be amplified by QEC if not addressed. To mitigate this drift in error rates, we leverage transient information readily available in surface code quantum error correction to predict logical error rates (LER) in real time. We infer a prediction model by sampling physical error rates from real hardware, and mapping detector fire rate (DFR), or parity of stabilizer measurements across QEC rounds, to LER. This allows for on-the-fly LER predictions without the typical characterization overhead required to determine LER. This method can easily be extended to other stabilizer codes. Importantly, we observe that this prediction should be accurate yet conservative (i.e. give an upper estimate) to enable appropriately fast responses to real-time physical error changes. That is, responses should be executed marginally ahead of time to allow for their execution to complete, and minimize time spent (ideally none) above intolerable error rates. More importantly, we pair this predictor with a scheme which remaps drifted logical qubits to fresh tiles in a patch-based architecture while their original tiles are recalibrated. Our results demonstrate DFR-based prediction to be an effective LER predictor, and remapping as a spatially efficient and timely mitigation response for small code distances, both of which are significant steps in furthering practical QEC.

Figures (15)

• Figure 1: Timeline of a drifted qubit. During $d$ rounds of error correction, a detector fire rate (DFR) is accrued for a surface code. Detectors are fired when measurements of a parity qubit in a given round don't agree with prior measurements of that same parity qubit. The DFR is the fraction of detectors that fire (the number of fired detectors divided by the total number of detectors). Each DFR is stored within a DFR buffer as the program executes, indexed by the time it was recorded. Higher DFR is strongly correlated with an increase in LER. If multiple recent DFRs are high, it's likely the underlying physical qubits have drifted. Thus, we use the mean of all DFRs in the buffer to predict the LER of the surface code tile. If the prediction is above some target LER threshold, a remap operation is triggered. Here, $q_0$ triggers a remap operation as the mean DFR of the DFR buffer exceeded the threshold. $q_0$ is moved away to a separate tile, or reloqation target, that is below target LER. After $q_0$ has moved away, $q_0's$ original tile is disabled while it undergoes recalibration. Once complete, that tile may once again be used, and is reinitialized for use as a reloqation target.
• Figure 2: $d=3$ surface code undergoing a remap operation. Stored on the left-most tile of the first row is a $d=3$ surface code. Each black dot denotes a physical qubit. Black dots at intersections indicate data qubits, while black dots within solid colors or on the round edges indicate parity qubits. The surface code first expands into the far right tile in the first row. Expansion is performed such that its edge orientation (solid vs. dashed) is consistent with the original edges of the patch. In the next step, the surface code patch contracts itself (also maintaining edge consistency) by measuring away any qubits on tiles passed. The expansion operation requires a single cycle, but contraction is completed constant time (independent of cycle duration).
• Figure 3: Examples of the drift noise models considered in this work. The slow model exhibits drift on the timescale of hours, while the volatile model varies on the timescale of seconds. (a) Lognormally-distributed physical qubit drift rates for the slow model, matching the distribution observed on an IBM device in Ref. caliscalpel. (b) Resulting logical error rate drift over time for $d=7$ surface code patches consisting of unevenly-drifting physical qubits. (c) Example trace of detector error rate over time from Google's surface code experiment google_qec_2024. (d) Resulting logical error rate traces over time for $d=7$ surface code patches with similarly-varying detector rates.
• Figure 4: Left: Detector fire rates and logical error rates sampled from instances of surface codes with lognormally-distributed physical error rates. The detector fire rate of a surface code patch can be used to accurately predict the logical error rate of the patch without directly measuring it. Right: Prediction performance of an LER trace for a $d=3$ surface code under various buffer sizes over time (cycles). Larger DFR buffer sizes are generally better performing.
• Figure 5: The fit to the DFR vs. LER data yield a predictor that can estimate the LER for a given observed DFR. We can tune the parameter $\alpha$ to determine the width of the prediction confidence interval, which allows us to tune the sensitivity of the drift detection module. A lower value of $\alpha$ yields a larger confidence interval, making the detection module more sensitive.