Accurate Leakage Speculation for Quantum Error Correction

TL;DR

This work tackles leakage errors in quantum error correction by introducing GLADIATOR, a graph-based, model-driven leakage-detection framework that operates offline to calibrate a code-aware error-propagation graph and online to label syndrome patterns in real time. Unlike prior heuristic-driven methods, GLADIATOR combines leakage and non-leakage transition graphs and temporal syndrome history to selectively trigger Leakage Reduction Circuits, dramatically reducing false positives and leakage accumulation. The approach generalizes from surface codes to color codes and LDPC/HGP families, achieving up to 3x fewer LRCs, 16% lower logical error rate, and 1.7x–3.9x faster QEC cycles across code distances and hardware platforms. These improvements translate into faster, more reliable fault-tolerant quantum computation with broader applicability to diverse quantum architectures.

Abstract

Quantum Error Correction (QEC) protects qubits against bit- and phase-flip errors in the |0> or |1> subspace, but physical qubits can also leak into higher energy levels (e.g., |2>). Leakage is especially harmful, as it corrupts all subsequent syndrome measurements and can spread to neighboring qubits. Detecting leakage on data qubits is particularly challenging, since they are never measured directly during QEC cycles. Prior work, such as eraser, addresses this by inferring leakage from syndrome patterns using a fixed heuristic. However, this approach often misclassifies benign syndromes, triggering excessive leakage-reduction circuits (LRCs). Because LRCs are themselves noisy and slow, these false triggers lengthen QEC cycles and inflate logical error rates. We propose gladiator, a general and adaptable leakage speculation framework that works across surface code, color code, and qLDPC codes. Offline, gladiator builds a code-aware error-propagation graph calibrated to device data. Online, it classifies each syndrome in a few nanoseconds and schedules LRC only when the observed pattern is provably leakage-dominated. This precise speculation eliminates up to 3x (and on average 2x) unnecessary LRCs, shortens QEC cycles, and suppresses false positives at their source. Evaluated on standard fault-tolerant benchmarks, gladiator delivers 1.7x-3.9x speedups and 16% reduction in logical error rate, advancing the efficiency of fault-tolerant quantum computing.

Figures (14)

• Figure 1: (a) Proposed gladiator Design. (b) Comparing the effectiveness of gladiator and eraser using False Negative (FN), False Positive (FP), and LRC utilization. (c) The leakage population for surface code with code distance d =11, when executed for $100d$ QEC rounds, assuming the probability of non-leakage error $p_{e}=10^{-3}$ and probability of leakage is $p_{leak} = lr\times p_{e} = 10^{-4}$.
• Figure 2: (a) Qubit device with computational basis corresponding to $\ket{0}$,$\ket{1}$ and leaked basis corresponds to higher energy quantum levels. (b) Surface code of distance 3, with black qubits corresponds to data qubits and others corresponding to the parity qubits. (c) Syndrome Generation for LRC insertion using Leakage Speculation Block (LSB).
• Figure 3: Leakage Injection Experiment on IBM hardware- (a) The probability of the measured state when circuit (b), a single physical CNOT with one of the qubits leaked, is executed. (c) The leakage population of measured qubit when circuit. (d) with one physical CNOT is repeatedly executed. We ran 10,000 shots using Qiskit Pulse QiskitIBMGuide.
• Figure 4: (a) Qubit coloring (Dotted lines as color groups) for round-robin LRC scheduling in Staggered-LRC. (b) Logical Error Rate (LER) across open-loop policies and ERASER+M.
• Figure 5: Unnecessary LRCs and leakage instances of (a) eraser+m (b) gladiator+m for 4-bit eraser patterns