Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit

Leakage from the computational subspace is a damaging source of noise that degrades the performance of most qubit types. Unlike other types of noise, leakage cannot be overcome by standard quantum error correction techniques and requires dedicated leakage reduction units. In this work, we study the effects of leakage mobility between superconducting qubits on the performance of a quantum stability experiment, which is a benchmark for fault-tolerant logical computation. Using the Fujitsu Quantum Simulator, we perform full density-matrix simulations of stability experiments implemented on the surface code. We observe improved performance with increased mobility, suggesting leakage mobility can itself act as a leakage reduction unit by naturally moving leakage from data to auxiliary qubits, where it is removed upon reset. We compare the performance of standard error-correction circuits with “patch wiggling”, a specific leakage reduction technique where data and auxiliary qubits alternate their roles in each round of error correction. We observe that patch wiggling becomes inefficient with increased leakage mobility, in contrast to the improved performance of standard circuits. These observations suggest that the damage of leakage can be overcome by stimulating leakage mobility between qubits without the need for a dedicated leakage reduction unit.

💡 Research Summary

The paper investigates how leakage – the process by which a qubit leaves the computational {|0⟩,|1⟩} sub‑space – can be mitigated in superconducting transmon devices without dedicated leakage‑reduction units (LRUs). Leakage is especially harmful because it is long‑lived and can propagate errors to neighboring qubits, and standard quantum error‑correction (QEC) codes have no built‑in mechanism to detect or correct it. Traditionally, LRUs are either hardware‑based (fast reset circuits) or circuit‑based (periodically swapping the roles of data and auxiliary qubits so that every qubit is reset). Both approaches add noise or increase circuit overhead.

The authors focus on a physical property of superconducting platforms: during a two‑qubit CZ gate, the higher‑frequency qubit can leak to the non‑computational |2⟩ state, and this leaked excitation can subsequently move to a neighboring qubit. They model this “leakage mobility” with a probability parameter L_m, while the intrinsic leakage probability per CZ gate is L_1. Using realistic parameters (L_1 = 0.1 %–0.5 %, L_m = 0.5 %–12.5 %) they construct a full density‑matrix simulation of a surface‑code patch (4 × 2 qubits) on the Fujitsu Quantum Simulator. Each physical qubit is represented as a qutrit (three‑level system) by encoding it into two simulator qubits, allowing them to capture both computational errors and leakage dynamics.

Two circuit variants are compared:

1. Standard (non‑wiggled) circuits – data qubits retain their role throughout, while auxiliary qubits are measured and reset after each QEC round.
2. Patch‑wiggling circuits – after every round the roles of data and auxiliary qubits are swapped, ensuring that every qubit is periodically reset (the most common low‑overhead circuit‑based LRU for surface codes).

The authors use a minimum‑weight perfect‑matching (MWPM) decoder. Because the decoder is not leakage‑aware, any measurement outcome of “2” (the leaked state) is treated as “1”. Logical failure probability P_fail is obtained from many Monte‑Carlo shots, and an exponential suppression rate Λ_s is extracted from the relation
P_fail ≈ P_SPAM·(Λ_s)^{‑n_r/2}, where n_r is the number of QEC rounds.

The key findings are:

• Increasing leakage mobility (L_m) improves the performance of standard circuits. As L_m grows, leaked excitations are more likely to hop from data qubits to auxiliary qubits, where they are removed by the regular reset step. Consequently, the error‑suppression rate Λ_s rises sharply, indicating stronger exponential decay of logical errors with additional rounds.
• Patch‑wiggling is beneficial only at low mobility. When L_m is small, swapping roles allows each qubit to be reset frequently, limiting the time a leaked qubit can corrupt the code. However, at higher L_m the same swapping repeatedly moves leaked excitations back into data qubits, negating the advantage and even degrading performance.
• The crossover occurs around L_m ≈ 6 % for the parameters studied; beyond this point, standard circuits outperform wiggled ones by a substantial margin. This trend holds for both low (L_1 = 0.1 %) and higher (L_1 = 0.5 %) intrinsic leakage rates.

These results demonstrate that leakage mobility itself can act as a natural LRU: by engineering the hardware (frequency layout, CZ gate timing, and coupling) to promote leakage hopping, one can rely on the existing reset of auxiliary qubits to cleanse the system. This eliminates the need for extra circuit layers or specialized hardware, simplifying the architecture and reducing overhead.

The paper concludes by suggesting that future work should explore larger code distances, different noise models, and experimental validation of engineered leakage mobility. If successful, this approach could become a practical tool for scaling superconducting quantum processors toward fault‑tolerant operation while keeping hardware complexity low.