🔬 mesoscale physics

Recovery dynamics of a gap-engineered transmon after a quasiparticle burst

This study experimentally demonstrates that while gap engineering in 3D transmon qubits reduces quasiparticle burst detection rates by a factor of five, the limited improvement compared to theoretical expectations is attributed to the slow thermalization of phonons following ionizing radiation events.

Original authors: Heekun Nho, Thomas Connolly, Pavel D. Kurilovich, Spencer Diamond, Charlotte G. L. Bøttcher, Leonid I. Glazman, Michel H. Devoret

Published 2026-02-06

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CC BY 4.0

Original authors: Heekun Nho, Thomas Connolly, Pavel D. Kurilovich, Spencer Diamond, Charlotte G. L. Bøttcher, Leonid I. Glazman, Michel H. Devoret

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a supercomputer built from tiny, super-cooled electrical circuits called transmons. These circuits are designed to hold delicate quantum information, like a spinning coin that is both heads and tails at the same time. For this computer to work, the coin must keep spinning without falling over.

However, the universe is full of invisible "bullets" (ionizing radiation like cosmic rays) that occasionally hit the computer's chip. When one of these bullets strikes, it creates a chaotic ripple effect, like a stone thrown into a calm pond. This ripple breaks the delicate quantum state, causing the computer to make errors.

This paper investigates how to stop these ripples from ruining the computer, specifically by looking at a design trick called "gap engineering."

The Problem: The "Quasiparticle" Storm

When a high-energy particle hits the chip, it creates a shower of high-energy sound waves (phonons). These sound waves smash into the superconducting metal, breaking apart pairs of electrons that were working together. These broken pieces are called quasiparticles.

Think of quasiparticles as mischievous gremlins. When they are calm, they sit quietly. But when a radiation burst happens, they get excited and start running around. If a gremlin jumps across a tiny bridge in the circuit (the Josephson junction), it steals energy from the qubit, causing the "coin" to fall over. This is a burst event.

The Proposed Solution: The "Gap" Barrier

The researchers tried to build a wall to stop these gremlins. They used a technique called gap engineering.

Imagine the bridge the gremlins need to cross has two sides:

Side A: A low wall (low energy gap).
Side B: A very high wall (high energy gap).

The idea was simple: If the wall on Side B is high enough, the gremlins won't have enough energy to jump over it. They would get stuck on Side A, and the qubit would remain safe. By making the difference in wall height large, they hoped to stop almost all the gremlins from crossing.

The Experiment: Testing the Wall

The team built three different versions of these bridges:

Small Gap: The walls are almost the same height. Gremlins can easily jump back and forth.
Medium Gap: The wall on one side is slightly higher.
Big Gap: The wall on one side is much, much higher.

They monitored these bridges for hours, waiting for radiation bursts to happen. They wanted to see if the "Big Gap" bridge stopped the gremlins better than the others.

The Surprise: The Wall Didn't Work as Expected

The researchers found that the "Big Gap" design did help, but not nearly as much as they hoped.

The Expectation: If the gremlins were calm and cold (like they usually are), the Big Gap should have stopped them almost 10,000 times more effectively than the Small Gap.
The Reality: The Big Gap only stopped them about 5 times better than the Small Gap.

Why didn't the wall work?

The Real Culprit: The "Hot Floor"

The paper reveals a hidden problem. When a radiation bullet hits the chip, it doesn't just create gremlins; it also heats up the entire floor (the substrate) of the chip.

Think of it like this:

The gremlins (quasiparticles) are trying to jump a wall.
Usually, they are cold and tired, so they can't jump a high wall.
But when the radiation hits, the floor gets hot (reaching about 90 millikelvin, which is very cold to us, but "hot" for these tiny particles).

Because the floor is hot, the gremlins get a sudden burst of energy. They become like sprinters on a hot day—they get enough energy to jump over even the Big Gap wall.

The researchers found that the floor stays hot for a long time (about 6 milliseconds) because the heat gets trapped in the chip and escapes very slowly. It's like trying to cool down a frying pan that is sitting on a thick, insulating blanket; the heat just won't leave.

The Conclusion

The paper concludes that while building a "Big Gap" wall is a good idea, it isn't enough on its own. The wall is only effective if the gremlins stay cold. Since the radiation impact heats up the floor and keeps the gremlins energetic, they can still jump the wall.

To truly fix this, the researchers suggest two things:

Make the wall even higher (use different materials with a bigger gap).
Most importantly: Fix the "blanket." They need to find a way to let the heat escape the chip much faster so the floor stays cold, keeping the gremlins too tired to jump the wall.

In short: You can build a taller fence, but if the ground gets hot enough to give the intruders a running start, they will still get over it. You need to cool the ground down, too.

Technical Summary: Recovery Dynamics of a Gap-Engineered Transmon After a Quasiparticle Burst

Problem Statement
Superconducting quantum processors rely on quantum error correction (QEC) protocols that assume errors are uncorrelated in space and time. However, ionizing radiation impacts create bursts of high-energy phonons that break Cooper pairs, generating a transient, non-equilibrium density of quasiparticles (QPs) across multiple qubits simultaneously. These "burst" events cause correlated errors and temporary degradation of qubit coherence, posing a significant threat to the scalability of QEC. While "gap engineering"—creating a superconducting energy gap difference ( $\delta\Delta$ ) across a Josephson junction—has been shown to suppress QP tunneling for resident (steady-state) QPs, its efficacy during the high-energy, non-equilibrium conditions of a radiation burst remains an open question. Specifically, it is unclear if the gap difference can prevent QP tunneling when the phonon bath itself is driven far from equilibrium.

Methodology
The authors experimentally investigated this problem using 3D aluminum transmon qubits fabricated on sapphire substrates. They engineered three distinct devices with different Josephson junction film thickness pairs, creating varying superconducting gap differences ( $\delta\Delta$ ) ranging from approximately 0 GHz to 10 GHz.

Gap Characterization: The authors first benchmarked the gap engineering by measuring the temperature dependence of charge-parity-switching rates in the steady state. By fitting these rates to a theoretical model of QP tunneling, they extracted the precise $\delta\Delta$ and the resident non-equilibrium QP density for each device.
Burst Detection: To simulate and detect radiation bursts, the team continuously monitored the qubit state, repeatedly projecting it into the excited state $|1\rangle$ and measuring relaxation events ( $|1\rangle \to |0\rangle$ ) every 5.7 $\mu$ s. Bursts were identified as windows (1 ms duration) containing an anomalous excess of relaxation events compared to the Poissonian background.
Recovery Dynamics: Upon identifying a burst, the authors analyzed the time evolution of the qubit relaxation rate ( $\Gamma_{10}$ ) and excitation rate ( $\Gamma_{01}$ ) to extract the effective qubit temperature ( $T_q$ ) and QP density ( $x_{QP}$ ) during the recovery phase.

Key Results

Limited Suppression of Burst Detection: Gap engineering reduced the burst detection rate by a factor of five in the device with the largest gap difference ( $\delta\Delta \approx 8.2$ GHz) compared to the device with negligible gap difference.
Discrepancy with Steady-State Expectations: This five-fold reduction falls four orders of magnitude short of the suppression observed for resident QPs in the steady state. In the steady state, the large $\delta\Delta$ effectively blocks QP tunneling because the QPs are thermalized to the fridge base temperature ( $\sim 25$ mK).
Elevated Substrate Temperature: The authors attribute the limited suppression during bursts to a transient elevation of the effective chip temperature. By analyzing the ratio of relaxation to excitation rates, they determined that during a burst, the effective qubit temperature spikes to approximately 90 mK.
Phonon Thermalization Bottleneck: The elevated temperature persists for a timescale of $\sim 6$ ms, which is roughly 10 times longer than the decay time of the QP density itself ( $\sim 0.7$ ms). This indicates that the "hot" phonons generated by the radiation impact are trapped in the substrate and escape slowly, likely limited by the thermal link through the chip clamps.
Mechanism of Failure: At $\sim 90$ mK, the thermal energy ( $k_B T$ ) is sufficient to allow QPs to overcome the gap difference barrier ( $\delta\Delta - hf_q$ ), rendering the gap engineering less effective at preventing tunneling-induced relaxation.

Significance and Claims
The paper establishes that while gap engineering is a powerful tool for suppressing steady-state QP-induced decoherence, its ability to mitigate correlated errors from radiation bursts is fundamentally limited by the thermalization dynamics of the substrate. The authors claim that the slow escape of hot phonons from the chip creates a transient thermal environment where the gap difference is insufficient to block QP tunneling.

Consequently, the authors argue that future strategies to suppress burst-induced errors must address two fronts:

Increasing the Gap Difference: Utilizing materials with higher superconducting gaps (e.g., granular aluminum) to ensure $\delta\Delta \gg k_B T$ even during the transient heating phase.
Improving Phonon Escape: Enhancing the thermal link between the chip and the cryostat base plate or incorporating normal-metal patches to absorb hot phonons, thereby accelerating the cooling of the substrate during and after an impact.

The work highlights that mitigating correlated errors in large-scale quantum processors requires not only qubit-level engineering but also a holistic approach to the thermal management of the entire chip-substrate system.