⚛️ quantum physics

Disentangling the Impact of Quasiparticles and Two-Level Systems on the Statistics of Superconducting Qubit Lifetime

This study analyzes temperature-dependent $T_1$ measurements across qubits with varying geometries and dielectrics to disentangle the distinct contributions of two-level systems, non-equilibrium quasiparticles, and equilibrium quasiparticles to lifetime fluctuations, revealing that smaller-footprint qubits are more susceptible to these noise sources while confirming that quasiparticle-induced variances align with diffusion theory.

Original authors: Shaojiang Zhu, Xinyuan You, Ugur Alyanak, Mustafa Bal, Francesco Crisa, Sabrina Garattoni, Andrei Lunin, Roman Pilipenko, Akshay Murthy, Alexander Romanenko, Anna Grassellino

Published 2026-03-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shaojiang Zhu, Xinyuan You, Ugur Alyanak, Mustafa Bal, Francesco Crisa, Sabrina Garattoni, Andrei Lunin, Roman Pilipenko, Akshay Murthy, Alexander Romanenko, Anna Grassellino

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 you are trying to build a super-advanced library where books (quantum information) are stored on shelves that are incredibly fragile. If a shelf wobbles even slightly, the book falls off and the information is lost. In the world of quantum computing, these "shelves" are called superconducting qubits, and the "wobble" is a loss of energy known as decoherence.

For years, scientists have been trying to make these shelves last longer (increase their "lifetime," or $T_1$ ). But they noticed something strange: even when they built perfect shelves, the lifetime would fluctuate wildly from moment to moment. Sometimes the shelf holds for a second; sometimes it lasts for a millisecond. It's like a clock that ticks perfectly one minute and then speeds up or slows down the next.

This paper by Shaojiang Zhu and his team at Fermi National Accelerator Laboratory is like a detective story trying to figure out who is shaking the shelves.

The Two Suspects: The "Static" and The "Drifters"

The researchers suspected two main culprits were causing the shelves to wobble:

The "Static" (Two-Level Systems or TLS): Imagine tiny, invisible dust mites living in the glue holding the shelves together. These are defects in the material. They are like little switches that flip back and forth. When they flip, they steal energy from the shelf.
- The Analogy: Think of these as a few loud, annoying neighbors (the "near-resonant" ones) who are constantly banging on your wall. They are the main source of the noise.
The "Drifters" (Quasiparticles or QPs): These are broken pieces of the superconducting material itself. In a perfect superconductor, electrons dance in pairs (Cooper pairs). But if they get hit by stray radiation or heat, they break apart and become "drifters" (quasiparticles) that wander around, causing chaos.
- The Analogy: Imagine a crowd of people (electrons) holding hands in a circle. If a few people let go and start running around randomly, they bump into things and disrupt the circle.

The Experiment: Building Different Shelves

To catch the culprits, the team built three different types of "shelves" (qubits) with different shapes and materials:

Qubit A: Small and compact.
Qubits B & C: Larger, with Qubit C having a special "shield" (a layer of Tantalum) on top to protect it from the "dust mites."

They watched these qubits for about 72 hours straight at temperatures colder than outer space (near absolute zero). They didn't just measure how long the shelf lasted; they measured how much the time fluctuated.

The Big Discovery: Size Matters!

Here is the "Aha!" moment of the paper, explained simply:

1. The "Small Room" Effect (Quasiparticles)
They found that the smaller qubit (Qubit A) was much more sensitive to the "Drifters" (Quasiparticles) than the big ones.

The Metaphor: Imagine a small room and a large warehouse. If a few people start running around randomly (quasiparticles), in the small room, they are going to bump into the walls and the furniture constantly. In the large warehouse, they have plenty of space to run without hitting anything important.
The Result: The small qubit had huge fluctuations because the "drifters" were crowded into a tiny space, hitting the junction (the sensitive part) over and over. The large qubits had more "breathing room," so the drifters caused less trouble.

2. The "Shield" Effect (Two-Level Systems)
They also found that the qubit with the special Tantalum shield (Qubit C) had much less "Static" (TLS) noise than the others.

The Metaphor: It's like putting soundproofing foam on the walls. The shield stopped the "dust mites" (TLS) from stealing energy.
The Result: By changing the material, they successfully quieted down the "loud neighbors."

3. The Temperature Switch
They discovered that temperature acts like a volume knob for these two suspects:

At very low temperatures: The "Static" (TLS) is the loudest noise. The "Drifters" are mostly frozen in place.
At slightly higher temperatures: The "Drifters" (Quasiparticles) wake up and start running around, becoming the main source of noise.

Why Does This Matter?

This paper is a roadmap for building better quantum computers.

For the "Drifters": If you want to stop the random running around, don't just make the material perfect; make the qubit bigger. A larger footprint gives the broken electrons more space to wander without hitting the sensitive parts.
For the "Static": Use better materials (like the Tantalum shield) to silence the defects in the glue.

The Bottom Line:
The researchers successfully separated the noise into two distinct categories. They proved that geometry (size) controls how much the "broken electrons" (quasiparticles) bother the computer, while material choice controls how much the "defects" (TLS) bother it.

By understanding exactly who is shaking the shelf, engineers can now design quantum computers that are not only longer-lasting but also more stable, bringing us one step closer to a future where quantum computers can solve problems that are currently impossible.

1. Problem Statement

Superconducting qubits are a leading candidate for fault-tolerant quantum computing, with coherence times ( $T_1$ ) improving from nanoseconds to milliseconds. However, a critical challenge remains: temporal fluctuations in $T_1$ . These fluctuations introduce noise that complicates quantum error correction and scalability.

Current Understanding: Fluctuations are generally attributed to two main sources:
1. Two-Level Systems (TLS): Defects in amorphous surface dielectrics that couple to the qubit and exchange energy with a bath of thermally fluctuating two-level fluctuators (TLFs).
2. Quasiparticles (QPs): Non-equilibrium or thermally excited quasiparticles that cause relaxation.
The Gap: While previous studies have identified these mechanisms individually, there is a lack of quantitative understanding regarding how these two distinct noise sources contribute to the variance (fluctuations) of the depolarization rate ( $\Gamma_1 = 1/T_1$ ) within the same device, and how device geometry influences this.

2. Methodology

The authors conducted a systematic statistical study using three fixed-frequency transmon qubits (labeled A, B, and C) fabricated on Sapphire chips with varying geometries and surface materials.

Device Variations:
- Qubit A: Small capacitor pads ( $120 \times 510 \, \mu m^2$ ) with a 20 $\mu m$ gap. Uses a Niobium (Nb) thin film.
- Qubit B: Large capacitor pads ( $150 \times 720 \, \mu m^2$ ) with a 150 $\mu m$ gap. Uses Nb.
- Qubit C: Large pads (same geometry as B) but with an additional in-situ sputtered Tantalum (Ta) encapsulation layer (~10 nm) on top of the Nb.
Experimental Protocol:
- Measurements were performed over a temperature range of 7 mK to 153 mK.
- At each temperature, continuous $T_1$ measurements were taken for ~72 hours to capture temporal statistics.
- The depolarization rate $\Gamma_1$ was extracted from single-exponential decay fits of energy relaxation curves.
Analysis Techniques:
- Spectral Density Analysis: The temporal fluctuations of $\Gamma_1$ were converted to spectral density ( $S_{\Gamma_1}$ ) via Fourier transform of the autocorrelation function.
- Model Fitting: The noise spectrum was fitted to the equation $S_{\Gamma_1}(f) = a/f + b$ , where the $1/f$ term represents TLS-TLF interactions and the white noise term ( $b$ ) represents QP fluctuations.
- Diffusion Modeling: A phenomenological energy-dependent diffusion model was used to calculate the effective volume of quasiparticles reaching the Josephson junction based on pad geometry.

3. Key Contributions

Disentanglement of Noise Sources: The study successfully separates the contributions of TLS and QPs to the variance of the depolarization rate, rather than just the average rate.
Geometry-Dependent QP Fluctuations: The authors demonstrate that qubit footprint size significantly impacts the sensitivity to quasiparticle fluctuations, introducing the concept of an "effective QP volume."
Quantitative Validation: The work provides quantitative support for theoretical frameworks regarding QP diffusion and fluctuation statistics (Poisson distribution) and TLS-TLF interaction models.
Material Optimization: It validates the efficacy of Ta encapsulation in reducing dielectric loss and TLS-related fluctuations.

4. Key Results

A. Noise Spectrum and Temperature Dependence

Low Temperature (< 100 mK): The noise spectrum is dominated by $1/f$ noise, characteristic of TLS-TLF interactions. The fluctuations exhibit telegraphic noise signatures.
High Temperature (> 100 mK): The spectrum transitions to white noise, indicating that QP number fluctuations (generation/recombination dynamics) become the dominant source of variance.
Transition: The crossover point confirms the theoretical prediction that TLS dominates at low $T$ while QPs dominate at higher $T$ .

B. Impact of Geometry on QP Fluctuations

Small vs. Large Footprints: Qubit A (small pads) exhibited QP-induced variance ( $\sigma^2_{QP}$ ) at least one order of magnitude higher than Qubits B and C (large pads) at low temperatures.
Effective Volume ( $V_{eff}$ ): The authors introduced an effective volume parameter to explain this.
- For non-equilibrium QPs, $V_{eff}^0 \propto (1/x_{QP}^0)^3$ .
- The smaller pad size in Qubit A results in a shorter diffusion path for QPs to reach the junction, leading to a higher local density and larger fluctuations.
- Experimental fitting yielded a ratio of effective volumes ( $V_{eff}^0$ ) between Qubit C and A of ~13, consistent with the diffusion model prediction.

C. Impact of Materials on TLS Fluctuations

Dielectric Loss: Qubit C (Ta encapsulated) showed a significant reduction in TLS-induced variance ( $\sigma^2_{TLS}$ ) compared to Qubit B (Nb only).
Energy Participation Ratio (EPR): Simulations showed Qubit A has an EPR roughly 2x larger than B/C due to its smaller pad size.
Material Loss: The dielectric loss of Ta oxide ( $\delta_{TaOx} \sim 10^{-3}$ ) is an order of magnitude lower than Nb oxide ( $\delta_{NbOx} \sim 10^{-2}$ ). This explains the reduced TLS loss in Qubit C.

D. Statistical Consistency

QP Variance: The observed variance in $\Gamma_1$ due to QPs follows the theoretical prediction $\sigma^2_{QP} \propto \eta^2(T) \frac{x_{QP}}{V_{eff}}$ , assuming a Poisson distribution of QP numbers.
TLS Variance: The TLS-induced variance showed weak temperature dependence with local minima, explained by the competition between increased TLF switching rates (increasing variance) and increased TLS linewidths (decreasing variance).

5. Significance and Implications

Design Guidelines: The findings suggest that larger qubit footprints are beneficial for reducing sensitivity to non-equilibrium quasiparticle fluctuations, while surface material engineering (e.g., Ta encapsulation) is crucial for mitigating TLS noise.
Engineering Optimization: The concept of "effective QP volume" provides a new metric for optimizing qubit layouts to minimize lifetime fluctuations, which is critical for scaling up to fault-tolerant quantum computers.
Stabilization Strategies: The work highlights that while TLS fluctuations might be stabilized via driving protocols, QP fluctuations require physical mitigation (e.g., better shielding, gap engineering, or larger effective volumes).

In conclusion, this paper provides a rigorous experimental and theoretical framework for understanding the statistical nature of qubit decoherence, offering actionable insights for the design of more stable and scalable superconducting quantum processors.