⚛️ quantum physics

Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

The paper presents a novel spectroscopy method for fixed-frequency transmon qubits that identifies and tracks microscopic two-level systems (TLSs) by analyzing correlations in the relaxation rates of the qubit's first and second excited states.

Original authors: Tanay Roy, Xinyuan You, David van Zanten, Francesco Crisa, Sabrina Garattoni, Shaojiang Zhu, Anna Grassellino, Alexander Romanenko

Published 2026-02-12

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CC BY 4.0

Original authors: Tanay Roy, Xinyuan You, David van Zanten, Francesco Crisa, Sabrina Garattoni, Shaojiang Zhu, Anna Grassellino, Alexander Romanenko

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

The "Ghost in the Machine" Problem: A Simple Guide to New Quantum Diagnostics

Imagine you are a master watchmaker, and you’ve built the most precise mechanical watch in the world. But there’s a problem: every few hours, the watch starts running slightly fast or slightly slow, and you have no idea why. You look under a microscope, but everything looks perfect.

In the world of quantum computing, scientists face this exact problem. They build "transmon qubits"—the tiny, delicate engines of a quantum computer—but these engines are haunted by "ghosts."

The Ghosts: Two-Level Systems (TLS)

These ghosts are called Two-Level Systems (TLSs). Think of them as microscopic, invisible "energy sponges" hiding in the materials used to build the computer. When a qubit is trying to hold onto its information, one of these tiny sponges might suddenly "soak up" the energy, causing the qubit to lose its data.

The annoying part? These sponges are restless. They drift around, changing their "frequency" (like a radio station tuning itself), which makes them appear and disappear at random.

The Old Way: The Tuning Fork Method

Until now, the only way to find these ghosts was to "tune" the qubit. Imagine you have a tuning fork, and you want to find a hidden ghost. You would slowly change the pitch of your tuning fork until—BAM!—it suddenly loses all its sound because it hit the ghost's frequency.

This works, but it’s a hassle. Many of the best quantum computers are "fixed-frequency," meaning they are built to stay at one specific pitch to remain stable. If you can't change the pitch, you can't find the ghosts.

The New Discovery: The "Correlated Decay" Trick

The researchers at Fermilab have found a way to spot the ghosts without changing the qubit's pitch at all.

Instead of tuning the qubit, they look at how the qubit "dies" (loses energy) across different levels. Think of a transmon qubit not just as a single note, but as a musical instrument that can play a low note ( $|1\rangle$ ) and a high note ( $|2\rangle$ ).

Here is their clever trick:

They push the qubit up to its "high note" ( $|2\rangle$ ).
They watch how fast it falls back down to the "middle note" ( $|1\rangle$ ) and then to the "ground note" ( $|0\rangle$ ).
They noticed something strange: When the middle note's life gets shorter, the high note's life often gets longer (and vice versa).

The Analogy: The Seesaw of Energy

Imagine a seesaw sitting between two different musical notes.

If a "ghost" (the energy sponge) moves closer to the low note, it sucks energy out of that note, making it die faster.
But because the ghost moved away from the high note, that high note is now safer and lives longer.

By watching this "seesaw" effect—where one note gets weaker while the other gets stronger—the scientists can mathematically "see" exactly where the ghost is hiding and how it is moving, even if they never touch the qubit's frequency.

Why This Matters

This is a huge deal for two reasons:

It’s Non-Invasive: We can now perform "medical checkups" on quantum computers without disturbing their delicate settings.
It Sees the "Invisible": They discovered that these ghosts can affect the computer even when they are "far away" (detuned) from the qubit's frequency. It’s like feeling a draft in a room even if the window is closed; the influence is still there.

In short: Scientists have developed a new way to "hear" the invisible ghosts haunting quantum computers, allowing them to map out the defects and eventually build much more stable, reliable machines.

Technical Summary: Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

Problem: The Challenge of TLS Characterization in Fixed-Frequency Qubits

In superconducting quantum computing, transmon qubits are frequently limited by energy relaxation ( $T_1$ ) caused by microscopic Two-Level Systems (TLSs)—defects located in amorphous dielectrics or material interfaces.

Traditionally, identifying and characterizing these individual TLSs requires bringing a qubit transition into resonance with the defect. This is typically achieved using flux-tunable qubits, where the frequency is swept across a spectrum to find "avoided level crossings." However, modern scalable architectures increasingly favor fixed-frequency transmons to avoid the complexity of flux lines and sensitivity to flux noise. In fixed-frequency devices, the inability to sweep the qubit frequency makes it difficult to isolate individual TLSs, especially those that are detuned from the primary qubit transition but still contribute to decoherence.

Methodology: Multilevel Relaxation Spectroscopy

The authors propose a novel spectroscopy method that does not require frequency tuning. Instead, it leverages the anharmonicity of the transmon to probe different frequencies simultaneously.

Three-Level Protocol: The method utilizes the first three energy levels of a transmon ( $|0\rangle, |1\rangle, |2\rangle$ ). Because the transmon is weakly anharmonic, the transition frequency between $|0\rangle \leftrightarrow |1\rangle$ ( $\omega_{01}$ ) is different from the transition between $|1\rangle \leftrightarrow |2\rangle$ ( $\omega_{12}$ ).
Simultaneous $T_1$ Extraction: By repeatedly preparing the second excited state ( $|2\rangle$ ) and monitoring the decay of the populations $P_2(t)$ , $P_1(t)$ , and $P_0(t)$ , the researchers can simultaneously extract the relaxation times of the first excited state ( $T_{1e} = 1/\Gamma_{10}$ ) and the second excited state ( $T_{1f} = 1/\Gamma_{21}$ ).
Correlation Analysis: The core of the method lies in observing how these two relaxation rates fluctuate over time. If a single TLS frequency ( $\omega_{TLS}$ ) drifts, it will move closer to one transition (increasing its decay rate) and further from the other (decreasing its decay rate), creating a characteristic anti-correlation between $T_{1e}$ and $T_{1f}$ .
Mathematical Modeling: The decay rates are modeled using a Lorentzian noise spectral density $S(\omega)$ centered at the TLS frequency. By fitting the time-dependent $T_{1e}(t)$ and $T_{1f}(t)$ data to this model, the researchers can reconstruct the TLS frequency trajectory.

Key Results

Device A (Single-TLS Dominance): The researchers observed strong anti-correlation between $T_{1e}$ and $T_{1f}$ over 60 hours. This allowed them to successfully reconstruct the frequency drift of a single dominant TLS, which wandered by approximately $\sim 10$ MHz.
Device B (Multi-TLS Regime): In a second device, the relaxation times showed minimal correlation and even intermittent inversions (where $T_{1f} > T_{1e}$ ). This indicated the presence of multiple TLSs, which was accurately captured by a two-TLS model.
Off-Resonant Impact: A significant finding was that TLSs detuned by $\gtrsim 100$ MHz from the qubit transition could still significantly influence relaxation via the Lorentzian tails of their noise spectrum.
Readout Fidelity: The team achieved a three-level readout fidelity ( $F_3$ ) of approximately $90\%$ by optimizing I-Q discrimination boundaries and applying error mitigation via an inverted confusion matrix.

Significance and Contributions

Non-Invasive Diagnostics: This method provides a powerful tool for TLS spectroscopy in fixed-frequency architectures without the need for flux-tunable inductors or large AC-Stark shifts.
Enhanced Sensitivity: By monitoring multiple transitions, the method provides a "dissipation fingerprint" that is far more diagnostic than standard single-transition $T_1$ measurements. It can distinguish between a single drifting defect and multiple stable defects.
Material Science Insights: The ability to track TLS frequency drift over long periods (days) provides critical data for understanding the microscopic dynamics of material defects, which is essential for engineering more stable, high-coherence quantum hardware.
Scalability: Because the protocol is "minimal in experimental overhead" and works on fixed-frequency devices, it is highly compatible with the roadmap for large-scale, scalable superconducting quantum processors.