⚛️ quantum physics

Probing the memory of a superconducting qubit environment

This paper demonstrates that analyzing non-Poissonian quantum jump traces and fitting them to Solomon equations allows researchers to distinguish and characterize long-lived two-level system (TLS) environments from standard Markovian baths in superconducting qubits, thereby revealing distinct TLS peaks that persist beyond the qubit's lifetime.

Original authors: Nicolas Gosling, Denis Bénâtre, Nicolas Zapata, Paul Kugler, Mitchell Field, Sumeru Hazra, Simon Günzler, Thomas Reisinger, Martin Spiecker, Mathieu Féchant, Ioan M. Pop

Published 2026-03-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nicolas Gosling, Denis Bénâtre, Nicolas Zapata, Paul Kugler, Mitchell Field, Sumeru Hazra, Simon Günzler, Thomas Reisinger, Martin Spiecker, Mathieu Féchant, Ioan M. Pop

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 Big Picture: A Quantum Qubit with a "Bad Memory"

Imagine you are trying to keep a delicate glass marble (the qubit) balanced on the tip of your finger. In a perfect world, if the marble falls, it just falls. It doesn't care what happened five minutes ago. This is how physicists usually think quantum computers work: they assume the environment is "forgetful" (memoryless).

However, this new research shows that the environment around our quantum marble isn't actually forgetful. It has a long memory. Sometimes, the environment remembers the marble's past movements and reacts to them later, causing the marble to wobble in weird, unpredictable ways.

The scientists in this paper developed a new way to "listen" to these memories and figure out exactly what is causing them, without even touching the marble.

The Problem: The "Ghost" in the Machine

For years, scientists have been trying to build better quantum computers. They've made the marbles (qubits) last longer and longer. But they noticed something strange:

Sometimes the marble falls at random times that don't follow a normal pattern.
The errors happen in clusters (like a string of bad luck) rather than being spread out evenly.

This suggests the environment isn't just a passive background; it's an active participant with a memory.

The Culprit: The paper identifies "Long-Lived Two-Level Systems" (TLSs) as the troublemakers.

The Analogy: Imagine the marble is in a room with a giant, slow-moving echo. When the marble drops a sound, the echo doesn't fade away immediately. Instead, the echo bounces around for a long time. If the marble drops again, it hears the old echo and gets confused.
In the quantum world, these "echoes" are tiny defects in the materials (TLSs) that absorb energy from the qubit, hold onto it for a long time, and then give it back later. This creates a "time-correlated" error, which is a nightmare for quantum error correction.

The Solution: Listening to the "Quantum Jumps"

Usually, to study a system, you have to poke it, push it, or reset it. But this team found a clever way to study the environment just by watching the qubit naturally relax.

The Analogy: The Strobe Light and the Fireflies
Imagine you are in a dark room with a single firefly (the qubit).

Standard View: You just watch the firefly blink. If it blinks once every 10 seconds, you think, "Okay, it's blinking steadily."
The New View: The scientists used a "strobe light" (rapid measurements) to watch the firefly blink thousands of times. They noticed something weird:
- Sometimes, the firefly blinks, and then immediately blinks again.
- Other times, it stays dark for a long time.
- This "bunching" of blinks (clumping together) happens because the firefly is interacting with a slow, lazy friend (the TLS) in the room. When the firefly gives energy to the friend, the friend holds it, gets excited, and then accidentally gives it back to the firefly, making it blink again sooner than expected.

By analyzing the timing of these blinks (called "quantum jumps"), the scientists could mathematically separate the "normal" background noise from the "long-memory" TLSs.

The Discovery: Mapping the "Echoes"

Once they could hear the echoes, they wanted to find out where they were coming from.

The Analogy: Tuning a Radio
The scientists slowly changed the "pitch" (frequency) of the qubit, like tuning a radio dial.

As they tuned the dial, they found specific spots where the "bunching" of blinks became very strong.
These spots were like radio stations broadcasting the presence of a specific TLS.
They found that these "stations" (TLSs) were very sensitive to electric fields. When they applied a small electric field (like a gentle breeze), the "stations" moved to different frequencies.

Why this matters:

Short-lived TLSs: These are like a quick shout. They disappear fast and blend into the background noise.
Long-lived TLSs: These are like a slow, lingering echo. They are the ones causing the memory errors.
The team successfully separated the "shouts" from the "echoes" and created a map showing exactly where these long-lived echoes live and how they react to electric fields.

Why This is a Big Deal

No Poking Required: Previous methods required "pumping" the qubit (hitting it with energy) to find these defects. This new method just watches the qubit naturally. It's like diagnosing a patient's heart by listening to their resting pulse rather than making them run a marathon.
Better Error Correction: Quantum computers need to fix errors to work. But if errors happen in "clumps" (because of memory), standard fixing methods fail. By understanding these long-lived memories, engineers can design better software to fix these specific types of errors.
Material Science: By mapping where these defects are and how they react to electric fields, scientists can now design better materials to get rid of them, making future quantum computers more stable.

The Takeaway

This paper is like finding out that your house has a "ghost" that remembers your footsteps. Instead of being scared, the scientists built a special microphone to listen to the ghost, figured out exactly where it lives, and how it reacts to the wind. Now, they can finally start fixing the house so the ghost stops messing with the furniture.

In short: They figured out how to listen to the quantum environment's memory, map the defects causing it, and do it all without disturbing the system.

1. Problem Statement

Superconducting quantum processors require fault tolerance, which relies on the Born-Markov approximation. This approximation assumes that the qubit environment is "memoryless," meaning dissipation occurs as a constant energy decay into a thermal bath with no temporal correlations. However, recent observations of non-exponential decay, non-Poissonian quantum jumps, and hyperpolarization suggest this approximation often fails.

The specific problem addressed is the presence of long-lived Two-Level Systems (TLSs) in the qubit's environment. Unlike standard thermal baths, these TLSs have lifetimes orders of magnitude longer than the qubit's intrinsic relaxation time ( $T_1$ ). When a qubit couples to such a TLS, the TLS can become polarized (retaining a "memory" of the qubit's state), leading to time-correlated errors. These correlations violate the assumptions of standard quantum error correction (QEC) algorithms, which expect independent, random errors. Existing methods to characterize these defects often require active qubit manipulation (pump-probe) or complex reset cycles, which introduce their own errors and limit measurement efficiency.

2. Methodology

The authors propose a passive, continuous monitoring technique called Quantum Jump Correlation Spectroscopy.

Experimental Setup: They utilize a fluxonium qubit fabricated with granular aluminum (to minimize charge noise and operate near a sweet spot) coupled to a readout resonator. The qubit is continuously monitored via stroboscopic readout (every 6 $\mu$ s) to detect quantum jumps (transitions between ground and excited states).
Data Analysis: Instead of measuring simple $T_1$ $T_{1}$ decay, they analyze the temporal correlations of quantum jumps using the second-order correlation function, $g_2(\tau)$ $g_{2} (τ)$ .
- For a standard Markovian bath, $g_2(\tau)$ shows antibunching at short times and approaches unity exponentially.
- For a system coupled to a long-lived TLS, $g_2(\tau)$ exhibits bunching (an increased probability of a second jump) at timescales much longer than the qubit's $T_1$ .
Modeling: The dynamics are modeled using the Solomon equations, which describe the coupled evolution of the qubit population ( $p_q$ $p_{q}$ ) and the TLS population ( $p_t$ $p_{t}$ ). The model includes:
- $\Gamma_q$ : Qubit decay rate into the thermal bath.
- $\Gamma_{qt}$ : Coupling rate between the qubit and the TLS.
- $\Gamma_t$ : TLS decay rate into the thermal bath (often negligible for long-lived TLSs).
Unraveling Hidden States: By conditioning the analysis on specific measurement outcomes (e.g., selecting trajectories immediately after a "jump down" vs. starting from the ground state), the authors can mathematically "unravel" the hidden population of the unobservable TLS. They fit the measured conditional dynamics to the Solomon equations to extract the specific coupling rates.
Spectroscopy: They sweep the qubit frequency and apply an external electric field bias to map the resonance frequencies and electric field susceptibility of individual TLSs.

3. Key Contributions

Passive Memory Detection: The paper demonstrates a method to detect and quantify long-lived environmental memory effects without active qubit manipulation (no pump-probe pulses) and without requiring qubit reset between cycles. This eliminates gate calibration errors and drive-induced leakage.
Disentanglement of Environments: The authors successfully separate the coupling to a Markovian background (standard thermal bath) from the coupling to individual long-lived TLSs.
Quantitative Spectroscopy: They introduce a spectroscopic technique that resolves distinct TLS peaks in the coupling rate $\Gamma_{qt}$ , allowing for the identification of specific defects across a frequency span.
Validation of Solomon Dynamics: The work provides experimental validation that the Solomon equations accurately describe the non-Markovian dynamics of qubit-TLS systems, including the "unraveling" of hidden TLS populations based on jump history.

4. Key Results

Observation of Bunching: The measured $g_2(\tau)$ function showed clear bunching persisting for timescales significantly longer than the qubit's $T_1$ , confirming the presence of a long-lived memory element.
Extracted Rates: By fitting the Solomon model to the data, they extracted distinct rates:
- A standard Markovian decay rate ( $\Gamma_q$ ).
- A specific qubit-TLS coupling rate ( $\Gamma_{qt}$ ) that varies with frequency.
- The TLS decay rate ( $\Gamma_t$ ) was found to be negligible (effectively zero) for the long-lived defects, confirming their "memory" nature.
Spectral Mapping: Sweeping the qubit frequency revealed distinct peaks in $\Gamma_{qt}$ (labeled A-H in the paper), each corresponding to a specific long-lived TLS.
Electric Field Susceptibility: Applying an electric field bias revealed that these long-lived TLSs are sensitive to electric fields. Some TLS frequencies shifted linearly with the field, while others remained constant or jumped, providing a "fingerprint" for their microscopic origin.
Short-lived vs. Long-lived: The method successfully distinguished between short-lived TLSs (which appear as part of the Markovian background $\Gamma_q$ ) and long-lived TLSs (which appear as distinct peaks in $\Gamma_{qt}$ ).

5. Significance

Impact on Quantum Error Correction (QEC): The findings highlight a critical challenge for fault-tolerant quantum computing. Time-correlated errors caused by long-lived TLSs can cause syndrome qubits to flag the same error multiple times, potentially confusing QEC decoders. Understanding and mitigating these memory effects is essential for achieving the thresholds required for logical qubits.
Material and Device Characterization: The technique offers a powerful, ready-to-use tool for materials scientists and device engineers to map defect landscapes in superconducting circuits. It can identify specific defect types (e.g., those sensitive to electric fields) without complex experimental overhead.
Scalability: Since the method relies on thermal fluctuations and standard readout, it is deployable on any standard qubit measurement setup, making it highly scalable for characterizing large-scale quantum processors.
Theoretical Advancement: The work bridges the gap between theoretical models of non-Markovian dynamics (Solomon equations) and experimental reality, providing a quantitative framework for understanding how qubits interact with complex, structured environments.

In summary, this paper provides a novel, passive spectroscopic tool to identify and characterize long-lived environmental defects that violate the Markovian approximation, offering crucial insights for improving the coherence and error correction capabilities of future superconducting quantum computers.