First Measurement of Correlated Charge Noise in Superconducting Qubits at an Underground Facility

The Gist

The Big Picture: Listening to the "Static" of a Quantum Computer

Imagine you have a very delicate, high-tech musical instrument (a superconducting qubit) that is supposed to play a perfect, steady note. This instrument is so sensitive that if a single dust mote lands on it, or if a tiny breeze hits it, the note changes pitch instantly.

Scientists want to build a "quantum computer" using many of these instruments playing together. But they have a problem: noise. Specifically, invisible particles from space (cosmic rays) and natural background radiation (gamma rays) are constantly hitting the instrument, causing it to "jump" or glitch. These glitches are called charge jumps.

This paper is about a team of scientists who took their delicate instrument deep underground to see if they could quiet the noise down enough to hear the music clearly.

The Experiment: Going Deep Underground

1. The Location (The Deep Bunker)
The scientists moved their experiment from a lab on the surface to a facility called NEXUS, located 107 meters (about 35 stories) underground inside a rock tunnel at Fermilab.

• The Analogy: Think of the Earth's surface as a busy highway where cars (cosmic rays) are zooming by constantly. The underground facility is like a deep bunker. The thick rock above acts as a massive shield, blocking over 99% of the "cars" trying to get in.

2. The Shield (The Lead Blanket)
Even underground, some radiation gets through. To test this further, the team built a movable "blanket" made of thick lead around their experiment.

• The Analogy: Imagine wearing a heavy, lead-lined raincoat. When the coat is on (Shield Closed), you are protected from the rain (gamma rays). When you take it off (Shield Open), you get wet. The scientists wanted to see how much "rain" was actually hitting their instrument in both scenarios.

3. The Measurement (The Charge Jumps)
The qubits in this experiment are designed to be "electrometers"—they are like tiny scales that can weigh electric charge. When a particle hits the chip, it creates a tiny burst of electricity, causing the "scale" to jump.

• The Analogy: Imagine a trampoline. If someone jumps on it, it bounces. If a tiny fly lands on it, it barely moves. The scientists were watching for the "bounces" (charge jumps) on their quantum trampoline. They were specifically looking for correlated jumps—times when two different trampolines jumped at the exact same time. This is bad for quantum computers because it means a single cosmic ray hit both, causing a double error.

What They Found

1. The "Rain" Got Lighter, But Not as Much as Expected
When they closed the lead shield, the number of charge jumps dropped.

• The Result: The jumps went down by a factor of about 2.7.
• The Surprise: The scientists measured the radiation hitting the shield and found that the "rain" (gamma rays) had actually decreased by a factor of 20.
• The Metaphor: It's like putting up a raincoat that blocks 95% of the rain, but you only feel 30% less wet. This told the scientists that while the shield blocked the external rain, there was still a "leak" somewhere else. There is an excess source of noise coming from inside the machine itself (perhaps from the materials inside the fridge or trapped charges in the chip) that the lead shield couldn't stop.

2. The "Silent" Zone (No Correlated Jumps)
The most exciting finding happened when they looked at how far apart the qubits were.

• The Setup: They had four qubits. Two were very close together (like neighbors), and two were far apart (like neighbors living on opposite sides of a street).
• The Result: When the shield was closed, the scientists ran the experiment for 22 consecutive hours. During that entire time, the two qubits that were far apart (more than 3 millimeters) never jumped at the same time.
• The Metaphor: Imagine two people standing 10 feet apart. If a single giant boulder falls from the sky, it might hit both of them. But in this experiment, for a whole day, no single "boulder" was big enough to hit both distant qubits at once. They achieved a "silent zone" where errors didn't spread between distant parts of the computer.

The Conclusion

The paper claims three main things:

1. Underground helps: Moving the experiment underground significantly reduced the number of errors caused by cosmic rays.
2. There's a mystery: Even deep underground with a lead shield, there is still more noise than expected. It's not just from outside; something inside the equipment is still causing "static."
3. Distance matters: For the first time, they proved that if you space your quantum bits out far enough (more than 3mm) and shield them well, you can stop "correlated errors" (where one mistake causes a chain reaction of mistakes) for long periods of time.

What they did NOT claim:
The paper does not say they built a working quantum computer that can solve problems yet. It does not claim this fixes all errors forever. It strictly reports on measuring the "static" and proving that deep underground, with shielding, the "static" can be reduced to a level where distant qubits don't mess with each other.

Technical Summary

Technical Summary: First Measurement of Correlated Charge Noise in Superconducting Qubits at an Underground Facility

Problem Statement
Ionizing radiation is increasingly recognized as a significant source of decoherence and correlated errors in superconducting qubits. Previous studies have established a correlation between ionizing radiation flux (specifically cosmic rays and environmental gammas) and qubit energy relaxation rates ($1/T_1$) as well as simultaneous multi-qubit errors. These correlated errors pose a challenge for the efficacy of quantum error-correcting surface codes. While surface-level laboratories are subject to high fluxes of cosmic ray muons and ambient gamma radiation, the specific contribution of these sources to charge noise in the qubit substrate, and the ability to mitigate them, requires isolation from surface-level backgrounds. Furthermore, the mechanisms by which ionizing events induce charge jumps in the substrate (via electron-hole pair production, phonon diffusion, and charge trapping) operate on timescales ranging from nanoseconds to days, necessitating long-duration monitoring to characterize the noise environment fully.

Methodology
The authors conducted measurements on a four-qubit weakly charge-sensitive transmon device (with $E_J/E_C = 24$) relocated from a surface laboratory in Madison, WI, to the Northwestern EXperimental Underground Site (NEXUS) at Fermilab, located 107 meters underground. This depth provides a rock overburden equivalent to 225 meters of water, reducing the cosmic ray muon flux by over 99% compared to sea level.

The experimental setup included:

• Shielding: A modular lead shield providing $4\pi$ coverage around the cryogenic payload to attenuate environmental gamma radiation.
• Cryogenics: The device operated in a dilution refrigerator at a base temperature of 10.5 mK within a cleanroom environment to minimize particulate contamination.
• Radiation Monitoring: A $Li_2MoO_4$ (LMO) crystal instrumented with a Transition Edge Sensor (TES) was placed 18.7 cm from the qubit chip within the same cryostat to independently measure the gamma flux and spectrum.
• Measurement Protocol: The team employed Ramsey tomography sequences ($X/2 - \text{Idle} - X/2$) to map the offset charge ($n_g$) on the qubit islands to the excited state probability ($P_1$). By scanning the charge bias and analyzing the phase evolution, the researchers detected discontinuous jumps in the induced charge.
• Data Analysis: A rolling $\chi^2$ minimization algorithm was used to fit tomography scans against a template derived from jump-free scans. This method identified charge jumps with magnitudes $0.1e \le |\Delta q| \le 0.5e$. The efficiency of this detection method was validated via simulation to be greater than 70%.

Two primary datasets were collected:

1. Shield Open (SO): Ambient gamma flux conditions.
2. Shield Closed (SC): Minimal gamma flux conditions (lead shield closed).

Key Results

• Charge Jump Rates: The average charge jump rate for the four qubits was measured at $0.51^{+0.05}_{-0.04}$ mHz in the Shield Open configuration and reduced to $0.19^{+0.04}_{-0.03}$ mHz in the Shield Closed configuration.
• Gamma Flux Correlation: The LMO detector measured a gamma flux reduction factor of $20 \pm 1$ (for energies $>150$ keV) when the shield was closed. However, the charge jump rate only decreased by a factor of 2.7. This discrepancy indicates that in the low-background SC configuration, the charge jump rate is not dominated by external gamma flux.
• Excess Rate: By subtracting the SC rate from the SO rate (accounting for a constant excess background), the authors calculated a gamma-induced jump rate of $0.34^{+0.07}_{-0.06}$ mHz and an excess rate of $0.17^{+0.04}_{-0.03}$ mHz present in both configurations. This excess is inconsistent with expected muon rates (which are $\sim 0.08$ mHz/cm$^2$) and ambient gamma flux alone.
• Correlated Noise: The study measured correlated charge jumps between qubit pairs. For qubits separated by less than 1 mm (340 $\mu$m and 640 $\mu$m), correlated jumps were observed. However, for qubit pairs separated by distances greater than 3 mm (specifically 3.18 mm to 3.33 mm), the team observed zero correlated charge jumps over 22 consecutive hours of continuous operation in the Shield Closed configuration.
• Magnitude of Jumps: The detected charge jumps ranged from $0.1e$ to $0.5e$.

Significance and Claims
The paper claims to present the first measurement of correlated charge noise in a charge-sensitive qubit chip operated in an underground environment. The primary significance lies in the demonstration that moving to an underground facility significantly reduces the rate of charge burst events, though not as drastically as the reduction in muon flux alone would suggest, pointing to other radiation sources or internal mechanisms.

Crucially, the authors report the first elimination of correlated charge noise in charge-sensitive qubits separated by distances exceeding 3 mm over timescales approaching one day. This finding is significant for fault-tolerant quantum computing, as it suggests that spatial separation of qubits can effectively mitigate correlated errors induced by ionizing radiation in low-background environments. Additionally, the results contribute to the understanding of superconducting qubits as particle detectors for fundamental physics, highlighting the need to characterize and mitigate specific radiation-induced error mechanisms. The authors note that the origin of the "excess" charge bursts observed in the shielded configuration remains an open question, with potential candidates including trapped charge relaxation, secondaries from cosmogenic interactions with cryostat materials, or anomalous local radiation sources.