On-Demand Correlated Errors in Superconducting Qubits from a Particle Accelerator

This paper introduces a novel facility coupling an electron linear accelerator to a dilution refrigerator to generate on-demand, correlated ionizing radiation, enabling the precise characterization of radiation-induced relaxation, excitation, and detuning errors in superconducting qubits that mimic cosmic-ray effects and depend on device geometry.

The Gist

The Big Picture: The "Quantum Rain" Problem

Imagine you are trying to build a super-advanced computer made of tiny, fragile switches called qubits. These switches are so sensitive that they can exist in two states at once (like a coin spinning in the air), which allows them to solve problems normal computers can't.

However, these qubits are incredibly delicate. They hate noise. One of the biggest sources of noise is ionizing radiation—invisible particles from space (like cosmic rays) or natural radioactivity in the ground.

Think of these particles like tiny, invisible hailstones falling from the sky. When a hailstone hits your quantum computer, it doesn't just make a small dent; it creates a shockwave that breaks the delicate "spinning coins" (qubits) and causes them to fall over. This is called an error.

The problem is that these hailstorms happen randomly. You never know when one will hit, or how big it will be. This makes it very hard to study exactly how the damage happens or how to fix it.

The Solution: The "Controlled Hail Machine" (CLIQUE)

The researchers at Johns Hopkins Applied Physics Laboratory built a special facility called CLIQUE. Instead of waiting for random cosmic rays to hit their computer, they built a machine that can shoot one single electron at their quantum computer whenever they want.

• The Analogy: Imagine you are trying to figure out how a specific type of glass breaks.
  • The Old Way: You wait for a random rock to fall from a cliff and hit the glass. You might wait weeks for one hit, and you don't know exactly when it's coming.
  • The CLIQUE Way: You have a machine that can fire a single, perfectly sized pebble at the glass exactly when you press a button. You can do this over and over again, instantly.

This machine uses a particle accelerator (a giant tube that speeds up electrons) connected directly to a fridge (a dilution refrigerator) that keeps the quantum computer near absolute zero.

What They Discovered: The "Butterfly Effect" in Microchips

When they fired these single electrons at their quantum chip, they saw something fascinating. Even though they only shot one particle, it caused a chain reaction that messed up many qubits at the same time.

Here is what happened, broken down simply:

1. The Impact: The electron hits the silicon chip (like a bullet hitting a wall).
2. The Shockwave: The energy from the hit creates a burst of sound waves (called phonons) that travel through the chip.
3. The Breakage: These waves break apart the "glue" holding the electrons together in the superconductor, creating "rogue electrons" (quasiparticles).
4. The Chaos: These rogue electrons wander around and crash into the qubits, causing them to lose their information.

The Key Finding:
The researchers found that where the damage happens depends on the design of the qubit.

• They had two types of qubits: those with a "low-gap" design and those with a "high-gap" design.
• The Low-Gap Qubits: When hit, they stayed broken for a long time (like a slow-healing wound).
• The High-Gap Qubits: They recovered much faster (like a quick bruise).

This is huge news because it tells engineers that if they want to build better quantum computers, they need to design their chips so that these "rogue electrons" can't get stuck in the wrong places.

Why This Matters: From "Guessing" to "Knowing"

Before this experiment, scientists were like detectives trying to solve a crime where the suspect runs away immediately after the crime. They had to wait for random cosmic rays to hit, guess when it happened, and hope they caught enough data.

With the CLIQUE facility:

• They can hit "Pause": They can fire an electron, watch exactly how the qubits react for a few microseconds, and then reset.
• They can see the invisible: They found subtle errors (like the qubit getting slightly "out of tune") that were previously impossible to see because the random background noise was too loud.
• They can test fixes: Now, they can test different materials or designs to see which ones stop the "hail" from breaking the computer.

The Bottom Line

This paper is about building a controlled laboratory for cosmic rays. By replacing the unpredictable "weather" of space radiation with a precise "spray bottle" of electrons, the researchers have given quantum engineers a new tool to understand why their computers fail and, more importantly, how to make them strong enough to survive the real world.

It's the difference between trying to learn how to surf by waiting for a random wave in the ocean, versus practicing in a wave pool where you can control the size and timing of every wave.

Technical Summary

1. Problem Statement

Superconducting qubits, a leading platform for quantum computing, are highly susceptible to decoherence caused by ionizing radiation. High-energy particles (such as cosmic-ray muons and atmospheric electrons) deposit energy into the substrate, generating ballistic phonons. These phonons break Cooper pairs in the superconducting layers, creating excess quasiparticles (QPs).

• The Challenge: When QPs reach the Josephson junctions of a qubit, they tunnel across, causing correlated errors (relaxation, excitation, and dephasing) across multiple qubits simultaneously. This threatens the viability of quantum error correction (QEC) surface codes.
• Limitations of Previous Studies:
  • Ambient Sources: Relying on natural cosmic rays provides stochastic, low-frequency events, making data collection slow and timing resolution poor.
  • Alternative Methods: Techniques like optical illumination or junction biasing to generate QPs do not faithfully replicate the energy deposition dynamics of a real ionizing particle.

2. Methodology: The CLIQUE Facility

The authors introduce CLIQUE (Controlled Linac Irradiation of Quantum Experiments), a novel facility that couples an electron linear accelerator (linac) directly to a dilution refrigerator.

• Hardware Setup:
  • Source: A repurposed Varian Clinac-2500 linac generates 18.5 MeV electrons.
  • Beam Control: The beam is pulsed at 10 Hz with 4 µs width. The fluence is tuned via the gun grid voltage to ensure an average of $\sim$0.2 electrons per pulse, ensuring single-electron events for the vast majority of triggers.
  • Delivery: The beam is bent 270° and directed through a 1.8 m reinforced concrete wall into an adjacent "quantum hall" containing a dilution refrigerator.
  • Target: A custom 9-qubit aluminum transmon chip (fixed-frequency) mounted inside the fridge. The beam path includes thin windows (Ti/Al) and thinned packaging (800 µm Al) to minimize energy loss before hitting the silicon die.
• Synchronization: A scintillation detector monitors the beam fluence off-axis. A trigger signal from the linac is sent to the quantum control system with high precision (<10 µs), allowing for "heralded" event detection.
• Simulation: MCNP Monte Carlo simulations confirmed that 18.5 MeV electrons deposit energy in silicon similarly to 400 MeV cosmic-ray muons (the primary ambient threat), validating the electron beam as a surrogate for cosmic rays.

3. Experimental Design

• Qubit Chip: A 5x5 mm chip with 9 transmon qubits. The design features two distinct junction orientations relative to the capacitor island:
  • Low-Gap-Island: The lower superconducting gap side of the junction connects to the capacitor island.
  • High-Gap-Island: The higher superconducting gap side connects to the capacitor island.
• Measurement Protocols:
  • Relaxation Errors: Qubits prepared in $|1\rangle$, followed by a variable detection delay, then measured.
  • Excitation Errors: Qubits prepared in $|0\rangle$ to detect spurious transitions to $|1\rangle$.
  • Detuning/Dephasing: A Ramsey-like sequence (superposition state) was used to measure frequency shifts and coherence loss ($T_2$).
• Data Analysis: Events were classified by correlating qubit state changes with the linac trigger. A phenomenological two-level rate model was used to fit the time dynamics of relaxation and excitation rates.

4. Key Results

The study successfully demonstrated that a single linac electron can induce correlated errors across the entire multi-qubit system, mimicking cosmic-ray impacts.

• Correlated Relaxation: Upon a linac trigger, the system error rate (qubits in wrong state) spiked immediately from a baseline of ~1 qubit to full system error, then slowly recovered.
• Junction Orientation Dependence:
  • Low-Gap-Island Qubits: Exhibited significantly longer recovery times (order of magnitude longer) for relaxation errors compared to high-gap qubits. This is attributed to QP trapping on the capacitor island and the difficulty of QPs tunneling from low-gap to high-gap regions.
  • High-Gap-Island Qubits: Showed faster recovery, suggesting QPs are more easily flushed away from the junction.
• Excitation Errors:
  • Detected primarily in $|0\rangle$ prepared states.
  • High-Gap-Island Qubits: Showed prolonged excitation errors, likely due to sustained QP density on the capacitor island driving tunneling from high-to-low gap.
  • Low-Gap-Island Qubits: Showed only brief excitation spikes, as the long-lived relaxation errors (dominant in this configuration) masked the excitation signal.
• Detuning and Dephasing:
  • High QP density reduced critical currents, causing negative detuning of the transmon frequency.
  • Crucial Finding: Detuning errors persisted much longer than relaxation errors. Since detuning depends on QP density rather than tunneling, these errors remain until QPs are flushed from the system, highlighting a critical vulnerability for QEC.
• Quantitative Modeling: The authors extracted decay constants ($\tau$) and amplitudes ($A$) for relaxation and excitation. For example, qubit q23 (high-gap) had a relaxation decay of ~370 µs but an excitation decay of ~960 µs, indicating complex, location-dependent QP dynamics.

5. Significance and Contributions

• On-Demand Radiation Source: CLIQUE provides the first facility to study radiation effects with high timing resolution and event statistics in minutes rather than weeks. It eliminates the stochastic nature of ambient radiation.
• Validation of Surrogates: Confirmed that 18.5 MeV electrons are excellent surrogates for cosmic-ray muons regarding energy deposition in silicon chips.
• Unveiling Subtle Errors: The facility revealed error types (detuning, long-lived excitation) that are difficult to detect with ambient sources due to masking by relaxation or low event rates.
• Design Implications: The results demonstrate that junction orientation and gap engineering are critical for mitigating radiation-induced errors. Strategies to "flush" QPs off the capacitor island (e.g., specific gap designs) are essential for robust QEC.
• Future Directions: The facility opens avenues for studying two-level system dynamics, charge-parity measurements, and higher-energy regimes (multi-electron depositions).

In conclusion, this work establishes a critical experimental capability for understanding and mitigating the fundamental limits of superconducting quantum processors imposed by ionizing radiation, providing actionable data for the design of radiation-hardened quantum hardware.