⚛️ quantum physics

Revealing Noise in Axial Motion Through Quantum Noise Spectroscopy on a Trapped Ion Processor

This paper utilizes dephasing-robust quantum noise spectroscopy on a trapped-ion processor to isolate and characterize axial-motion-induced control noise caused by thermal motion coupling with beam curvature, enabling the extraction of motional parameters and the identification of beam inflection points as optimal operating regions to suppress such noise.

Original authors: Vivian Maloney, Matthew Chow, Leigh Norris, Melissa Revelle, Daniel Lobser, Brian McFarland, Edward Tortorici, Christopher Yale, Susan Clark, Gregory Quiroz

Published 2026-08-06

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CC BY 4.0

Original authors: Vivian Maloney, Matthew Chow, Leigh Norris, Melissa Revelle, Daniel Lobser, Brian McFarland, Edward Tortorici, Christopher Yale, Susan Clark, Gregory Quiroz

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-fast, super-smart computer that uses the weird rules of quantum physics to solve problems no normal computer ever could. This is the world of quantum computing, and one of the most promising ways to build these machines is by trapping tiny, charged atoms (called ions) in a cage made of invisible electric and magnetic fields. These ions act like the computer's memory bits, or "qubits." But here's the catch: just like a violin string that vibrates when you blow on it, these trapped ions are never perfectly still. They jiggle and wiggle due to heat and the environment. If you try to tell an ion what to do using a laser beam, and that ion is wobbling, the laser might hit it at the wrong spot or with the wrong strength. This causes the computer to make mistakes, turning a brilliant calculation into a garbled mess. Scientists have long known that this "jiggling" is a problem, but it's been incredibly hard to figure out exactly how the wobble messes up the laser commands, especially when the laser is hitting the ion from the side.

Now, picture a group of scientists acting like detectives in a high-tech lab. They are working with a trapped-ion processor, a machine where ions are lined up like beads on a string. Their goal was to solve a specific mystery: when the ions wiggle back and forth along the string (axial motion), how does that movement turn into "noise" or errors in the laser commands? Usually, to measure this, you'd need a second laser shining from a different angle to catch the wobble, but that's hard to do in tiny, crowded quantum machines. Instead, these researchers used a clever trick called "Quantum Noise Spectroscopy." Think of it like listening to a song to figure out what kind of car is driving by. By playing specific, rhythmic patterns of laser pulses (called "Dephasing-Robust" waveforms) that are immune to other types of static, they could isolate the specific "hum" caused by the ion's wobble. They discovered that the ion's wobble acts like a shaky hand holding a flashlight; if the flashlight beam is curved, a tiny shake makes the light intensity on the wall fluctuate wildly. But if you shine the light on a spot where the beam is flat (an "inflection point"), that same shake barely changes the light at all.

The paper, titled "Revealing Noise in Axial Motion Through Quantum Noise Spectroscopy on a Trapped Ion Processor," details how the team, led by researchers from Johns Hopkins University and Sandia National Laboratories, used this method to map out exactly how the ion's movement creates control errors. They found that the "noise" isn't random; it's directly linked to the shape of the laser beam and how fast the ion is wiggling. By moving the ion to different spots within the laser beam, they could separate the noise caused by the laser itself from the noise caused by the ion's motion. Their measurements showed that the ion's wobble creates a low-frequency "rumble" in the control signal, which is most intense when the ion is near the center of the beam where the curvature is highest.

The team also proved that this technique works even when you have multiple ions at once. They ran the experiment on a chain of four ions simultaneously, showing that you can fix the noise for an entire group of qubits just by shifting their position to a "sweet spot" in the laser beam. However, there is a trade-off: the spot where the wobble causes the least noise (the inflection point) is also where the laser pushes the ion the least, meaning the computer has to work slower to get the same job done. The researchers measured the temperature of the ion's wobble to be about 0.32 millikelvin and found the wobble frequency to be around 0.327 MHz. They didn't just guess these numbers; they calculated them by fitting their experimental data to a mathematical model, which matched their results across a huge range of conditions.

In short, this paper doesn't just say "wiggling is bad." It gives a precise recipe for how to measure that wobble without needing extra lasers, and it shows exactly where to position the ions to minimize the errors. The authors suggest that by operating near these "inflection points," engineers can significantly reduce motion-induced errors, even if it means accepting a slightly slower processing speed. This is a crucial step toward building larger, more reliable quantum computers, as it provides a way to diagnose and fix a major source of errors using the tools already built into the machine. The study confirms that while the trade-off between speed and stability exists, understanding the specific "noise spectrum" allows scientists to navigate it much more effectively than before.

Technical Summary: Revealing Noise in Axial Motion Through Quantum Noise Spectroscopy on a Trapped Ion Processor

Problem Statement
Quantum processors, particularly those based on trapped ions, suffer from native noise processes that are often difficult to isolate because multiple error mechanisms contribute to the same measured loss of coherence. A specific challenge arises from ion motion orthogonal to the laser-beam propagation direction (axial motion in the context of transverse addressing beams). When ions undergo thermal axial motion, they sample the spatial intensity profile of the addressing laser beam. If the beam has local curvature, this motion couples to the beam profile, producing effective amplitude control noise (fluctuations in the Rabi rate). Characterizing this noise is difficult because the axial direction is often inaccessible to conventional laser-based motional spectroscopy techniques, which typically require a laser beam with a propagation component along the motional axis. Furthermore, distinguishing these motion-induced control fluctuations from intrinsic laser-amplitude noise and dephasing noise presents a significant experimental hurdle.

Methodology
The authors employ Dephasing-Robust Quantum Noise Spectroscopy (DR-QNS) to characterize laser-amplitude control noise while simultaneously probing axial motional dynamics. The methodology relies on the following components:

Dephasing-Robust (DR) Waveforms: The team utilizes a specific family of control waveforms defined by $\Omega_{DR}(t) = \Omega_0 \sin(\lambda t)$ . These waveforms are engineered to suppress detuning and low-frequency dephasing noise (to fourth order in the Magnus expansion) while preserving sensitivity to control noise. This allows the isolation of amplitude fluctuations arising from both native laser noise and qubit-axial coupling.
Theoretical Modeling: The authors develop a model where the effective Rabi rate is modulated by a stochastic laser gain and a position-dependent axial gain function $f(x)$ . By Taylor expanding the beam profile to second order ( $f(x) \propto a + bx + dx^2$ ), they derive that axial motion contributes to the noise spectrum via a term proportional to the square of the local beam curvature ( $d^2$ ). The model predicts that the decay exponent $\chi$ scales as $\Omega_0^2$ and can be decomposed into a curvature-independent native noise term and a curvature-dependent axial-motion term.
Experimental Platform: Experiments were conducted on the Quantum Scientific Computing Open User Testbed (QSCOUT), a trapped-ion processor at Sandia National Laboratories using $^{171}\text{Yb}^+$ ions. The axial direction is perpendicular to the 355 nm Raman addressing beams.
Measurement Protocol:
- Single-Ion Characterization: A single ion was displaced along the trap axis to sample different local beam intensities and curvatures. The team measured survival probabilities in X, Y, and Z bases across 37 ion positions (spaced by 25 nm) and 9 modulation frequencies ( $\lambda$ ) up to 3 kHz, with varying drive amplitudes.
- Beam Profiling: To account for beam asymmetry and temporal drift, the team performed independent skew-Gaussian beam-profile calibrations for each experimental configuration to determine the local curvature at the ion's position.
- Multi-Ion Extension: The protocol was applied in parallel to a four-ion register within a six-ion chain to test scalability.

Key Contributions and Results

Separation of Noise Sources: The study successfully separates curvature-dependent axial-motion noise from curvature-independent native control noise. By varying the ion position, the authors demonstrated that the decay factor $\xi$ varies strongly with beam curvature. Near the beam center (high curvature), motion-induced noise is significant; near beam inflection points (near-zero curvature), this contribution is suppressed.
Extraction of Motional Parameters: Using the DR-QNS data and the theoretical model, the authors extracted motional parameters that are otherwise difficult to access on this platform without additional spectroscopy beams. They determined:
- The center-of-mass (COM) mode occupation number: $\langle n_0 \rangle = 205 \pm 49$ (corresponding to a temperature of $0.32 \pm 0.08$ mK).
- The axial mode linewidth: $\gamma = 0.165 \pm 0.112$ kHz.
  These values are consistent with independent sideband-based temperature estimates.
Spectral Reconstruction: The native control-noise spectrum $S_\eta(\omega)$ was reconstructed using a non-negative least-squares inversion. The results show that the residual native control noise is concentrated at low frequencies, suggesting that standard mitigation techniques like dynamical decoupling or composite pulses would be effective.
Trade-off Identification: The work quantifies the trade-off between gate speed and sensitivity to motion-induced noise. Operating near the beam center maximizes the Rabi rate but increases sensitivity to axial motion. Operating near an inflection point suppresses motion-induced noise but reduces the drive strength. On the QSCOUT platform, this trade-off corresponds to roughly a factor-of-two reduction in Rabi rate for an order-of-magnitude reduction in control noise.
Scalability: The protocol was successfully extended to a four-ion register, demonstrating that the position-dependent noise suppression at beam inflection points applies simultaneously across multiple qubits.

Significance
The paper claims that this work provides a method to characterize axial-motion-induced control noise and extract motional parameters (such as occupation numbers and relaxation rates) without requiring a dedicated laser beam along the motional axis. By utilizing the transverse addressing beams already present for qubit control, DR-QNS offers a scalable diagnostic tool. The study identifies beam inflection points as operating regions that can suppress axial-motion-induced noise, providing a practical strategy for optimizing beam alignment in trapped-ion processors. Furthermore, the ability to perform parallel characterization across multiple ions suggests a pathway for spatially mapping correlated control noise and optimizing fault-tolerant protocols in larger registers.

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