⚛️ quantum physics

Impact of control signal phase noise on qubit fidelity

This paper investigates how phase noise in control signals degrades qubit fidelity during complex pulse sequences by combining numerical simulations with Qiskit-Dynamics and analytical approximations to identify the specific spectral components of noise that most critically impact performance.

Original authors: Agata Barsotti, Paolo Marconcini, Gregorio Procissi, Massimo Macucci

Published 2026-03-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Agata Barsotti, Paolo Marconcini, Gregorio Procissi, Massimo Macucci

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: Tuning a Radio in a Stormy Room

Imagine you are trying to tune an old-fashioned radio to a specific station to hear a clear song. In the world of quantum computing, the "radio station" is a qubit (the basic unit of information), and the "song" is a complex calculation.

To play the song, you send a control signal (a pulse of electricity) to the qubit. Ideally, this signal is perfect. But in the real world, the equipment generating these signals isn't perfect. It has a little bit of "static" or "jitter" called phase noise.

This paper asks a very important question: How much does this static ruin the song?

For a long time, scientists worried that high-frequency static (fast, sharp crackles) was the biggest enemy. They thought the qubit was like a sensitive microphone that would pick up every tiny, fast vibration.

The authors of this paper say: "Actually, you're worrying about the wrong noise."

They discovered that the qubit is mostly bothered by noise that matches the rhythm of the music itself, not the fast crackles in the background.

The Analogy: The Metronome and the Dancer

To understand their findings, let's use an analogy of a dancer (the qubit) and a metronome (the control signal).

The Dance: The dancer is trying to perform a specific routine (a quantum gate). They need to spin exactly 180 degrees, stop, spin again, and so on.
The Metronome: The dancer relies on a metronome to keep time.
The Problem (Phase Noise): The metronome is slightly broken. Sometimes it ticks a tiny bit early, sometimes a tiny bit late. This is the "phase noise."

The Old Belief (The "High-Frequency" Fear)

Previous researchers thought that if the metronome had a high-pitched, rapid wobble (high-frequency noise), the dancer would get dizzy and fall. They believed the dancer was sensitive to any vibration, no matter how fast.

The New Discovery (The "Rhythm Match")

The authors ran thousands of computer simulations (using a tool called Qiskit-Dynamics) to see what actually happens. They found:

The "Rhythm Match" (The Real Danger): The dancer only gets messed up if the metronome's wobble happens at the same speed as the dancer's spin.
- If the dancer spins once every second, and the metronome wobbles once every second, the dancer gets confused and loses their balance.
- In quantum terms, this "speed" is called the Rabi Frequency. It's the natural rhythm of the qubit's operation.
- Conclusion: Noise that matches the qubit's operating speed is the biggest killer of accuracy.
The "Fast Wobble" (The False Alarm): If the metronome wobbles super fast (like 100 times a second), the dancer doesn't even notice. The dancer is too slow to react to such fast changes.
- The authors found that high-frequency noise has almost zero effect on the final result, contrary to what some hardware manufacturers believed.

How They Did It: The "Noise Generator"

The team didn't just guess; they built a digital machine to create "fake noise" that looked exactly like real-world electrical noise.

Creating the Noise: They used math to generate random jitters that matched the "fingerprint" (Power Spectral Density) of real electronic oscillators.
The Simulation: They fed this noisy signal into a virtual qubit and watched how the qubit's state changed over time.
The Comparison: They compared the "noisy" result to a "perfect" result to see how much the "song" was ruined.

The Surprising Twist: Low Frequency Matters Too

While they proved that high frequency noise is harmless, they found another twist: Very low frequency noise (slow, drifting static) can also be bad, but only if you play a very long song.

Short Song: If you do a quick calculation, slow drift doesn't matter much.
Long Song: If you run a long sequence of operations, the slow drift accumulates. It's like a clock that loses one second every hour. If you only run for 10 minutes, it doesn't matter. If you run for 10 years, you'll be very late.

Why This Matters

This paper is a "relief valve" for quantum engineers.

Stop Worrying About the Wrong Thing: Engineers don't need to spend millions of dollars trying to eliminate every single high-frequency crackle in their electronics. Those are mostly harmless.
Focus on the Rhythm: Instead, they should focus on stabilizing the signal at the specific frequency where the qubit is operating (the Rabi frequency).
Better Design: This helps them design cheaper, more efficient control electronics because they know exactly which parts of the noise spectrum actually matter.

Summary in One Sentence

The paper proves that a quantum computer is like a dancer who only trips if the music stutters at the exact beat of their dance, not if the room is just a little bit noisy with fast, high-pitched sounds.

1. Problem Statement

As superconducting qubit coherence times ( $T_1$ and $T_2^*$ ) improve and readout technologies advance, the primary bottleneck for achieving high-fidelity quantum operations shifts from intrinsic qubit decoherence to non-idealities in the control electronics, specifically phase noise in the reference oscillators driving the control pulses.

While previous studies (e.g., Ball et al., 2016) have analyzed the impact of phase noise using filter function formalisms, they often rely on specific reference frame assumptions that can obscure the physical interaction between noise and the qubit. A critical point of contention in the field is the relative importance of different spectral components of phase noise. Some literature suggests that high-frequency phase noise components are the dominant source of infidelity, a claim that influences hardware vendor specifications. The authors argue this view may stem from an analytical oversight and aim to provide a more intuitive and comprehensive understanding of how specific noise frequencies degrade fidelity.

2. Methodology

The authors developed a two-step numerical simulation framework to directly model the interaction between phase noise and qubit evolution:

Phase Noise Generation:
- They generate pseudorandom phase sequences consistent with a target Power Spectral Density (PSD).
- The method involves designing a Finite Impulse Response (FIR) filter using the Impulse Response Truncation (IRT) method. The filter's frequency response is set to the square root of the desired noise PSD.
- A white Gaussian process is convolved with this filter (accelerated via FFT) to produce a baseband phase noise signal with the correct spectral characteristics.
- This baseband signal is upsampled and applied as an instantaneous phase deviation $\phi(t)$ to the carrier of the control pulses: $s(t) = \Re\{f(t) e^{i(2\pi\nu t + \phi(t))}\}$ .
Qubit Simulation:
- The qubit's time evolution is simulated using Qiskit-Dynamics, which numerically integrates the time-dependent Schrödinger equation for the system Hamiltonian.
- The simulation compares the final state of the qubit under noisy control pulses against the ideal, noiseless evolution.
- Fidelity Estimation: The process is repeated over multiple noise realizations (different random seeds) to average out stochastic effects and estimate the average fidelity degradation.
- Reference Frame Handling: The authors explicitly account for the accumulation of phase error between the reference clock and the qubit's rotating frame. For states on the equatorial plane of the Bloch sphere, they align the target state with the instantaneous phase of the local oscillator to correctly evaluate fidelity.

3. Key Contributions

Direct Interaction Modeling: Unlike previous filter-function approaches that shift noise to the qubit frame, this work models the direct interaction between the noisy control field and the qubit in the rotating frame, offering a more intuitive physical picture.
Spectral Component Analysis: The paper systematically isolates and analyzes the contribution of individual noise frequency components (using Gaussian-shaped noise filters centered at various offsets) to determine which frequencies are most detrimental.
Correction of Prevailing Misconceptions: The authors provide a rigorous analytical and numerical refutation of the claim that high-frequency phase noise is the primary driver of infidelity. They demonstrate that the apparent relevance of high frequencies in previous works arises from an incorrect handling of the conversion between phase noise and frequency noise PSDs (specifically, a failure to cancel the $\omega^2$ factor in the fidelity expression).
Analytical Approximation: They derive an approximate analytical representation of a carrier affected by phase noise, separating the effects into:
1. Double Sideband Modulation: Direct coupling of noise sidebands to the qubit (dominant near Rabi frequency).
2. Residual Amplitude Modulation: Fluctuations in carrier amplitude caused by the $1 - \theta(t)^2/2$ term (dominant at very high frequencies but generally negligible).

4. Key Results

Dominance of Rabi Frequency Noise: The simulations reveal that the most significant contribution to fidelity loss comes from phase noise components with frequency offsets close to the Rabi frequency of the control pulses.
- Example: For 50 ns pulses (Rabi frequency $\approx 10$ MHz), noise centered at 10 MHz caused the maximum fidelity drop.
- Mechanism: This is due to resonant coupling between the noise sidebands and the qubit transition.
Low-Frequency Noise Impact: For realistic oscillators, low-frequency noise (close to the carrier) also contributes significantly, primarily because these components often have much higher amplitudes (PSD) in real-world oscillators. Their impact accumulates over the duration of long pulse sequences.
Negligible High-Frequency Impact: Noise components far from the carrier (e.g., >50–100 MHz offset) have a negligible effect on fidelity.
- The qubit acts as a resonator and is intrinsically insensitive to high-frequency detuning.
- The only remaining effect is via residual amplitude modulation, which is minimal.
Validation with Real Hardware: Using measured phase noise data from a custom microwave oscillator (3.4 GHz carrier), the authors confirmed that the actual fidelity loss is extremely small ( $\sim 10^{-5}$ ), dominated by low-frequency components and the specific shape of the measured PSD, not high-frequency tails.
Synthetic Noise Experiments: By artificially synthesizing noise spectra where high-frequency components were boosted and low-frequency components suppressed, the authors demonstrated that even with high-amplitude high-frequency noise, the fidelity degradation remained marginal compared to scenarios with strong low-frequency or Rabi-frequency noise.

5. Significance

Hardware Optimization: The findings suggest that hardware vendors and quantum engineers should prioritize the suppression of phase noise near the Rabi frequency and at low offsets (within the loop bandwidth of the PLL) rather than obsessing over high-frequency noise tails.
Control Pulse Design: The results validate the use of Dynamical Error Suppression (DES) techniques specifically tuned to filter out noise at the Rabi frequency.
Theoretical Clarification: The paper corrects a significant analytical error in the literature regarding the weighting of high-frequency phase noise, providing a clearer physical basis for understanding control signal limitations.
Methodological Benchmark: The proposed numerical framework (combining PSD-based noise generation with Qiskit-Dynamics) offers a robust tool for predicting fidelity limits in complex control sequences under realistic noise conditions.

In conclusion, the paper establishes that phase noise near the Rabi frequency and low-frequency noise with high amplitude are the critical factors limiting qubit fidelity, while high-frequency phase noise components play a minor role, contrary to some previous assertions.