Department of Information Engineering, University of Pisa

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The increasing demand for high‑fidelity quantum computation highlights the critical role of minimising errors arising from control‑signal imperfections. Barsotti, Marconcini, Procissi, and Macucci investigate the impact of phase noise on qubit fidelity using detailed numerical simulations. Their research directly addresses a growing limitation in quantum systems as qubit coherence times improve and read‑out technologies advance. By modelling realistic phase fluctuations and analysing their effect on qubit evolution, the team provides valuable insight into how different spectral components of noise contribute to performance degradation. This work offers a crucial step towards developing more robust control strategies and achieving fault‑tolerant quantum computing.

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Phase Noise Limits Quantum Control Fidelity

As qubit decoherence times lengthen and read‑out technologies advance, imperfections in drive signals—specifically phase noise—are poised to become a significant limitation to achieving high fidelity in complex quantum control pulse sequences. This research investigates the impact of phase noise originating from reference oscillators on qubit fidelity using detailed numerical simulations. The team directly accounts for the interaction between fluctuating phases in control signals and the evolving state of the qubit, offering a novel approach to understanding this critical challenge. Their method centres on generating realistic phase noise consistent with a defined power spectral density, then applying this noise to the pulse carrier within simulations performed using Qiskit‑Dynamics, a powerful tool for modelling qubit temporal evolution.

Scientists demonstrate a robust methodology for estimating fidelity degradation by comparing the final qubit state after a noisy pulse sequence with its ideal, noise‑free counterpart, averaging results across numerous noise realisations. By exploiting an analytical representation of a carrier affected by phase fluctuations, the study dissects the contributions of different spectral components of phase noise to overall performance. This work establishes a detailed connection between the characteristics of phase noise and the resulting errors in qubit control, providing crucial insights for optimising quantum systems. The research unveils a method for accurately modelling and predicting the impact of realistic noise conditions on qubit performance, moving beyond simplified theoretical models.

The study’s approach differs from previous analyses by directly evaluating the interaction between the qubit and noise present in the control pulses, considering the qubit’s rotating frame as the reference. This allows for a more intuitive understanding of how specific noise components contribute to fidelity loss in particular final states. Furthermore, the team challenges a previously held assertion regarding the relevance of high‑frequency phase noise, demonstrating that this conclusion stemmed from an oversight in earlier analytical work. The simulations utilise a sampling frequency of 1 GHz, generating a baseband signal limited to 500 MHz, and subsequently resampling to achieve a temporal resolution of 83.3 ps for accurate phase modulation of a 6 GHz carrier.

Experiments show the effectiveness of generating pseudorandom phase sequences distributed according to a specified noise power spectral density (PSD), then inputting these sequences into Qiskit‑Dynamics for simulating qubit evolution. This two‑step process provides a powerful framework for quantifying the impact of control‑pulse phase noise on qubit fidelity, offering a valuable tool for the development of more robust and reliable quantum computers. The work opens avenues for designing control pulses that are less susceptible to phase noise, ultimately improving the performance of quantum algorithms and computations.

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Simulating Phase Noise Impact on Qubit Fidelity

The study investigates the impact of phase noise on qubit fidelity through detailed numerical simulations, directly accounting for interactions between fluctuating control signals and qubit state evolution. Researchers engineered a method to generate realistic phase‑noise realizations based on a given PSD, subsequently applying these fluctuations to the carrier pulse within simulations performed using Qiskit‑Dynamics. This technique models the temporal evolution of the qubit, enabling precise analysis of noise effects. Experiments employed a comparative approach, contrasting the final qubit state after a noisy pulse sequence with its ideal, noise‑free counterpart.

By averaging results across numerous noise realizations, the team estimated the resulting fidelity degradation with high accuracy. Crucially, the work pioneers a novel analytical representation of a carrier signal affected by phase fluctuations, allowing for a granular examination of how different spectral components of the noise contribute to overall performance loss. The research builds upon existing quantum‑control theory and extends the filter‑transfer‑function formalism to specifically address phase noise impacting qubit coherence. Unlike previous approaches that shifted phase fluctuations onto the qubit by altering the reference frame, this study directly evaluates the interaction between the qubit and noise present in the control pulses, within the qubit’s rotating frame.

This innovative perspective facilitates a more intuitive understanding of fidelity contributions in specific final states. The methodology involves generating pseudorandom phase sequences aligned with the assumed noise PSD, and then utilizing these sequences as input for the Qiskit‑Dynamics simulations. This precise approach enables the team to challenge previously held assumptions regarding the relevance of high‑frequency noise components, revealing potential oversights in earlier analyses and offering a refined understanding of noise‑mitigation strategies for quantum computing.

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Phase Noise Quantifies Qubit Fidelity Loss

Scientists achieved a significant breakthrough in quantifying the impact of phase noise on qubit fidelity through detailed numerical simulations. The research team meticulously modeled the interaction between phase fluctuations in control signals and qubit state evolution, generating phase‑noise realizations consistent with specified PSDs. These realizations were then applied to pulse carriers within simulations using Qiskit‑Dynamics, allowing for direct assessment of fidelity degradation. By averaging results across multiple noise realizations, the study established a robust method for estimating fidelity loss due to phase noise.

Experiments revealed a two‑step approach, combining synthetic phase‑noise generation with quantum simulation of time‑domain evolution. A finite‑impulse‑response (FIR) filter, synthesized based on the desired noise PSD, was used to generate pseudorandom sequences of baseband phase values. These values were then incorporated as phase modulation into control pulses, simulating their effect on qubit evolution with a sampling frequency initially set at 1 GHz, then resampled to 83.3 ps temporal resolution. The team employed Qiskit‑Dynamics to numerically integrate the time‑dependent Schrödinger equation, calculating qubit state evolution under the control Hamiltonian and ultimately quantifying fidelity between the final and ideal states.

Results demonstrate that the largest contributions to fidelity loss occur around the Rabi frequency, specifically measured at 10 MHz for a series of 50 ns πₓ‑pulses. Initial simulations utilized a Gaussian phase‑noise PSD with a 3 kHz bandwidth and a constant amplitude of ‑85 dBc/Hz, centered on varying frequencies to isolate the impact of individual spectral components. Tests involved applying sequences of 12 consecutive 50 ns rectangular control pulses, spaced 20 ns apart, to a qubit initially set to |0⟩, and then evaluating the fidelity after each pulse. Further investigations with pulse sequences of varying durations and separations—including 25 ns pulses separated by 10 ns intervals and 150 ns pulses separated by 60 ns intervals—confirmed the prominence of the Rabi frequency in driving fidelity degradation.

The work establishes a detailed understanding of how different frequency components within the phase‑noise spectrum contribute to qubit infidelity, challenging previously held assumptions regarding the relevance of high‑frequency noise components. This breakthrough delivers a powerful tool for optimizing control‑pulse design and mitigating the effects of noise in quantum‑computing systems.