Impact of control signal phase noise on qubit fidelity

As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a crucial limitation to the fidelity achievable at the end of complex control pulse sequences. Although the effect of phase noise of reference oscillators on qubit performance has been studied previously, its interaction with realistic time-dependent control pulses and its contribution to fidelity degradation have not yet been investigated in sufficient detail, and remains a critical challenge. Here we study the impact on fidelity of phase noise affecting reference oscillators with the help of numerical simulations, which allow us to directly take into account the interaction between the phase fluctuations in the control signals and the evolution of the qubit state, thereby achieving a comprehensive understanding of the actual role played by the different spectral components of phase noise. In particular, we perform an analysis of the effect of the individual noise frequency contributions, providing a clear identification of the spectral regions that most critically impact fidelity and establishing their relative weight in the overall fidelity degradation. Our method is based on the generation of phase noise realizations consistent with a given power spectral density, that are then applied to the pulse carrier in simulations, with Qiskit-Dynamics, of the qubit temporal evolution. By comparing the final state obtained at the end of a noisy pulse sequence with that in the ideal case and averaging over multiple noise realizations, we estimate the resulting degradation in fidelity, and, exploiting an approximate analytical representation of a carrier affected by phase fluctuations, we shed new light on the nature of the different contributions, and provide an intuitive physical picture.As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a crucial limitation to the fidelity achievable at the end of complex control pulse sequences. Although the effect of phase noise of reference oscillators on qubit performance has been studied previously, its interaction with realistic time-dependent control pulses and its contribution to fidelity degradation have not yet been investigated in sufficient detail, and remains a critical challenge. Here we study the impact on fidelity of phase noise affecting reference oscillators with the help of numerical simulations, which allow us to directly take into account the interaction between the phase fluctuations in the control signals and the evolution of the qubit state, thereby achieving a comprehensive understanding of the actual role played by the different spectral components of phase noise. In particular, we perform an analysis of the effect of the individual noise frequency contributions, providing a clear identification of the spectral regions that most critically impact fidelity and establishing their relative weight in the overall fidelity degradation. Our method is based on the generation of phase noise realizations consistent with a given power spectral density, that are then applied to the pulse carrier in simulations, with Qiskit-Dynamics, of the qubit temporal evolution. By comparing the final state obtained at the end of a noisy pulse sequence with that in the ideal case and averaging over multiple noise realizations, we estimate the resulting degradation in fidelity, and, exploiting an approximate analytical representation of a carrier affected by phase fluctuations, we shed new light on the nature of the different contributions, and provide an intuitive physical picture.

quant-pharXiv:2601.09014Jan 15, 20260 citations

Agata Barsotti, Paolo Marconcini, Gregorio Procissi +1 more

Abstract As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a crucial limitation to the fidelity achievable at the end of complex control pulse sequences. While prior studies have addressed the impact of reference oscillator phase noise on qubit performance, its interaction with realistic control pulses and its role in fidelity degradation have not been examined in sufficient detail. Furthermore, previous analyses grounded in the filter-function formalism identify high-frequency spectral components as the dominant source of fidelity loss, a conclusion that has also been used as a compelling marketing feature by some hardware vendors. Here we reevaluate this assertion by means of direct time-domain numerical simulations, in which phase noise realizations with a given power spectral density are applied to the carrier of realistic control pulse sequences, and the resulting qubit evolution is computed with Qiskit-Dynamics and averaged over multiple noise realizations. We show that the claimed dominance of high-frequency components originates from an oversight in interpreting the conversion between the phase-noise and the frequency-noise power spectral densities: at equal power, the components close to the Rabi frequency are by far the most detrimental, while those far from the carrier act only marginally, mainly through residual amplitude modulation. We performed an analysis using both two- and three-level models, the latter capturing leakage outside the computational subspace. We further show that, for realistic phase noise spectra of local oscillators, whose power is concentrated in the low-offset region, the fidelity loss is dominated by such high-power low-frequency components.Abstract As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a crucial limitation to the fidelity achievable at the end of complex control pulse sequences. While prior studies have addressed the impact of reference oscillator phase noise on qubit performance, its interaction with realistic control pulses and its role in fidelity degradation have not been examined in sufficient detail. Furthermore, previous analyses grounded in the filter-function formalism identify high-frequency spectral components as the dominant source of fidelity loss, a conclusion that has also been used as a compelling marketing feature by some hardware vendors. Here we reevaluate this assertion by means of direct time-domain numerical simulations, in which phase noise realizations with a given power spectral density are applied to the carrier of realistic control pulse sequences, and the resulting qubit evolution is computed with Qiskit-Dynamics and averaged over multiple noise realizations. We show that the claimed dominance of high-frequency components originates from an oversight in interpreting the conversion between the phase-noise and the frequency-noise power spectral densities: at equal power, the components close to the Rabi frequency are by far the most detrimental, while those far from the carrier act only marginally, mainly through residual amplitude modulation. We performed an analysis using both two- and three-level models, the latter capturing leakage outside the computational subspace. We further show that, for realistic phase noise spectra of local oscillators, whose power is concentrated in the low-offset region, the fidelity loss is dominated by such high-power low-frequency components.

EPJ Quantum TechnologyJul 30, 20260 citations

Upper-Bounds on Qubit Coherence Set by Master Clock Instabilities

William D. Oliver, Harrison Ball, Michael J. Biercuk

Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on improvements to qubit designs, materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is ultimately that of the qubit relative to the system clock, rather than that of the qubit in isolation. In this manuscript we clarify the impact of clock instability on qubit dephasing and provide quantitative estimates of fidelity upper-bounds set by noisy phase fluctuations in the clock. We first indicate analytically that such phase fluctuations in the clock - typically referred to as the local oscillator (LO) - are indistinguishable from a pure dephasing field arising from other environmental mechanisms. Using these results, we apply commonly quoted LO phase-noise specifications to calculate the resultant performance bounds on qubit operational fidelities. We find that laboratory grade LOs contribute error probabilities beyond $10^{-4}$ for operation times $<1\;\mu$ s, while the use of precision LOs can suppress error rates by $10^{4}$ . We find that in either case phase fluctuations at frequencies far from the carrier dominate operational error rates, and due to their high-frequency spectral content, are difficult to mitigate using dynamic error suppression strategies. Further, we consider the importance of LO noise bandwidth and its impact on the degree to which thermal phase fluctuations in the LO contribute an effective error floor. These observations and analysis of the flow-down effects of such errors on the implementation of benchmarking and quantum error correction protocols highlight challenges and advantages that particular qubit technologies possess in the context of phase-noise-induced errors and motivate enhanced research in precision frequency metrology.Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on improvements to qubit designs, materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is ultimately that of the qubit relative to the system clock, rather than that of the qubit in isolation. In this manuscript we clarify the impact of clock instability on qubit dephasing and provide quantitative estimates of fidelity upper-bounds set by noisy phase fluctuations in the clock. We first indicate analytically that such phase fluctuations in the clock - typically referred to as the local oscillator (LO) - are indistinguishable from a pure dephasing field arising from other environmental mechanisms. Using these results, we apply commonly quoted LO phase-noise specifications to calculate the resultant performance bounds on qubit operational fidelities. We find that laboratory grade LOs contribute error probabilities beyond $10^{-4}$ for operation times $<1\;\mu$s, while the use of precision LOs can suppress error rates by $10^{4}$. We find that in either case phase fluctuations at frequencies far from the carrier dominate operational error rates, and due to their high-frequency spectral content, are difficult to mitigate using dynamic error suppression strategies. Further, we consider the importance of LO noise bandwidth and its impact on the degree to which thermal phase fluctuations in the LO contribute an effective error floor. These observations and analysis of the flow-down effects of such errors on the implementation of benchmarking and quantum error correction protocols highlight challenges and advantages that particular qubit technologies possess in the context of phase-noise-induced errors and motivate enhanced research in precision frequency metrology.

Jan 10, 20163 citations

Noise Filtering in Quantum Information

Todd J. Green

We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.

Oct 14, 20160 citations

Quantum Noise Dynamic Suppression in Quantum Control Theory

Jincheng Zhang

This paper investigates the dynamic suppression of quantum noise within the framework of quantum control theory. The core challenge in implementing precise quantum operations lies in the significant influence of environmental noise, which introduces uncertainties and degrades control fidelity. We propose a novel approach utilizing real-time feedback control, leveraging quantum sensors to monitor the noise levels within a quantum system. Based on this continuous assessment, control parameters are dynamically adjusted to mitigate the impact of noise. The effectiveness of this method is demonstrated through theoretical analysis and mathematical modeling. We aim to enhance the accuracy and stability of quantum control processes, ultimately contributing to the reliable execution of complex quantum operations. The system is described by the following Hamiltonian: $H = H_0 + H_I$ , where $H_0$ is the system Hamiltonian and $H_I$ represents the interaction Hamiltonian. The time evolution of the system is governed by the equation: $\frac{d|ψ(t)>}{dt} = \frac{i}{\hbar} [H, |ψ(t)]$ . Noise is modeled as a stochastic term, adding to the Hamiltonian: $H = H_0 + H_I + H_N$ , where $H_N$ represents the noise Hamiltonian. The control pulse can be described as: $U(t) = \sum_{i=1}^N \alpha_i \, e^{-i\omega_i t}$ , where $\alpha_i$ are the amplitudes and $\omega_i$ are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states: $Fidelity = ||^2$ . The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation: $|ψ(t+\delta t)> = U(t) |ψ(t)>$ , where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as: $\sigma^2 = - ^2$ , where N is the noise operator.This paper investigates the dynamic suppression of quantum noise within the framework of quantum control theory. The core challenge in implementing precise quantum operations lies in the significant influence of environmental noise, which introduces uncertainties and degrades control fidelity. We propose a novel approach utilizing real-time feedback control, leveraging quantum sensors to monitor the noise levels within a quantum system. Based on this continuous assessment, control parameters are dynamically adjusted to mitigate the impact of noise. The effectiveness of this method is demonstrated through theoretical analysis and mathematical modeling. We aim to enhance the accuracy and stability of quantum control processes, ultimately contributing to the reliable execution of complex quantum operations. The system is described by the following Hamiltonian: $H = H_0 + H_I$, where $H_0$ is the system Hamiltonian and $H_I$ represents the interaction Hamiltonian. The time evolution of the system is governed by the equation: $\frac{d|ψ(t)>}{dt} = \frac{i}{\hbar} [H, |ψ(t)]$. Noise is modeled as a stochastic term, adding to the Hamiltonian: $H = H_0 + H_I + H_N$, where $H_N$ represents the noise Hamiltonian. The control pulse can be described as: $U(t) = \sum_{i=1}^N \alpha_i \, e^{-i\omega_i t}$, where $\alpha_i$ are the amplitudes and $\omega_i$ are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states: $Fidelity = ||^2$. The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation: $|ψ(t+\delta t)> = U(t) |ψ(t)>$, where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as: $\sigma^2 = - ^2$, where N is the noise operator.

Sep 5, 20260 citations

Influence of fast and slow laser phase noise on the fidelity of the Mølmer-Sørensen trapped-ion gate

Nikita Semenin, Ksenia Khabarova, Nikolay Kolachevsky

High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer-Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges which influence the gate fidelity the most: "fast" noise at frequencies near the motional mode spectrum, and "slow" noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer-Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges which influence the gate fidelity the most: "fast" noise at frequencies near the motional mode spectrum, and "slow" noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.

quant-pharXiv:2609.26912Quantum ReportsSep 24, 20260 citations

10^{-4}

for operation times

<1\;\mu

s, while the use of precision LOs can suppress error rates by

10^{4}

. We find that in either case phase fluctuations at frequencies far from the carrier dominate operational error rates, and due to their high-frequency spectral content, are difficult to mitigate using dynamic error suppression strategies. Further, we consider the importance of LO noise bandwidth and its impact on the degree to which thermal phase fluctuations in the LO contribute an effective error floor. These observations and analysis of the flow-down effects of such errors on the implementation of benchmarking and quantum error correction protocols highlight challenges and advantages that particular qubit technologies possess in the context of phase-noise-induced errors and motivate enhanced research in precision frequency metrology.

H = H_0 + H_I

, where

H_0

is the system Hamiltonian and

H_I

represents the interaction Hamiltonian. The time evolution of the system is governed by the equation:

\frac{d|ψ(t)>}{dt} = \frac{i}{\hbar} [H, |ψ(t)]

. Noise is modeled as a stochastic term, adding to the Hamiltonian:

H = H_0 + H_I + H_N

, where

H_N

represents the noise Hamiltonian. The control pulse can be described as:

U(t) = \sum_{i=1}^N \alpha_i \, e^{-i\omega_i t}

, where

\alpha_i

are the amplitudes and

\omega_i

are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states:

Fidelity = ||^2

. The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation:

|ψ(t+\delta t)> = U(t) |ψ(t)>

, where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as:

\sigma^2 = - ^2

, where N is the noise operator.