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Preserving Quantum Coherence in Thermal Noisy Systems Via Qubit Frequency Modulation

Mahshid Khazaei Shadfar, Farzam Nosrati, Mortezapour A., Vincenzo Macrí, Roberto Morandotti, Lo Franco R.

Published Jun 22, 2026• 0 citations
Publisher

Abstract

Quantum coherence is a key resource underpinning quantum technologies, yet it is highly susceptible to environmental decoherence, especially in thermal settings. While frequency modulation (FM) has shown promise in preserving coherence at zero temperature, its effectiveness in realistic, noisy thermal environments remains unclear. In this work, we investigate a single frequency-modulated qubit interacting with a thermal phase-covariant reservoir composed of dissipative and dephasing channels. We demonstrate that FM significantly preserves coherence in the presence of thermal dissipation while being ineffective under thermal pure-dephasing noise due to commutation between system and interaction Hamiltonians. When both noise channels are present, FM offers protection only for weak dephasing coupling. Our findings clarify the limitations and potential of FM-based coherence protection under thermal noise, supplying practical insights into designing robust quantum systems for quantum applications.

DOI
10.1002/qute.70349

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Quantum coherence is a key resource underpinning quantum technologies, yet it is highly susceptible to environmental decoherence, especially in thermal settings. While frequency modulation (FM) has shown promise in preserving coherence at zero temperature, its effectiveness in realistic, noisy thermal environments remains unclear. In this work, we investigate a single frequency-modulated qubit interacting with a thermal phase-covariant reservoir composed of dissipative and dephasing channels. We demonstrate that FM significantly preserves coherence in the presence of thermal dissipation while being ineffective under thermal pure-dephasing noise due to commutation between system and interaction Hamiltonians. When both noise channels are present, FM offers protection only for weak dephasing coupling. Our findings clarify the limitations and potential of FM-based coherence protection under thermal noise, supplying practical insights into designing robust quantum systems for quantum applications.
ABSTRACT Quantum coherence is a key resource underpinning quantum technologies, yet it is highly susceptible to environmental decoherence, especially in thermal settings. While frequency modulation (FM) has shown promise in preserving coherence at zero temperature, its effectiveness in realistic, noisy thermal environments remains unclear. In this work, we investigate a single frequency‐modulated qubit interacting with a thermal phase‐covariant reservoir composed of dissipative and dephasing channels. We demonstrate that FM significantly preserves coherence in the presence of thermal dissipation while being ineffective under thermal pure‐dephasing noise due to commutation between system and interaction Hamiltonians. When both noise channels are present, FM offers protection only for weak dephasing coupling. Our findings clarify the limitations and potential of FM‐based coherence protection under thermal noise, supplying practical insights into designing robust quantum systems for quantum applications.
Abstract We present a comprehensive study of quantum coherence dynamics in a qubit–qutrit system coupled to a resonator and exposed to an external noisy environment. Unlike prior works, we focus on the comparative analysis of three distinct coherence measures–l 1-norm of coherence, relative entropy of coherence, and Jensen–Shannon coherence–under dynamic modulation of the resonator frequency. Our key innovation lies in introducing time-dependent sinusoidal and standing wave modulations to the oscillator frequency, revealing nontrivial effects on coherence preservation that are highly sensitive to the modulation parameters. Remarkably, we uncover parameter regimes where coherence revivals are enhanced, even under strong decoherence, a phenomenon not observed in static systems. Additionally, our results demonstrate distinct sensitivity patterns among the coherence measures, highlighting their complementary roles in capturing system-environment interactions. This reanalysis is crucial as it reveals previously unexplored mechanisms for coherence control in hybrid quantum systems, offering novel strategies for improving the robustness of quantum technologies against environmental disturbances.
Finding strategies to preserve quantum resources in open systems is nowadays a main requirement for reliable quantum-enhanced technologies. We address this issue by considering structured cavities embedding qubits whose transition frequency is modulated by a driving field. We first focus on a single-qubit system to determine the optimal modulation parameters and the qubit-cavity coupling regime allowing a long-time preservation of both coherence and quantum Fisher information. We relate this behavior to the inhibition of the qubit effective decay rate rather than to stronger memory effects (non-Markovianity) of the system. We then use these findings to efficiently control resources like entanglement, discord and coherence in a system of two separated qubits. We discuss the feasibility of the system and show that individual qubit frequency modulation can produce quantum resource lifetimes orders of magnitude longer than their natural (uncontrolled) decay times. These results provide new useful insights towards efficient experimental strategies against decoherence.
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 10−410^{-4}10−4 for operation times <1  μ<1\;\mu<1μs, while the use of precision LOs can suppress error rates by 10410^{4}104. 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.
Finding strategies to preserve quantum resources in open systems is nowadays a main requirement for reliable quantum-enhanced technologies. We address this issue by considering structured cavities embedding qubits driven by a control technique known as frequency modulation. We first study a single qubit in a lossy cavity to determine optimal modulation parameters and qubit-cavity coupling regime allowing a gain of four orders of magnitude concerning coherence lifetimes. We relate this behavior to the inhibition of the qubit effective decay rate rather than to stronger memory effects (non-Markovianity) of the system. We then exploit these findings in a system of noninteracting qubits embedded in separated cavities to gain basic information about scalability of the procedure. We show that the determined modulation parameters enable lifetimes of quantum resources, such as entanglement, discord and coherence, three orders of magnitude longer than their natural (uncontrolled) decay times. We discuss the feasibility of the system within the circuit-QED scenario, typically employed in the current quantum computer prototypes. These results provide new insights towards efficient experimental strategies against decoherence.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto N∼10N\sim 10N∼10. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on NNN for 4<N<104< N<104<N<10 and saturate for $10