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arXiv:2511.08725

Hybrid Atomistic-Parametric Decoherence Model for Molecular Spin Qubits

Katy Aruachan, Sanoj Raj, Yamil J. Colón, Daniel Aravena, Felipe Herrera

quant-phphysics.chem-phSubmitted Nov 11, 2025• Announced Nov 13, 2025
arXivHTMLPDF

Abstract

Solid-state molecular qubits with open-shell ground states have great potential for addressability, scalability, and tunability, but understanding the fundamental limits of quantum coherence in these systems is challenging due to the complexity of the qubit environment. To address this, we develop a random Hamiltonian approach where the molecular $g$-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic $g$-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation $T_1$ and dephasing $T_2$ times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, $1/T$ temperature scaling and $1/B^3$ magnetic field scaling of $T_1$ are established using atomistic bath correlation functions. Atomistic $T_1$ predictions overestimate the available experimental data by orders of magnitude. Quantitative agreement with measurements at all magnetic fields is restored by introducing a magnetic field noise model to describe lattice nuclear spins, with field-dependent noise amplitude in the range $δB\sim 10\,μ{\rm T}- 1\,{\rm mT}$ for the copper porphyrin system. We show that while $T_1$ scales as $1/B$ experimentally due to a combination of spin-lattice and magnetic noise contributions, $T_2$ scales strictly as $ 1/B^2$ due to low-frequency dephasing processes associated with magnetic field noise. Our work demonstrates the potential of dynamical methods for modeling the open quantum system dynamics of molecular spin qubits.

Journal reference
J. Chem. Phys. 164, 124101, 2026
DOI
10.1063/5.0312242
Comments
7 pages, 4 figures

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Solid-state molecular qubits with open-shell ground states have great potential for addressability, scalability, and tunability, but understanding the fundamental limits of quantum coherence in these systems is challenging due to the complexity of the qubit environment. To address this, we develop a random Hamiltonian approach where the molecular ggg-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic ggg-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation T1T_1T1​ and dephasing T2T_2T2​ times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, 1/T1/T1/T temperature scaling and 1/B31/B^31/B3 magnetic field scaling of T1T_1T1​ are established using atomistic bath correlation functions. Atomistic T1T_1T1​ predictions overestimate the available experimental data by orders of magnitude. Quantitative agreement with measurements at all magnetic fields is restored by introducing a magnetic field noise model to describe lattice nuclear spins, with field-dependent noise amplitude in the range δB∼10 μT−1 mTδB\sim 10\,μ{\rm T}- 1\,{\rm mT}δB∼10μT−1mT for the copper porphyrin system. We show that while T1T_1T1​ scales as 1/B1/B1/B experimentally due to a combination of spin-lattice and magnetic noise contributions, T2T_2T2​ scales strictly as 1/B2 1/B^21/B2 due to low-frequency dephasing processes associated with magnetic field noise. Our work demonstrates the potential of dynamical methods for modeling the open quantum system dynamics of molecular spin qubits.
Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.
The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. In this paper, we extend the cluster correlation expansion (CCE) technique, which has proven useful for predicting solid-state qubit coherence times across various settings but is limited to shorter time scales, to incorporate stochastic treatments of cluster dynamics in order to efficiently predict slow drifting Overhauser fields over longer time scales. This approach combines quantum evolution with classical rate matrices to enable simulation across a wide range of temporal regimes required to simulate, for example, the long-time convergence of the ergodic T2∗T_2^*T2∗​ from Ramsey experiments. Our methodology is validated against experimental data from various silicon spin qubit systems, demonstrating a strong agreement between simulation and measurement of Ramsey experiments presented in the form of T2∗T_2^*T2∗​ versus averaging time, autocorrelation functions, as well as power spectral densities. Furthermore, we demonstrate significant back-action effects through modeling and experiment; specifically, the dynamics of the nuclear spin bath depends upon the electron spin occupation schedule. Finally, our modeling quantitatively predicts the benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured ΔtΔtΔt in the past results in an effective T2∗T_2^*T2∗​, which we denote T~2∗(Δt)\tilde{T}_2^*(Δt)T~2∗​(Δt) for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic T2∗T_2^*T2∗​ if the Overhauser rotation is re-characterized every 100 milliseconds; that is, T~2∗(Δt=100 ms)\tilde{T}_2^*(Δt = 100~{\rm ms})T~2∗​(Δt=100 ms) can be 101010 to 100100100 times larger than T2∗T_2^*T2∗​.
Molecular spin qubits are promising candidates for quantum technologies, but their performance is limited by decoherence arising from diverse mechanisms. The complexity of the environment makes it challenging to identify the main source of noise and target it for mitigation. Here we present a systematic experimental and theoretical framework for analyzing the mechanisms of transverse relaxation in copper(II) phthalocyanine (CuPc) diluted into diamagnetic phthalocyanine hosts. Using pulsed EPR spectroscopy together with first-principles cluster correlation expansion simulations, we quantitatively separate the contributions from hyperfine-coupled nuclear spins, spin--lattice relaxation, and electron--electron dipolar interactions. Our detailed modeling shows that both strongly and weakly coupled nuclei contribute negligibly to T2T_2T2​, while longitudinal dipolar interactions with electronic spins, through instantaneous and spectral diffusion, constitute the main decoherence channel even at moderate spin densities. This conclusion is validated by direct comparison between simulated spin-echo dynamics and experimental data. By providing a robust modeling and experimental approach, our work identifies favorable values of the electron spin density for quantum applications, and provides a transferable methodology for predicting ensemble coherence times. These insights will guide the design and optimization of molecular spin qubits for scalable quantum devices.
Optically active solid-state spin defects are promising candidates for quantum applications, however a unified theoretical framework to predict their spin dynamics at high temperatures is not yet available. Here, using Kubo linear--response theory, we derive expressions of spin-lattice and decoherence times T1T_1T1​ and T2T_2T2​ in terms of correlation functions of spin--lattice couplings. We then evaluate T1T_1T1​ and T2T_2T2​ from molecular dynamics and spin--lattice interaction time--series generated by state--of--the--art machine learning models trained on {\it ab--initio} data. Finally we measure T1T_1T1​ times for the NV center in diamond and compare experimental and theoretical results, showing excellent agreement.
Multi-qubit systems are essential for scalable quantum technologies, but their performance is often limited by decoherence from qubit--qubit interactions and environmental noise. Although environmental decoherence in single-qubit systems and gate fidelity in multi-qubit systems have been widely studied, a predictive framework connecting qubit interactions, concentration, spatial distribution, and bath occupation to relaxation and decoherence times remains lacking. Here, we develop a multi-qubit mean-field Lindblad master equation (MQMF-LME) framework for the population and coherence dynamics of a solid-state qubit in an interacting multi-qubit environment. The framework treats one qubit as the system of interest and the surrounding qubits as an effective bath, incorporating intrinsic relaxation and bidirectional excitation transfer between the system and the bath. Analytical solutions provide closed-form expressions for density-matrix dynamics, steady-state populations, relaxation time T1T_1T1​, and decoherence time T2T_2T2​, while numerical simulations extend the framework to concentration-dependent dynamics, 1/f1/f1/f-noise-induced dephasing, and material-specific excitation-transfer mechanisms. For a model system with Förster resonance energy transfer (FRET)-mediated excitation exchange, higher qubit concentrations reduce both T1T_1T1​ and T2T_2T2​, whereas 1/f1/f1/f noise reduces T2T_2T2​ without changing T1T_1T1​. Applied to Er3+^{3+}3+-doped CeO2_22​, the framework shows that long-range FRET-mediated excitation transfer reproduces the experimental decrease in relaxation time with dopant concentration, whereas short-range Dexter-type exchange does not, identifying FRET-mediated excitation transfer as the dominant mechanism. The MQMF-LME framework provides a modular route for linking microscopic interactions and environmental noise sources to measurable decoherence times in solid-state multi-qubit systems.
A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence - the process whereby phase information encoded in a qubit is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times T2T_2T2​, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, possess 'optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. Analysis of sharp variations of T2T_2T2​ near OWPs was previously based on insensitivity to classical noise, even though hybrid qubits are situated in highly correlated quantum environments, such as the nuclear spin bath of 29^{29}29Si impurities. This presented limited understanding of the decoherence mechanism and gave unreliable predictions for T2T_2T2​. I present quantum many-body calculations of the qubit-bath dynamics, which (i) yield T2T_2T2​ for hybrid qubits in excellent agreement with experiments in multiple regimes, (ii) elucidate the many-body nature of the nuclear spin bath and (iii) expose significant differences between quantum-bath and classical-field decoherence. To achieve these, the cluster correlation expansion was adapted to include electron-nuclear state mixing. In addition, an analysis supported by experiment was carried out to characterise the nuclear spin bath for a bismuth donor as the hybrid qubit, a simple analytical formula for T2T_2T2​ was derived with predictions in agreement with experiment, and the established method of dynamical decoupling was combined with operating near OWPs in order to maximise T2T_2T2​. Finally, the decoherence of a 29^{29}29Si spin in proximity to the hybrid qubit was studied, in order to establish the feasibility for its use as a quantum register.