Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.
Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.
Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate 1/T1 as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.
We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.
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 T1 and dephasing T2 times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, 1/T temperature scaling and 1/B3 magnetic field scaling of T1 are established using atomistic bath correlation functions. Atomistic T1 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∼10μT−1mT for the copper porphyrin system. We show that while T1 scales as 1/B experimentally due to a combination of spin-lattice and magnetic noise contributions, T2 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.
Mobile spin qubit architectures promise flexible connectivity for efficient quantum error correction and relaxed device layout constraints, but their viability rests on preserving spin coherence during transport. While shuttling transforms spatial disorder into time-dependent noise, its net impact on spin coherence remains an open question. Here we demonstrate systematic noise mitigation during spin shuttling in a linear 28Si/SiGe quantum dot device. First, by passively reducing magnetic field gradients, we minimize charge-noise coupling to the spin and double the spatially averaged dephasing time T2∗(xn) from 4.4 to 8.5μs. Next, we exploit motional narrowing by periodically shuttling the qubit, achieving a further enhancement in coherence time up to T2∗,sh=11.5μs. Finally, we incorporate dynamical decoupling techniques while periodically shuttling over distances exceeding 200nm, reaching T2H,sh=32μs. For the same setup, we demonstrate that dressed-state shuttling provides robust protection against low-frequency noise with a decay time TRsh=21μs, without the overhead of pulsed control and allowing protection during one-way spin transport. By preserving coherence over timescales exceeding typical gate and readout operations, the demonstrated strategies establish mobile spin qubits as a viable solution for scalable silicon quantum processors.
We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. A hybrid qubit behaves as a charge qubit when the detuning is close to zero and as a spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e., the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.
Silicon-based spin qubits in Si/SiGe heterostructures are a leading platform for scalable quantum computing, yet bridging the gap between theoretical computer-aided design(CAD) models and experimental reality remains a significant challenge. Standard simulations often fail to capture critical physical phenomena, such as interface dipoles, parasitic charge accumulation, and the magnetic hysteresis of on-chip micromagnets. In this work, we present a comprehensive, experimentally calibrated 3D simulation pipeline for a 6-dot Si/SiGe device. We refine the semiconductor band alignment and introduce a semi-empirical classical charge screening model to accurately capture the formation of parasitic wells and their suppression of gate lever-arms. Furthermore, we apply the Jiles-Atherton model to account for the hysteresis and pre-magnetization of integrated cobalt micromagnets, successfully reproducing the experimental resonant frequencies across all six qubits. By coupling these calibrated electrostatic and magnetic profiles into a time-dependent rotating wave approximation (RWA) Hamiltonian, we reproduce experimental observables, including microwave power chevrons. This framework provides a robust foundation for predicting device behavior, evaluating microwave line losses, and optimizing future scalable spin qubit architectures prior to fabrication.