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arXiv:2610.08984

Valley transitions during spin shuttling in Si/SiGe heterostructures

Jonas R F Lima, Guido Burkard

cond-mat.mes-hallquant-phSubmitted Oct 6, 2026• Announced Oct 8, 2026
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Abstract

Valley excitations are considered one of the biggest challenges for a coherent spin shuttling in Si/SiGe heterostructures. In this work we theoretically investigate the valley dynamics during spin shuttling in a Si/SiGe heterostructure by considering a two-level system given by the two low-lying valley states of the mobile quantum dot. We assume that the electron is initially in the valley ground state and analyze the evolution of this state during shuttling. We find that, depending on the shuttling velocity, the system can be in three distinct regimes. In one of these regimes, the quantum information is preserved even in the presence of the valley excitations, allowing for coherent spin shuttling independently of the shuttling distance. This regime is obtained for a shuttling velocity of tens of m/s, a desired regime where dephasing mechanisms, such as spin-valley hotspots and spatially varying spin splitting, can be suppressed. This result is in accordance with recent experimental work that obtained a high spin shuttling fidelity after a fast and long shuttling. We also propose strategies based on the Partial Landau-Zener model to enhance the valley shuttling fidelity, which was found to be much more efficient than previously proposed strategies based on the standard Landau-Zener model.

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Spatial variations of the valley splitting in a quantum well present a key challenge for conveyor-mode shuttling of electron spins in Si/SiGe, giving rise to Landau-Zener-like excitations that cause leakage outside the qubit subspace. Here, we propose an unconventional two-electron qubit encoding, based on valley-singlet states, that is largely immune to Landau-Zener leakage processes. In contrast to single-electron spins, the shuttling fidelity actually improves for small valley splittings, in this case. We show that high fidelities can be achieved without applying any special procedures, such as fine-tuning of the shuttling path.

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Conveyor-mode shuttling is a key approach for implementing intermediate-range coupling between electron-spin qubits in quantum dots. Initial implementations are encouraging; however, long shuttling trajectories are guaranteed to encounter regions of low conduction-band valley-energy splittings, due to the presence of random-alloy disorder in Si / Si Ge quantum wells. Here, we theoretically explore two schemes for avoiding valley-state excitations at these valley-splitting minima, by allowing the electrons to detour around them. A scheme allows electrons to tunnel between parallel channels, while a provides full omnidirectional control. Using simulations, we estimate shuttling fidelities in these two schemes, obtaining a clear preference for the 2D shuttler. Based on such encouraging results, we propose a modular qubit architecture based on 2D shuttling, which enables all-to-all connectivity within qubit plaquettes and high-fidelity communication between different plaquettes.

arXiv:2412.09574•PRX Quantum•Jan 2, 2026•1 citation
Valley excitations are considered one of the biggest challenges for a coherent spin shuttling in Si/SiGe heterostructures. In this work we theoretically investigate the valley dynamics during spin shuttling in a Si/SiGe heterostructure by considering a two-level system given by the two low-lying valley states of the mobile quantum dot. We assume that the electron is initially in the valley ground state and analyze the evolution of this state during shuttling. We find that, depending on the shuttling velocity, the system can be in three distinct regimes. In one of these regimes, the quantum information is preserved even in the presence of the valley excitations, allowing for coherent spin shuttling independently of the shuttling distance. This regime is obtained for a shuttling velocity of tens of m/s, a desired regime where dephasing mechanisms, such as spin-valley hotspots and spatially varying spin splitting, can be suppressed. This result is in accordance with recent experimental work that obtained a high spin shuttling fidelity after a fast and long shuttling. We also propose strategies based on the Partial Landau-Zener model to enhance the valley shuttling fidelity, which was found to be much more efficient than previously proposed strategies based on the standard Landau-Zener model.
Spatial variations of the valley splitting in a quantum well present a key challenge for conveyor-mode shuttling of electron spins in Si/SiGe, giving rise to Landau-Zener-like excitations that cause leakage outside the qubit subspace. Here, we propose an unconventional two-electron qubit encoding, based on valley-singlet states, that is largely immune to Landau-Zener leakage processes. In contrast to single-electron spins, the shuttling fidelity actually improves for small valley splittings, in this case. We show that high fidelities can be achieved without applying any special procedures, such as fine-tuning of the shuttling path.
Single electron spins can be used to encode and process information in semiconductor quantum devices. Progress has been hindered by materials challenges, such as the small energy splitting between low-lying valley states and hyperfine coupling to nuclear spins. Here we use density functional theory to optimize the valley splitting and spin dephasing time in realistic Si/SiGe heterostructures. Reductions in the Si quantum well width generally increase the valley splitting. However, in narrow quantum wells, a larger fraction of the electronic wavefunction resides in the SiGe buffer layers, which increases the hyperfine coupling with spinful 73^{73}73Ge. Our work shows that Si/SiGe heterostructures with 3~--~4~nm wide quantum wells and 73^{73}73Ge and 29^{29}29Si concentrations of 50 ppm should support average valley splittings EvE_{v}Ev​~>>>~500~μμμeV and spin dephasing times T2∗T_2^*T2∗​ exceeding 15~μμμs assuming an effective quantum dot area of 700 nm2^22. In addition, sharper Si/SiGe interfaces in general result in larger valley splittings and longer spin dephasing times.
Coherent electron shuttling is a key requirement for realizing scalable silicon quantum computing architectures. However, in silicon qubits, the existence of nearly degenerate conduction-band valleys poses a significant challenge because non-adiabatic transitions to excited valley states cause spin dephasing via spin-valley mixing. In this paper, we propose a smooth velocity shuttling protocol to suppress these valley excitations. By mapping the time-domain design of the shuttling velocity profile onto the design problem of window functions in signal processing, we establish an analytical and intuitive design guideline that does not require computationally expensive numerical optimization. We demonstrate that the high-frequency sidelobes of the shuttling velocity spectrum can be effectively suppressed by applying a frequency-modulated gate voltage based on the Tukey window. Through statistical numerical simulations incorporating realistic spatial randomness of the valley landscape, we show that the proposed smooth velocity control significantly reduces the average spin infidelity in the moderate-to-low disorder regime (∣Δ0∣/σΔ≃O(1)|Δ_0|/σ_Δ\simeq \mathcal{O}(1)∣Δ0​∣/σΔ​≃O(1)). Our results underscore that this simple, control-level velocity shaping provides a robust pathway toward high-fidelity spin transport in large-scale silicon quantum processors.
Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
As silicon spin qubit chips are increasing in qubit number and area, methods for the screening of qubit related material parameters become vital. Here we demonstrate the two-dimensional mapping of small variations of the electron g-factor of quantum dots formed in planar Si/SiGe quantum wells with precision better than 10−310^{-3}10−3 and with nanometer lateral resolution. We scan the electron g-factor across a 40 nm ×\times× 400 nm area and observe two g-factors per QD site which obey a striking symmetry and bimodal distribution across the area. These two g-factors relate to valley states of the electron in the quantum dot in agreement with a recent theoretical model. Using conveyor-belt shuttling of entangled electron spin pairs, complementary to the mapping of the local valley-splitting, we map the g-factor. We compare g-factor and valley splitting maps measured on the same device, and extract the complex intervalley coupling parameter along the shuttle trajectories applying a theoretical model of g-factor dependence on intervalley coupling. These maps will allow unprecedented insights into the spin-valley dynamics during qubit manipulation, readout and shuttling and serve as a benchmark for the engineering of Si/SiGe heterostructures for large-scale quantum chips.
Conveyor-mode shuttling is a key approach for implementing intermediate-range coupling between electron-spin qubits in quantum dots. Initial implementations are encouraging; however, long shuttling trajectories are guaranteed to encounter regions of low conduction-band valley-energy splittings, due to the presence of random-alloy disorder in Si / Si Ge quantum wells. Here, we theoretically explore two schemes for avoiding valley-state excitations at these valley-splitting minima, by allowing the electrons to detour around them. A scheme allows electrons to tunnel between parallel channels, while a provides full omnidirectional control. Using simulations, we estimate shuttling fidelities in these two schemes, obtaining a clear preference for the 2D shuttler. Based on such encouraging results, we propose a modular qubit architecture based on 2D shuttling, which enables all-to-all connectivity within qubit plaquettes and high-fidelity communication between different plaquettes.