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arXiv:2407.11964 · npj Quantum Information

Dephasing and error dynamics affecting a singlet-triplet qubit during coherent spin shuttling

Natalie Foster, Jacob Henshaw, Martin Rudolph, Dwight R. Luhman, Ryan Jock

Published Apr 12, 2025• 8 citations
arXivHTMLPDF

Abstract

Abstract Quantum information transport over micron to millimeter scale distances is critical for the operation of practical quantum processors based on spin qubits. One method of achieving a long-range interaction is by coherent electron spin shuttling through an array of silicon quantum dots. In order to execute many shuttling operations with high fidelity, it is essential to understand the dynamics of qubit dephasing and relaxation during the shuttling process in order to mitigate them. However, errors arising after many repeated shuttles are not yet well documented. Here, we probe decay dynamics contributing to dephasing and relaxation of a singlet-triplet qubit during coherent spin shuttling over many N repeated shuttle operations. We find that losses are dominated by magnetic dephasing for small N<\i> < 103 and by incoherent shuttle errors for large N<\i> > 103<\sup>. Additionally, we estimate shuttle error rates below 1×10-4<\sup> out to at least N<\i>=103<\sup>, representing an encouraging figure for future implementations of spin shuttling to entangle distant qubits.

DOI
10.1038/s41534-025-00996-0

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Abstract Quantum information transport over micron to millimeter scale distances is critical for the operation of practical quantum processors based on spin qubits. One method of achieving a long-range interaction is by coherent electron spin shuttling through an array of silicon quantum dots. In order to execute many shuttling operations with high fidelity, it is essential to understand the dynamics of qubit dephasing and relaxation during the shuttling process in order to mitigate them. However, errors arising after many repeated shuttles are not yet well documented. Here, we probe decay dynamics contributing to dephasing and relaxation of a singlet-triplet qubit during coherent spin shuttling over many N repeated shuttle operations. We find that losses are dominated by magnetic dephasing for small N<\i> < 103 and by incoherent shuttle errors for large N<\i> > 103<\sup>. Additionally, we estimate shuttle error rates below 1×10-4<\sup> out to at least N<\i>=103<\sup>, representing an encouraging figure for future implementations of spin shuttling to entangle distant 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 28^{28}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)T_2^*(x_n)T2∗​(xn​) from 4.44.44.4 to 8.5 μs8.5\,μ\text{s}8.5μs. Next, we exploit motional narrowing by periodically shuttling the qubit, achieving a further enhancement in coherence time up to T2∗,sh=11.5 μsT_{2}^{*,sh} = 11.5\,μ\text{s}T2∗,sh​=11.5μs. Finally, we incorporate dynamical decoupling techniques while periodically shuttling over distances exceeding 200 nm200\,\text{nm}200nm, reaching T2H,sh=32 μsT_\text{2}^{H,sh}= 32\,μ\text{s}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=21 μsT_R^{\text{sh}} = 21\,μ\text{s}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 demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.
Abstract We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting JJJ. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large JJJ and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.
Qubit shuttling promises to advance some quantum computing platforms to the qubit register sizes needed for effective quantum error correction (QEC), but also introduces additional errors whose impact must be evaluated. The established method to investigate the performance of QEC codes in a realistic scenario is to employ a standard noise model known as circuit-level noise, where all quantum operations are modeled as noisy. In the present work, we take this noise model and single out the effect of shuttling errors by introducing them as an additional so-called error location. This hardware abstraction is motivated by the SpinBus architecture and allows a systematic numerical investigation to map out the resulting two-dimensional parameter space. To this end, we take the Surface code and perform large scale simulations, most notably extracting the threshold across said two-dimensional parameter space. We study two scenarios for shuttling errors, depolarization on the one hand and dephasing on the other hand. For a purely dephasing shuttling error, we find a threshold of several percent, provided that all other operations have a high fidelity. The qubit overhead needed to reach a logical error rate of 10 − 12 (known as the "teraquop" regime \cite{Gidney2021Jul} increases only moderately for shuttling error rates up to about 1 % per shuttling operation. The error rates at which practically useful, i.e. well below threshold error correction is predicted to be possible are comfortably higher than what is expected to be achievable for spin qubits. Our results thus show that it is reasonable to expect shuttling operations to fall below threshold already at surprisingly large error rates. With realistic efforts in the near term, this offers positive prospects for spin qubit based quantum processors as a viable avenue for scalable fault-tolerant error-corrected quantum computing.
Long-ranged coherent qubit coupling is a missing function block for scaling up spin qubit based quantum computing solutions. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture. Its key feature is the operation by only few easily tuneable input terminals and compatibility with industrial gate-fabrication. Single electron shuttling in conveyor-mode in a 420 nm long quantum bus has been demonstrated previously. Here we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an Einstein-Podolsky-Rosen (EPR) spin-pair. Compared to previous work we boost the shuttle velocity by a factor of 10000. We observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing and estimate the spin-shuttle infidelity due to dephasing to be 0.7% for a total shuttle distance of nominal 560 nm. Shuttling several loops up to an accumulated distance of 3.36 μm, spin-entanglement of the EPR pair is still detectable, giving good perspective for our approach of a shuttle-based scalable quantum computing architecture in silicon.