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Tom Struck

Publications and source records attributed to Tom Struck.

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Singlet-triplet oscillations in multivalley Si double quantum dots

Charge separation from the $(4,0)$ to the $(3,1)$ 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 $(3,1)$ 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 $g$-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.

cond-mat.mes-hall

Mapping g-factors and complex intervalley coupling in Si/SiGe by conveyor-mode shuttling

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 $10^{-3}$ 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.

quant-ph

Impact of the local valley splitting on the coherence of conveyor-belt spin shuttling in $^{28}$Si/SiGe

Silicon quantum chips offer a promising path toward scalable, fault-tolerant quantum computing, with the potential to host millions of qubits. However, scaling up dense quantum-dot arrays and enabling qubit interconnections through shuttling are hindered by uncontrolled lateral variations of the valley splitting energy $E_{VS}$. We map $E_{VS}$ across a $40 \, $nm x $400 \, $nm region of a $^{28}$Si/Si$_{0.7}$Ge$_{0.3}$ shuttle device and analyze the spin coherence of a single electron spin transported by conveyor-belt shuttling. We observe that the $E_{VS}$ varies over a wide range from $1.5 \, \mu$eV to $200 \, \mu$eV and is dominated by SiGe alloy disorder. In regions of low $E_{VS}$ and at spin-valley resonances, spin coherence is reduced and its dependence on shuttle velocity matches predictions. Rapid and frequent traversal of low-$E_{VS}$ regions induces a regime of enhanced spin coherence explained by motional narrowing. By selecting shuttle trajectories that avoid problematic areas on the $E_{VS}$ map, we achieve transport over tens of microns with coherence limited only by the coupling to a static electron spin entangled with the mobile qubit. Our results provide experimental confirmation of the theory of spin-decoherence of mobile electron spin-qubits and present practical strategies to integrate conveyor-mode qubit shuttling into silicon quantum chips.

quant-ph

Mapping of valley-splitting by conveyor-mode spin-coherent electron shuttling

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with high spatial and energy resolution are lacking. Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling, we introduce a method for two-dimensional mapping of the local valley splitting by detecting magnetic field dependent anticrossings of ground and excited valley states using entangled electron spin-pairs as a probe. The method has sub-{\mu}eV energy accuracy and a nanometer lateral resolution. The histogram of valley splittings spanning a large area of 210 nm by 18 nm matches well with statistics obtained by the established but time-consuming magnetospectroscopy method. For the specific heterostructure, we find a nearly Gaussian distribution of valley splittings and a correlation length similar to the quantum dot size. Our mapping method may become a valuable tool for engineering Si/SiGe heterostructures for scalable quantum computing.

quant-ph

Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe

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 $\mu$m, 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.

quant-ph

Si/SiGe QuBus for single electron information-processing devices with memory and micron-scale connectivity function

The connectivity within single carrier information-processing devices requires transport and storage of single charge quanta. Our all-electrical Si/SiGe shuttle device, called quantum bus (QuBus), spans a length of 10 $\mathrmμ$m and is operated by only six simply-tunable voltage pulses. It operates in conveyor-mode, i.e. the electron is adiabatically transported while confined to a moving QD. We introduce a characterization method, called shuttle-tomography, to benchmark the potential imperfections and local shuttle-fidelity of the QuBus. The fidelity of the single-electron shuttle across the full device and back (a total distance of 19 $\mathrmμ$m) is $(99.7 \pm 0.3)\,\%$. Using the QuBus, we position and detect up to 34 electrons and initialize a register of 34 quantum dots with arbitrarily chosen patterns of zero and single-electrons. The simple operation signals, compatibility with industry fabrication and low spin-environment-interaction in $^{28}$Si/SiGe, promises spin-conserving transport of spin qubits for quantum connectivity in quantum computing architectures.

cond-mat.mes-hall

Conveyor-mode single-electron shuttling in Si/SiGe for a scalable quantum computing architecture

Small spin-qubit registers defined by single electrons confined in Si/SiGe quantum dots operate successfully and connecting these would permit scalable quantum computation. Shuttling the qubit carrying electrons between registers is a natural choice for high-fidelity coherent links provided the overhead of control signals stays moderate. Our proof-of-principle demonstrates shuttling of a single electron by a propagating wave-potential in an electrostatically defined 420 nm long Si/SiGe quantum-channel. This conveyor-mode shuttling approach requires independent from its length only four sinusoidal control signals. We discuss the tuning of the signal parameters, detect the smoothness of the electron motion enabling the mapping of potential disorder and observe a high single-electron shuttling fidelity of $99.42\pm0.02\,\%$ including a reversal of direction. Our shuttling device can be readily embedded in industrial fabrication of Si/SiGe qubit chips and paves the way to solving the signal-fanout problem for a fully scalable semiconductor quantum-computing architecture.

cond-mat.mes-hall

Robust and fast post-processing of single-shot spin qubit detection events with a neural network

Establishing low-error and fast detection methods for qubit readout is crucial for efficient quantum error correction. Here, we test neural networks to classify a collection of single-shot spin detection events, which are the readout signal of our qubit measurements. This readout signal contains a stochastic peak, for which a Bayesian inference filter including Gaussian noise is theoretically optimal. Hence, we benchmark our neural networks trained by various strategies versus this latter algorithm. Training of the network with 10$^{6}$ experimentally recorded single-shot readout traces does not improve the post-processing performance. A network trained by synthetically generated measurement traces performs similar in terms of the detection error and the post-processing speed compared to the Bayesian inference filter. This neural network turns out to be more robust to fluctuations in the signal offset, length and delay as well as in the signal-to-noise ratio. Notably, we find an increase of 7 % in the visibility of the Rabi-oscillation when we employ a network trained by synthetic readout traces combined with measured signal noise of our setup. Our contribution thus represents an example of the beneficial role which software and hardware implementation of neural networks may play in scalable spin qubit processor architectures.

quant-ph

Large, tunable valley splitting and single-spin relaxation mechanisms in a Si/Si$_x$Ge$_{1-x}$ quantum dot

Valley splitting is a key figure of silicon-based spin qubits. Quantum dots in Si/SiGe heterostructures reportedly suffer from a relatively low valley splitting, limiting the operation temperature and the scalability of such qubit devices. Here, we demonstrate a robust and large valley splitting exceeding 200 $μ$eV in a gate-defined single quantum dot, hosted in molecular-beam epitaxy-grown $^{28}$Si/SiGe. The valley splitting is monotonically and reproducibly tunable up to 15 % by gate voltages, originating from a 6 nm lateral displacement of the quantum dot. We observe static spin relaxation times $T_1>1$ s at low magnetic fields in our device containing an integrated nanomagnet. At higher magnetic fields, $T_1$ is limited by the valley hotspot and by phonon noise coupling to intrinsic and artificial spin-orbit coupling, including phonon bottlenecking.

cond-mat.mes-hall

Low-frequency spin qubit detuning noise in highly purified $^{28}$Si/SiGe

The manipulation fidelity of a single electron qubit gate-confined in a $^{28}$Si/SiGe quantum dot has recently been drastically improved by nuclear isotope purification. Here, we identify the dominant source for low-frequency qubit detuning noise in a device with an embedded nanomagnet, a remaining $^{29}$Si concentration of only 60$\,$ppm in the strained $^{28}$Si quantum well layer and a spin echo decay time $T_2^{\text{echo}}=128\,μ$s. The power spectral density (PSD) of the charge noise explains both the observed transition of a $1/f^2$- to a $1/f$-dependence of the detuning noise PSD as well as the observation of a decreasing time-ensemble spin dephasing time from $T_2^* \approx 20\,μ$s with increasing measurement time over several hours. Despite their strong hyperfine contact interaction, the few $^{73}$Ge nuclei overlapping with the quantum dot in the barrier do not limit $T_2^*$, as their dynamics is frozen on a few hours measurement scale. We conclude that charge noise and the design of the gradient magnetic field is the key to further improve the qubit fidelity.

quant-ph