Semiconductor quantum dots are favorable candidates for quantum information processing due to their long coherence time and potential scalability. However, the calibration and characterization of interconnected quantum dot arrays have proven to be challenging tasks. One method to characterize the configuration of such an array involves using the Hubbard model. In this paper, we present an automated characterization algorithm that efficiently extracts the Hubbard model parameters, including tunnel coupling and capacitive coupling energy, from experimental stability diagrams. Leveraging the dual annealing optimizer, we determine the set of Hubbard parameters that best characterize the experimental data. We compare our method with an alternate, well-established measure of the tunnel coupling and find good agreement within the investigated regime. Our extracted tunnel couplings range from 69 to 517 $μ$ eV, and we discuss the limiting factors of our method.Semiconductor quantum dots are favorable candidates for quantum information processing due to their long coherence time and potential scalability. However, the calibration and characterization of interconnected quantum dot arrays have proven to be challenging tasks. One method to characterize the configuration of such an array involves using the Hubbard model. In this paper, we present an automated characterization algorithm that efficiently extracts the Hubbard model parameters, including tunnel coupling and capacitive coupling energy, from experimental stability diagrams. Leveraging the dual annealing optimizer, we determine the set of Hubbard parameters that best characterize the experimental data. We compare our method with an alternate, well-established measure of the tunnel coupling and find good agreement within the investigated regime. Our extracted tunnel couplings range from 69 to 517 $μ$eV, and we discuss the limiting factors of our method.

arXiv:2309.03400Sep 6, 20230 citations

Automated tuning of inter-dot tunnel coupling in double quantum dots

Cornelis Jacobus van Diepen, Pieter T. Eendebak, Bruno T. Buijtendorp +5 more

Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation.Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation.

arXiv:1803.10352Applied Physics LettersJul 16, 201870 citations

Theory of charge stability diagrams in coupled quantum dot qubits

Nathan L. Foulk, S. Das Sarma

We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with $N=3$ electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with $N=3$ electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.

arXiv:2409.02301Physical review. B./Physical review. BNov 25, 20245 citations

Direct measurement of the energy spectrum of a quantum dot qubit

J. Reily, Daniel J. King, Jonathan C. Marcks +8 more

The mapping between gate voltages applied to a double quantum dot, and the parameters of a Hubbard-like Hamiltonian, is of utmost importance for understanding and operating spin qubits. State-of-the-art techniques for measuring Hamiltonian parameters (e.g., detuning axis pulsed spectroscopy, DAPS) provide details about energy levels; however, tunnel coupling estimates typically reveal only a small portion of the full Hamiltonian. Here, we demonstrate a Hamiltonian-agnostic technique for measuring the double dot energy spectrum over a wide energy range, at every value of the detuning, called delta-axis spectroscopy (DAXS). We apply the DAXS method to obtain the energy spectrum of a Si/SiGe double quantum dot and use this data to extract the diagonal and off-diagonal couplings of a 15-level Hubbard-like Hamiltonian, demonstrating very good agreement with the experimental measurements.The mapping between gate voltages applied to a double quantum dot, and the parameters of a Hubbard-like Hamiltonian, is of utmost importance for understanding and operating spin qubits. State-of-the-art techniques for measuring Hamiltonian parameters (e.g., detuning axis pulsed spectroscopy, DAPS) provide details about energy levels; however, tunnel coupling estimates typically reveal only a small portion of the full Hamiltonian. Here, we demonstrate a Hamiltonian-agnostic technique for measuring the double dot energy spectrum over a wide energy range, at every value of the detuning, called delta-axis spectroscopy (DAXS). We apply the DAXS method to obtain the energy spectrum of a Si/SiGe double quantum dot and use this data to extract the diagonal and off-diagonal couplings of a 15-level Hubbard-like Hamiltonian, demonstrating very good agreement with the experimental measurements.

quant-pharXiv:2603.29229Apr 1, 20260 citations

Tuning Methods for Semiconductor Spin Qubits

Tim Botzem, Michael Shulman, Arne Ludwig +13 more

We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are developed for double quantum dots in GaAs heterostructures, but they can easily be adapted to other quantum-dot-based qubit systems. These tuning procedures include the characterization of the interdot tunnel coupling, the tunnel coupling to the surrounding leads, and the identification of various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor process technology and hence promise good prospects of scalability, the challenge of efficiently tuning the dot’s parameters will only grow in the near future, once the multiqubit stage is reached. With the anticipation of being used as the basis for future automated tuning protocols, all measurements presented here are fast-to-execute and easy-to-analyze characterization methods. They result in quantitative measures of the relevant qubit parameters within a couple of seconds and require almost no human interference.We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are developed for double quantum dots in GaAs heterostructures, but they can easily be adapted to other quantum-dot-based qubit systems. These tuning procedures include the characterization of the interdot tunnel coupling, the tunnel coupling to the surrounding leads, and the identification of various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor process technology and hence promise good prospects of scalability, the challenge of efficiently tuning the dot’s parameters will only grow in the near future, once the multiqubit stage is reached. With the anticipation of being used as the basis for future automated tuning protocols, all measurements presented here are fast-to-execute and easy-to-analyze characterization methods. They result in quantitative measures of the relevant qubit parameters within a couple of seconds and require almost no human interference.

Jan 1, 201836 citations

Generic Hubbard model description of semiconductor quantum-dot spin qubits

Shuo Yang, Xin Wang, S. Das Sarma

We introduce a Hubbard model as the simple quantum generalization of the classical capacitance circuit model to study semiconductor quantum-dot spin qubits. We prove theoretically that our model is equivalent to the usual capacitance circuit model in the absence of quantum fluctuations. However, our model naturally includes quantum effects such as hopping and spin exchange. The parameters of the generalized Hubbard model can either be directly read off from the experimental plot of the stability diagram or be calculated from the microscopic theory, establishing a quantitative connection between the two. We show that, while the main topology of the charge stability diagram is determined by the ratio between intersite and on-site Coulomb repulsion, fine details of the stability diagram reveal information about quantum effects. Extracting quantum information from experiments using our Hubbard model approach is simple, but would require the measurement resolution to increase by an order of magnitude.We introduce a Hubbard model as the simple quantum generalization of the classical capacitance circuit model to study semiconductor quantum-dot spin qubits. We prove theoretically that our model is equivalent to the usual capacitance circuit model in the absence of quantum fluctuations. However, our model naturally includes quantum effects such as hopping and spin exchange. The parameters of the generalized Hubbard model can either be directly read off from the experimental plot of the stability diagram or be calculated from the microscopic theory, establishing a quantitative connection between the two. We show that, while the main topology of the charge stability diagram is determined by the ratio between intersite and on-site Coulomb repulsion, fine details of the stability diagram reveal information about quantum effects. Extracting quantum information from experiments using our Hubbard model approach is simple, but would require the measurement resolution to increase by an order of magnitude.

arXiv:1101.3311Physical Review BApr 7, 201191 citations

μ

eV, and we discuss the limiting factors of our method.

N=3

electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.