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arXiv:1803.10352 · Applied Physics Letters

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

Cornelis Jacobus van Diepen, Pieter T. Eendebak, Bruno T. Buijtendorp, U. Mukhopadhyay, T. Fujita, Christian Reichl, W. Wegscheider, Lieven M. K. Vandersypen

Published Jul 16, 2018• 70 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.5031034

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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 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 μμμeV, and we discuss the limiting factors of our method.
Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.
As with any quantum computing platform, semiconductor quantum dot devices require sophisticated hardware and controls for operation. The increasing complexity of quantum dot devices necessitates the advancement of automated control software and image recognition techniques for rapidly evaluating charge stability diagrams. We use an image analysis toolbox developed in Python to automate the calibration of virtual gates, a process that previously involved a large amount of user intervention. Moreover, we show that straightforward feedback protocols can be used to simultaneously tune multiple tunnel couplings in a triple quantum dot in a computer automated fashion. Finally, we adopt the use of a “tunnel coupling lever arm” to model the interdot barrier gate response and discuss how it can be used to more rapidly tune interdot tunnel couplings to the gigahertz values that are compatible with exchange gates.
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.
Spin qubits in quantum dots are a compelling platform for fault-tolerant quantum computing due to the potential to fabricate dense two-dimensional arrays with nearest neighbour couplings, a requirement to implement the surface code. However, due to the proximity of the surface gate electrodes, cross-coupling capacitances can be substantial, making it difficult to control each quantum dot independently. Increasing the number of quantum dots increases the complexity of the calibration process, which becomes impractical to do heuristically. Inspired by recent demonstrations of industrial-grade silicon quantum dot bilinear arrays, we develop a theoretical framework to mitigate the effect of cross-capacitances in 2x2 arrays of quantum dots and extend it to 2xN and NxN arrays. The method is based on extracting the gradients in gate-voltage space of different charge transitions in multiple two-dimensional charge stability diagrams to determine the system's virtual gates. To automate the process, we train an ensemble of regression models to extract the gradients from a Hough transformation of charge stability diagrams and validate the algorithm on simulated and experimental data of a 2x2 quantum dot array. Our method provides a completely automated tool to mitigate cross-capacitance effects in arrays of QDs which could be utilised to study variability in device electrostatics across large arrays.
Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.