A Three-Dimensional Array of Quantum Dots

TL;DR

This work demonstrates a three-dimensional quantum-dot architecture by fabricating an eight-quantum-dot cuboid in a Ge/SiGe bilayer heterostructure. Using a multilayer gate stack and triangulation-based gate control, they realize four $2\times 2$ planar arrays and coherently couple dots across two stacked wells, achieving single-hole loading into all eight dots. They show coherent spin operations, including Ramsey control with $T_2^*=2.31$ $\mu$s and shuttling-induced rotations between wells, indicating high-fidelity cross-layer qubit manipulation. The results highlight the potential of three-dimensional quantum-dot connectivity for scalable quantum simulation and computation, while also identifying design challenges that motivate co-design of materials, devices, and control architectures.

Abstract

Quantum dots can confine single electrons or holes to define spin qubits that can be operated with high fidelity. Experimental work has progressed from linear to two-dimensional arrays of quantum dots, enabling qubit interactions that are essential for quantum simulation and computation. Here, we explore architectures beyond planar geometries by constructing quantum dot arrays in three dimensions. We realize an eight-quantum dot system in a silicon-germanium heterostructure comprising two stacked germanium quantum wells, where quantum dots are positioned at the vertices of a cuboid. Using electrostatic gate control, we load a single hole into any of the eight quantum dots. To demonstrate the potential of multilayer quantum dot systems, we show coherent spin control and hopping-induced spin rotations by shuttling between the quantum wells. The ability to extend quantum dot arrays in three dimensions provides opportunities for novel quantum hardware and high-connectivity quantum circuits.

Figures (33)

• Figure 1: Heterostucture and device layout for the three-dimensional quantum dot array a, Schematic vision of how bilayer quantum heterostructures could be scaled to create bilayer qubit systems. The highlighted quantum dots forming a cube are the focus of the presented experimental work. b, Schematic of the Ge/SiGe double quantum well heterostructure, with 10 nm of Si0.2Ge0.8 separating two Ge quantum wells with a thickness of 10 nm and 16 nm. c, False-colored SEM image of a nominally identical device. A planar $2\times2$ array of plunger gates Pi (red) is used to accumulate charges in the underlying germanium quantum wells. The barrier gates Bij (blue) and screening gates Si (blue) provide further control. For charge readout, two RF-single hole transistors (SHT) are defined using the gates labeled PN,S and BN,S. The scale bar denotes 100 nm. d, Simplified gate layout showing the gates involved in triangulating the position of the quantum dots. e, Schematic representation of the cuboid quantum dot configuration in this work, with $i$u($\ell$) denoting a quantum dot in the upper (lower) quantum well, under plunger gate Pi.
• Figure 1: Sensor operation. In the left panel, the sensor is a single quantum dot. The experiments show measurement of a quantum dot under P3. In the right panel, the sensor contains a vertical double quantum dot.
• Figure 2: Simulated and measured vertical double quantum dot charge stability diagrams in 10nm separated quantum wells.a, Reflected signal of the rf-SHT underneath PS showing a charge-stability diagram that corresponds to a vertical double quantum dot located beneath P3, while P4 is not yet accumulated. b, The simulated charge-stability diagram based on a constant-capacitance model qarray of a vertical double quantum dot localised under the plunger gate P3. c, Schematic of the respective vertical double dot and triangulation heatmap. The triangulation results stem form the fitted charge transition lines, providing the relative lever arm of each gate to the respective quantum dots. d, Reflected signal of the rf-SHT underneath PN showing a charge-stability diagram that corresponds to a $2 \times 2$ array underneath P2 and P3 in the $yz$-plane. Two quantum dots are located underneath each plunger gate. The gates O2 and O3 represent the orthogonalized virtualized plunger gates, with respect to the quantum dots in the upper layer, QD2u and QD3u. e, Simulated charge stability diagram of a 2$\times$2 array aligned in the $xz$ plane. The capacitances are chosen to find qualitative agreement with the experimental results. f, Schematic denoting the respective facet of the quantum dot cuboid.
• Figure 2: Tuning between the planar regime and the bilayer regime.a We can actively tune between the single layer regime, seen in the left most panel, to the bilayer regime (right most panel). We observe four charge transition lines, with two dots strongly coupled to O3, and two dots strongly coupled to O4, indicating the presence of two vertical double dots in the system. b We qualitatively replicate this effect using quantum capacitance simulator Qarrayqarray. Deviations between experiment in a and simulation b is attributed to change in the quantum dot shape, and thereby leverarms, as function of the barrier gate which is not captured in the constant capacitance model.
• Figure 3: Vertically aligned $\mathbf{2 \times 2}$ quantum dot arrays, and a $\mathbf{2 \times 2 \times 2}$ quantum dot array.a-d, Reflectometry signal VS exhibiting stability diagrams of different facets of the cuboid. Here, the plunger gates that are not swept on the x or y axes are kept far from the accumulation voltage, so there are only four quantum dots in the system. e-h, Schematics and triangulation heatmaps of the quantum dots denoting the relative lever arms $\alpha_{\mathrm{G}_i}/\alpha_{\mathrm{P}_i}$ of the relevant gates. e-h correspond to a-d in alphabetic order and the color code indicates the considered charging transition. See Fig. \ref{['fig:device_schematic']}c for a labeled gate schematic. The relative lever arms are extracted from auxiliary gate-sweeps. i Schematic of a cuboid quantum dot configuration. j-m, Stability diagrams corresponding to the eight quantum dot system. Here, the DC voltages (center of the 2D maps) lay $\sim$ 10 mV above single-hole accumulation. The color of the star in the single hole regime corresponds to the quantum dot in the schematic in i. By sweeping pairs of virtualized plunger gate voltages $\Delta \mathrm{L}_i$, we identify eight distinct charging transitions that correspond to quantum dots on all corners of a cuboid underneath the plunger gates. The virtual gate voltages $\Delta \mathrm{L}i$ correspond to orthogonal control of the lower quantum dots. The virtualization matrices are reported in the Appendix \ref{['supp:virtualisation']}.