Simultaneous operation of an 18-qubit modular array in germanium

Abstract

Utility-scale quantum computing requires the integration and operation of a large-scale qubit register. Semiconductor spin qubits are a primary candidate for this, due to the prospects of building integrated hybrid quantum-classical architectures. However, scaling spin-qubit systems while preserving performance and control has remained a challenge. Here, we demonstrate the operation of an 18-qubit array in germanium based on an extendable 2xN architecture. We achieve simultaneous initialization, control, and readout across the entire array, enabled by parallel operation of modular unit cells. Across the array, we achieve average and median single-qubit gate fidelities of 99.8% and 99.9%, respectively. Finally, we characterize the nearest-neighbor exchange couplings throughout the device and implement high-quality controlled-Z gates to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state. These results demonstrate that spin-qubit arrays can be scaled while maintaining high-fidelity operation and establish a modular, extendable architecture for planar semiconductor quantum processors.

Figures (15)

• Figure 1: Device and measurement protocol of the 18-qubit modular array.a, False-colored scanning electron microscope image of the 18-qubit device. Ohmic contacts, screening gates, plunger gates, and barrier gates are indicated in green, magenta, blue and red, respectively. The 18 qubits, located below the plunger gates, are labeled Q$_{1}$-Q$_{18}$. Three charge sensors S$_i$ ($i$ the unit cell index) are positioned above (S$_1$, S$_3$) and below (S$_2$) the array. The reference frame of the external magnetic field $B_{x,y,z}$ is indicated by the black arrows. b, Few-hole charge stability diagram in the operational regime for all vertical double quantum dot (DQD) pairs Q$_i$Q$_j$, shown as a function of the detuning ($\epsilon_{ij}$) and on-site ($U_{ij}$) energy. c-h, Tuning procedure to characterize the spin qubits. c, Charge stability diagram of a representative DQD, measured as a function of the virtual plunger gates voltages $\text{vP}_i$ and $\text{vP}_j$. d, The charge stability diagram of the two-hole regime shows the relevant charge transitions, with Pauli spin blockade (PSB) appearing as a latched signal near the (1,1)-(0,2) transition, when sweeping towards positive detuning. A typical pulse sequence, including initialization (I), operation (O) and readout (R), is indicated. e, Singlet-triplet ($\text{S}-\text{T}_0$) oscillations measured in the blocked state probability $P_\text{blocked}$ as a function of the dwell time at the operation point $\tau_\text{O}$. f, Spin resonance spectroscopy using a chirped microwave pulse, showing two resonance peaks corresponding to the two spins in the DQD. g, Rabi chevron pattern showing the spin-flip probability as a function of microwave pulse duration ($t_\text{drive}$) and drive frequency ($f_\text{drive}$). h, Exchange-coupling spectroscopy, where the splitting of the target qubit resonance frequency $f_\text{qubit}$ as a function of the applied barrier gate voltage $V_\text{B}$, with the control qubit initialized in the $\ket{\downarrow}$ (squares) or $\ket{\uparrow}$ (circles) state.
• Figure 1: Extendable $\bm{2\times N}$ quantum dot array in germanium.a, Schematic of the generalized $2\times N$ quantum dot architecture. The 18-qubit array studied in the main text, is based on a repeating 2x3 unit cell that can be extended along one dimension. Each unit cell includes a dedicated charge sensor, while ohmic contacts on either end of the array act as reservoirs to load holes into the system. This modular design enables the realization of arrays with various sizes (e.g. 6, 12, or 18 qubits) and can be extended into larger systems. b-d, Examples of layouts generated from the 2xN architecture: b, 2x3 array; c, 2x6 array; d, 2x9 array, corresponding to the device studied in the main text (see Fig. \ref{['fig:1']}a). Ohmic contacts, screening gates, plunger gates, and barrier gates are indicated in green, magenta, blue and red, respectively.
• Figure 2: Statistical analysis of single-qubit coherence and gate fidelities across the array.a, Chevron pattern measurements for all 18 spin-qubits, showing four full rotations as a function of the drive frequency ($f_{\rm drive}$). All measurements are performed sequentially without changing the dc voltage settings of the device. b, Color scale mapping of the qubit driving efficiency ($f_\text{Rabi}/A$, top panel) and $g$-factors (bottom panel) for all qubits. c-e, Empirical cumulative distribution function (ECDF) of $T_2^*$ (c), $T_2^\text{CPMG}$ (d), and the single qubit gate error probability (e) of all 18-qubits, respectively. The black and red dashed lines show the average and median values, respectively. The mean, median, and standard deviation of the distribution are summarized in the top right corner.
• Figure 2: Horizontal and vertical double quantum dot charge stability diagrams in the 18-qubit array. Charge stability diagrams of all double quantum dot (DQD) pairs, measured as a function of the virtual plunger gates voltages of two neighboring dots ($vP_i$, $vP_j$), for both horizontal (e.g. Q1,Q3) and vertical (e.g. Q1,Q2) pairs. Blue circles indicate the plungers gate defining the quantum dots. The gate virtualization minimizes crosstalk between control gates, ensuring that tuning a given dot does not significantly shift the chemical potentials of neighboring dots. For all DQD pairs, the top-right corner in the CSD, corresponds to the (0,0) charge configuration.
• Figure 3: Multi-qubit initialization, control and readout.a, Pulse sequence used for multi-qubit initialization, control, and readout. The horizontal lines correspond to the vertical pairs of the array. The shaded regions indicate the three unit cells. Within each unit cell, initialization and reference operations (I/R) are executed sequentially across the three pairs, while the same sequence is performed in parallel across all unit cells. During the control stage, X gates are applied to individual qubits. Finally, each unit cell is read out by a dedicated charge sensor that measures the parity of the three corresponding vertical pairs sequentially, allowing simultaneous readout of all unit cells. b, Measurement results of each vertical pair using the multi-qubit sequence described in a, with the simultaneous control of all qubits in the bottom channel of the device (pink). For comparison, we overlay the results of a similar experiment, where an individual-qubit sequence is used (blue). The presented data are vertically offset by 1 per qubit. c, Measured spin flip probabilities $P_\text{flip}$ for all vertical pairs as a function of the addressed qubit. Each column corresponds to a measurement of the full array after a single X-gate is applied to the targeted qubit.