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arXiv:2009.04268 · Nature

A four-qubit germanium quantum processor

Nico W. Hendrickx, William I. L. Lawrie, Maximilian Rimbach-Russ, F. van Riggelen, Sander L. de Snoo, Raymond N. Schouten, Amir Sammak, Giordano Scappucci, Menno Veldhorst

Published Mar 24, 2021• 427 citations
arXivHTMLPDF
DOI
10.1038/s41586-021-03332-6

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Abstract In semiconductor hole spin qubits, low magnetic field ( B ) operation extends the coherence time ( $${T}_{2}^{*}$$ T 2 * ) but proportionally reduces the gate speed. In contrast, singlet-triplet (ST) qubits are primarily controlled by the exchange interaction ( J ) and can thus maintain high gate speeds even at low B . However, a large J introduces a significant charge component to the qubit, rendering ST qubits more vulnerable to charge noise when driven. Here, we demonstrate a highly coherent ST hole spin qubit in germanium, operating at both low B and low J . By modulating J , we achieve resonant driving of the ST qubit, obtaining an average gate fidelity of 99.68% and a coherence time of $${T}_{2}^{*}=1.9\,\mu {{{\rm{s}}}}$$ T 2 * = 1.9 μ s . Moreover, by applying the resonant drive continuously, we realize a dressed ST qubit with a tenfold increase in coherence time ( $${T}_{2\rho }^{*}=20.3\,\mu {{{\rm{s}}}}$$ T 2 ρ * = 20.3 μ s ). Frequency modulation of the driving signal enables universal control, with an average gate fidelity of 99.63%. Our results demonstrate the potential for extending coherence times while preserving high-fidelity control of germanium-based ST qubits, paving the way for more efficient operations in semiconductor-based quantum processors.

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High-purity germanium (Ge) has re-emerged as a versatile semiconductor platform for spin-based quantum information processing because it combines mature materials processing, access to spin-free isotopes, high mobilities, small effective masses, and strong but engineerable spin--orbit coupling. However, ``Ge qubits'' are not a single technology. Donor spin qubits, acceptor spin qubits, gate-defined hole spin qubits, and gate-defined electron spin qubits exploit different parts of the Ge band structure and therefore make distinct trade-offs among coherence, controllability, fabrication complexity, and scalability. Here we compare these four Ge-based spin-qubit modalities on a common physical and architectural footing. We review the shared Ge materials physics, including isotopic purification, the multivalley \(L\)-point conduction band, the spin-\(3/2\) valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified \(T_1\) using a calibrated reference relaxation rate, a geometry-dependent strain-density-of-states suppression factor, and parasitic relaxation channels. The comparison shows that gate-defined Ge hole-spin qubits currently offer the strongest combination of all-electrical control, demonstrated multiqubit operation, and scalability. Donor, acceptor, and gate-defined electron qubits remain important complementary directions for memory, hybrid, and exploratory architectures. Overall, Ge supports a diverse qubit ecosystem, with gate-defined hole-spin qubits presently providing the clearest path toward scalable Ge-based quantum processors.

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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.
Abstract In semiconductor hole spin qubits, low magnetic field ( B ) operation extends the coherence time ( T2∗{T}_{2}^{*}T2∗​ T 2 * ) but proportionally reduces the gate speed. In contrast, singlet-triplet (ST) qubits are primarily controlled by the exchange interaction ( J ) and can thus maintain high gate speeds even at low B . However, a large J introduces a significant charge component to the qubit, rendering ST qubits more vulnerable to charge noise when driven. Here, we demonstrate a highly coherent ST hole spin qubit in germanium, operating at both low B and low J . By modulating J , we achieve resonant driving of the ST qubit, obtaining an average gate fidelity of 99.68% and a coherence time of T2∗=1.9 μs{T}_{2}^{*}=1.9\,\mu {{{\rm{s}}}}T2∗​=1.9μs T 2 * = 1.9 μ s . Moreover, by applying the resonant drive continuously, we realize a dressed ST qubit with a tenfold increase in coherence time ( T2ρ∗=20.3 μs{T}_{2\rho }^{*}=20.3\,\mu {{{\rm{s}}}}T2ρ∗​=20.3μs T 2 ρ * = 20.3 μ s ). Frequency modulation of the driving signal enables universal control, with an average gate fidelity of 99.63%. Our results demonstrate the potential for extending coherence times while preserving high-fidelity control of germanium-based ST qubits, paving the way for more efficient operations in semiconductor-based quantum processors.
High-purity germanium (Ge) has re-emerged as a versatile semiconductor platform for spin-based quantum information processing because it combines mature materials processing, access to spin-free isotopes, high mobilities, small effective masses, and strong but engineerable spin--orbit coupling. However, ``Ge qubits'' are not a single technology. Donor spin qubits, acceptor spin qubits, gate-defined hole spin qubits, and gate-defined electron spin qubits exploit different parts of the Ge band structure and therefore make distinct trade-offs among coherence, controllability, fabrication complexity, and scalability. Here we compare these four Ge-based spin-qubit modalities on a common physical and architectural footing. We review the shared Ge materials physics, including isotopic purification, the multivalley LLL-point conduction band, the spin-3/23/23/2 valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified T1T_1T1​ using a calibrated reference relaxation rate, a geometry-dependent strain-density-of-states suppression factor, and parasitic relaxation channels. The comparison shows that gate-defined Ge hole-spin qubits currently offer the strongest combination of all-electrical control, demonstrated multiqubit operation, and scalability. Donor, acceptor, and gate-defined electron qubits remain important complementary directions for memory, hybrid, and exploratory architectures. Overall, Ge supports a diverse qubit ecosystem, with gate-defined hole-spin qubits presently providing the clearest path toward scalable Ge-based quantum processors.