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arXiv:2501.14627 · Nature Communications

A dressed singlet-triplet qubit in germanium

Konstantinos Tsoukalas, Uwe von Lüpke, Alexei Orekhov, Bence Hetényi, Inga Seidler, Lisa Sommer, Eoin G. Kelly, Leonardo Massai, Michele Aldeghi, Marta Pita‐Vidal, Nico W. Hendrickx, Stephen W. Bedell, Stephan Paredes, Felix J. Schupp, Matthias Mergenthaler, Gian Salis, Andreas Fuhrer, Patrick Harvey-Collard

Published Jan 20, 2026• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41467-025-65569-3

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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.
We report a resonantly driven singlet–triplet (ST) qubit in a silicon metal–oxide–semiconductor (SiMOS) device operated without an applied external magnetic field. By resonantly modulating the exchange interaction at the qubit frequency, f q = 36 MHz , we observe coherent Rabi oscillations at f R = 1.69 MHz . A Ramsey measurement gives a dephasing time T 2 ∗ = 1.83 μ s , and randomized benchmarking yields an average single-qubit gate fidelity of 99.48%. These results demonstrate that the residual micromagnet field gradient is sufficient to support high-fidelity resonant control without a continuously applied external magnetic field.
Singlet-triplet qubits offer an attractive encoding for semiconductor quantum computing, combining ancilla-free readout, reduced sensitivity to common-mode noise, and baseband voltage control. However, the Zeeman energy difference ΔEZΔE_\mathrm{Z}ΔEZ​ is typically fixed by local magnetic field gradients or ggg-factor inhomogeneities, leaving the exchange interaction JJJ as the only dynamically tunable parameter. This always-on ΔEZΔE_\mathrm{Z}ΔEZ​ precludes orthogonal control of the qubit's rotation axes and introduces unwanted state rotations during idling. Here we demonstrate all-electrical orthogonal control of a degenerate singlet-triplet (DST) qubit formed by two hole spins in a germanium double quantum dot. Exploiting the electrically tunable anisotropic ggg-factors of the two spins, we identify a regime where both ΔEZΔE_\mathrm{Z}ΔEZ​ and JJJ vanish, making the SSS and T0T_0T0​ states degenerate at the idle point. By applying only baseband voltage pulses, we independently control both JJJ and ΔEZΔE_\mathrm{Z}ΔEZ​, enabling fully orthogonal ZZZ- and XXX-axis rotations. Randomized benchmarking yields an average physical single-qubit gate fidelity of 99.53\% for a gate duration of approximately 100 ns. Finally, we electrically tune the degenerate point across a wide range of magnetic field orientations, enabling operation in a regime of enhanced coherence time and offering a route towards multi-qubit scaling under a shared global magnetic field.
There is a huge, worldwide effort to build a quantum computer due to its potential to perform chemical and materials simulations and to break current cryptography schemes. While there has been incredible progress in recent years, each potential platform still faces meaningful obstacles. The singlet-triplet qubit in gallium arsenide, which is based on electric spin, boasts several advantages, including fast single-gate times and readout, long lifetimes, and a clear path to large-scale integration using current semiconductor manufacturing techniques. However, it also suffers from electric and magnetic field noise that limits coherence time and weak two-qubit interactions, which have prevented the construction of multi-qubit systems so far. In this thesis, I will discuss my research measuring and working to improve noise and entangling gates in singlet-triplet qubits and will examine the viability of the singlet-triplet qubit as the building block for a quantum computer. \nBy measuring the dynamics of the electric and magnetic field noise that the singlet-triplet experiences, we can develop an understanding of their origins and how to reduce their impact. The singlet-triplet can be operated rapidly enough to use it as a sensor and directly measure the fluctuating magnetic field arising from the nuclear spins in the semiconductor heterostructure surrounding it. We use Hamiltonian parameter estimation, a technique that maximizes the rate at which we learn information, given the strange properties of quantum measurement, to measure magnetic noise to within 15 μT at a rate of 2 kHz, and we use these measurements to provide real-time feedback to system controls, increasing the coherence time by a factor of 30. Charge noise has much larger high-frequency components than magnetic noise, and thus requires use of dynamical decoupling methods borrowed from NMR to measure it. We measure its power spectrum up to 1 MHz and find that it has a 1/f spectrum. We perform these measurements for several different devices and have begun to determine how our growth and fabrication processes affect dephasing. \nPlacing a high-impedance resonator between two singlet-triplet qubits to mediate their interaction shows promise as way to create long-distance entanglement and to increase the speed of the entangling gate. We analyze this gate theoretically, finding that we expect the fidelity to be over 95%, with a straightforward path to increasing it to above 99% with improved resonator parameters. However, because the singlet-triplet qubit is extremely sensitive to changes in its electrostatic environment, which can be affected both by the resonator’s fabrication process and the presence of the proximal resonator gate, implementing this gate experimentally is challenging. We have developed processes for fabricating narrow, thin, NbN resonators directly adjacent to the double quantum dots that compose singlet-triplet qubits. These processes yield quantum dots that can be tuned into low-noise, stable singlet-triplet qubits, and superconducting resonators with impedances over 1 kOhm.
Germanium quantum dot hole spin qubits are compatible with fully electrical control and are progressing toward multi-qubit operations. However, their coherence is limited by charge noise and driving field induced frequency shifts, and the resulting ensemble 1/f1/f1/f dephasing. Here we theoretically demonstrate that a bichromatic driving scheme cancels the second order frequency shift from the control field without sacrificing the electric dipole spin resonance (EDSR) rate, and without additional gate design or microwave engineering. Based on this property, we further demonstrate that bichromatic control creates a wide operating window that reduces sensitivity to quasi-static charge noise and thus enhances single qubit gate fidelity. This method provides a low-power route to a stabler frequency operation in germanium hole spin qubits and is readily transferable to other semiconductor spin qubit platforms.
We model a controlled-NOT (CNOT) gate mediated by exchange interactions in a realistic Ge/GeSi hole spin-qubit device. We use for that purpose a computationally efficient framework based on a compact dressed basis of many-body singlet and triplet states, which enables fast time-dependent simulations that would be prohibitive within a conventional configuration-interaction approach. We discuss the dominant sources of infidelity in ideal (noise-free) devices. On the one hand, the nonadiabaticity of the tunnel barrier ramps, enhanced by the transverse component of the exchange interaction, imposes limits on the speed of the CNOT gate. On the other hand, the AC Stark shift of the conditional resonance and the off-resonant driving of the complementary transition can significantly degrade the gate fidelity and call for a careful optimization of the driving conditions. Finally, we investigate the impact of quasi-static charge noise on the fidelity of the CNOT gate. We find that the capture of charges near the qubits can strongly disrupt the conditional operation, while the nanometer-scale motion of charges results in a loss of fidelity that sensitively depends on the position and strength of the corresponding dipole. Our results quantify the requirements on barrier control, microwave driving, and charge-noise stability for high-fidelity two-qubit operations in Ge/GeSi hole-spin qubits.
Hole spin qubits are frontrunner platforms for scalable quantum computers because of their large spin-orbit interaction that enables ultrafast all-electric qubit control at low power. The fastest spin qubits to date are defined in long quantum dots with two tight confinement directions, when the driving field is aligned to the smooth direction. However, in these systems the lifetime of the qubit is strongly limited by charge noise, a major issue in hole qubits. We propose here a different, scalable qubit design, compatible with planar CMOS technology, where the hole is confined in a curved germanium quantum well surrounded by silicon. This design takes full advantage of the strong spin-orbit interaction of holes, and at the same time suppresses charge noise in a wide range of configurations, enabling highly coherent, ultrafast qubit gates. While here we focus on a Si\mathrm{Si}Si/Ge\mathrm{Ge}Ge/Si\mathrm{Si}Si curved quantum well, our design is also applicable to different semiconductors. These devices allow for ultrafast operations even in short quantum dots by a transversal electric field. This additional driving mechanism relaxes the demanding design constraints, and offers a way to reliably interface spin qubits in a single quantum dot to microwave photons. By considering state-of-the-art high-impedance resonators and realistic qubit designs, we estimate interaction strengths of a few hundreds of megahertz, largely exceeding the decay rate of spins and photons. Reaching such a strong coupling regime in hole spin qubits will be a significant step towards high-fidelity entangling operations between distant qubits, as well as fast single-shot readout, and could pave the way towards the implementation of a large-scale semiconducting quantum processor.