Parametric longitudinal coupling between a high-impedance superconducting resonator and a semiconductor quantum dot singlet-triplet spin qubit

nature communications Article https://doi.org/10.1038/s41467-022-32236-w Parametric longitudinal coupling between a high-impedance superconducting resonator and a semiconductor quantum dot singlettriplet spin qubit Received: 19 July 2021 1234567890():,; 1234567890():,; Accepted: 20 July 2022 Check for updates C. G. L. Bøttcher1 , S. P. Harvey 1,8, S. Fallahi2, G. C. Gardner2, M. J. Manfra 2,3,4,5, U. Vool 1,6, S. D. Bartlett 7 & A. Yacoby 1 Coupling qubits to a superconducting resonator provides a mechanism to enable long-distance entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a controllable spinphoton coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator’s frequency. We measure the energy splitting of the qubit as a function of the drive amplitude and frequency of a microwave signal applied near the resonator antinode, revealing pronounced effects close to the resonator frequency due to longitudinal coupling. By tuning the amplitude of the drive, we reach a regime with longitudinal coupling exceeding 1 MHz. This mechanism for qubit-resonator coupling represents a stepping stone towards producing high-fidelity two-qubit gates mediated by a superconducting resonator. Electron spins in semiconducting materials, such as gallium arsenide (GaAs) and silicon, are promising candidates for realizing a quantum computer1–5. Their long coherence times and fast control allow for high-fidelity single-qubit gates, reaching ~99.95 % in single-electron spin qubits6. In addition to single-spin qubits, several varieties of spin qubits that are comprised of multiple spins and multiple quantum dots, including hybrid qubits, exchange-only qubits, and singlet-triplet qubits (S−T0)7–9, have been demonstrated. These qubits typically have increased coupling to charge, allowing fast, voltage-controlled qubit gates. The S−T0 qubit is desirable due to its reduced coupling to homogeneous magnetic fields and has achieved single qubit gate fidelities of 99.5%10. While two-qubit gates have previously been demonstrated for these qubits with a fidelity of ~90%11, these gates are slow and rely on nearest neighbor coupling, limiting scalability. Much attention is now focused on achieving long-range two-qubit coupling, for example, using arrays of quantum dots for charge transfer12–15 or a superconducting resonator by adapting circuit QED (cQED) techniques, thus making electron spins a scalable platform for quantum computing technology. Extensive work on implementation of cQED techniques in spin qubits has recently been demonstrated16–22, and despite promising progress23,24, a two-qubit gate has not yet been achieved. The qubitresonator coupling explored relies on the strong electric fields produced by a resonator, which couple to the dipole moment of a spin qubit. The most commonly considered coupling scheme is a transverse coupling between the spin and resonator, where an excitation of 1 Department of Physics, Harvard University, Cambridge, MA 02138, USA. 2Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA. 3School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA. 4Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA. 5School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA. 6John Harvard Distinguished Science Fellowship, Harvard University, Cambridge, MA 02138, USA. 7Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, e-mail: Australia. 8Present address: Stanford University, Stanford, CA 94305, USA. Nature Communications | (2022)13:4773 1 Article the spin qubit can be exchanged for a resonator excitation25. This requires the qubit energy splitting to be near the resonator frequency, and typically leads to lower lifetimes due to the Purcell effect. In recent years, there has therefore been growing interest in alternative coupling schemes based on longitudinal interactions, which do not have these limitations26–32. Spin qubits are highly amenable to longitudinal coupling, although it has not been demonstrated experimentally before. In previous theoretical work33, such a coupling scheme was explored for singlet-triplet qubits, predicting encouraging average two-qubit gate fidelities of 96% and gate times of the order of 10 ns. This approach, analogous to the Mølmer–Sørensen gate34 that is commonly used for high fidelity two-qubit gates in ion trap qubits35,36, relies on a purely longitudinal interaction between the spin and resonator to produce a two-qubit coupling. In this article, we demonstrate experimental efforts towards achieving longitudinal coupling between a singlet-triplet (S−T0) qubit and high-impedance superconducting resonator. We show that our device has significant longitudinal coupling, tunable by a direct drive, in addition to a fixed spurious dispersive coupling. We present a measurement sequence that allows one to separate each coupling term and measure their individual coupling strengths. The sequence takes advantage of the qubit’s exquisite sensitivity, enabling us to extract resonator parameters as well as qubit-resonator coupling strengths. By tuning the drive amplitude we can achieve a longitudinal coupling strength that exceeds the dispersive term, which is an exciting regime within hybrid circuit QED systems as well as an important stepping stone towards producing two-qubit coupling mediated by a resonator. Results https://doi.org/10.1038/s41467-022-32236-w the left and right DQD (Fig. 1b), marked QL and QR in Fig. 1a. The resonator is fabricated in the etched area from a 20 nm superconducting film made of niobium nitride (NbN) and meandered across the sample. Using a thin film of NbN as the resonator material, one can obtain a large kinetic inductance, LK. The kinetic inductance, LK = (me/2nse2)(l/A)37, depends on the superfluid density, ns, and scales with resonator length l and cross-sectional area A, thus we achieve a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi high impedance close to Z r = ðLK + Lm Þ=C r ~ 2 k Ω for a resonator design with a meander width of 150 nm (Fig. 1c). The retracted ground plane minimizes resonator capacitance Cr, and magnetic inductance Lm, such that the resonator is largely dominated by its kinetic inductance. The resonator’s high impedance makes it well suited for coupling to systems such as electrons in DQDs, which have small electric dipole moments. Our S−T0 qubits each consist of two electrons trapped in a DQD defined using electrostatic gates for static potential confinement shown in Fig. 1d. The logical of the qubits consists the ffiffiffi ffiffiffi   of p  psubspace singlet, ∣Si = ð∣ "#  ∣ #" Þ= 2 and triplet ∣T 0 = ð∣ "# + (...truncated)