Experimental setup for the combined study of spin ensembles and superconducting quantum circuits

TL;DR

The paper addresses the challenge of integrating spin-ensemble memories with superconducting qubits in a cryogenic setting by introducing a dual-volume dilution refrigerator architecture with magnetically decoupled regions. A NbTi superconducting solenoid provides up to $50\,\mathrm{mT}$ in the spin-volume, while an engineered cryogenic magnetic shield suppresses stray fields by factors up to $10^{-8}$–$10^{-9}$ at the qubit location, validated by direct qubit-frequency measurements under field sweeps. The results demonstrate stable qubit operation despite substantial spin-control fields and quantify the thermal and magnetic isolation required for scalable hybrids, including measurements showing a $\Delta f_{\text{qubit}}$ corresponding to $\Delta B \approx 0.468\,\mathrm{nT}$ at the qubit site for a 50 mT solenoid change. This work provides a practical pathway toward low-loss, scalable hybrid quantum systems that leverage the strengths of spin-based memories and superconducting processors within a single cryogenic platform.

Abstract

A hybrid quantum computing architecture combining quantum processors and quantum memory units allows for exploiting each component's unique properties to enhance the overall performance of the total system. However, superconducting qubits are highly sensitive to magnetic fields, while spin ensembles require finite fields for control, creating a major integration challenge. In this work, we demonstrate the first experimental setup that satisfies these constraints and provides verified qubit stability. Our cryogenic setup comprises two spatially and magnetically decoupled sample volumes inside a single dilution refrigerator: one hosting flux-tunable superconducting qubits and the other a spin ensemble equipped with a superconducting solenoid generating fields up to 50 mT. We show that several layers of Cryophy shielding and an additional superconducting aluminum shield suppress magnetic crosstalk by more than eight orders of magnitude, ensuring stability of the qubit's performance. Moreover, the operation of the solenoid adds minimal thermal load on the relevant stages of the dilution refrigerator. Our results enable scalable hybrid quantum architectures with low-loss integration, marking a key step toward scalable hybrid quantum computing platforms.

Figures (4)

• Figure 1: Schematics of the dilution refrigerator and hybrid cryogenic setup. The refrigerator is represented by six temperature stages with additional microwave attenuation of input lines and low-noise preamplification of the output lines (not shown here for simplicity). All the magnetic shields as well as the experimental samples are thermally anchored to the mixing chamber plate (MXC) at the base temperature of less than 10mK. The superconducting solenoid magnet is thermally anchored to the intermediate cold plate at the temperature of $\simeq$100mK. The magnet is powered via superconducting wires between the MXC- and the 4K-stage and via copper DC-lines between the 4K-stage and room temperature.
• Figure 2: (a) Three-dimensional graphic representation of the sample volume 2 and its mounting within the cryostat. The representation has an in-cut to show all inner layers of the assembly. Different colors are used for parts anchored at different temperature stages (blue: 100mK plate, purple: MXC base plate) of the refrigerator. The superconducting aluminum shield (red color) is also thermally anchored to the MXC base plate. (b) Diagram of the winding pattern of the superconducting solenoid, which features the winding direction, layering and number of turns. (c) Photo of the superconducting solenoid without the shielding layers when installed into the cryostat.
• Figure 3: (a) Vertical cross-sectional view of the assembly with the color-coded magnetic field magnitude generated by the coil for the millikelvin thermal conditions. The respective level of the Earth's magnetic field is marked on the color bar. The dots P$_1$ and P$_0$ mark the best sample positions according to the model calculation and the measurement, respectively. The dashed lines mark the positions along the radial direction at z=-40mm and along the vertical cylinder axis at $r=0$. The field distributions along these lines are plotted in (b) and (d), respectively. The black solid lines in (b) and (d) represent the distribution of the magnetic field generated by the solenoid, and the red line shows the suppression of the ambient Earth's magnetic field. In (c) and (e), the homogeneity of the magnetic field is plotted as the relative field change with respect to the magnetic field value at position P$_0$ along radial and vertical directions, respectively. In (e), the field values obtained from two room-temperature measurements are plotted as orange dots, while the black line shows the simulation result within the plotted window.
• Figure 4: Time-traces of (a,d) coil current (magnetic field), (b,e) deviation $\Delta f_{\text{qubit}}$ of the flux-tunable qubit transition frequency from the value of 4.877 at the chosen flux bias point, and (c,f) temperatures at several stages of the dilution refrigerator. The traces are measured for two experimental configurations of magnetic shields of sample volume 2: (a)-(c) with three Cryophy® shields, and (d)-(f) with two Cryophy® shields and one outermost superconducting aluminum shield. The temperatures for the Still and the 4 K-stage are given as differences, $\Delta T=T-T_\text{ref}$, from reference values $T_\text{ref}$. The reference values are the following: (c) $T_{\text{ref,Still}}=1.24K$ and $T_{\text{ref,4K}}=3.1K$, and (f) $T_{\text{ref,Still}}=1.26K$ and $T_{\text{ref,4K}}=3.1K$.