Superconducting Ring Resonators: A Game Changer for Efficient Quantum Computing

Superconducting ring resonators are key in circuit quantum electrodynamics (cQED), the dominant paradigm for superconductor-based quantum processors. These resonators, often formed from planar transmission lines, have large physical footprints. However, using metamaterials formed from lumped-element inductors and capacitors allows for unconventional wave dispersion.

The interaction between artificial atoms is mediated by a multimode left-handed superconducting ring resonator, resulting in a compact footprint. Theoretical modeling is crucial in understanding these interactions. The findings could lead to more efficient quantum computing systems and the development of quantum processors with a higher density of qubits. Further research is needed to explore potential applications.

What is the Significance of Superconducting Ring Resonators in Quantum Computing?

Superconducting ring resonators are a crucial component in the field of circuit quantum electrodynamics (cQED), which is the dominant paradigm for current superconductor-based quantum processors. These resonators are often formed from planar transmission lines with a single mode near the frequency range of the qubits, resulting in physically large footprints of several millimeters. Devices with dense mode spectra near the qubit frequency range have been realized using ultralong linear resonators. These multimode cQED systems have been studied for implementing quantum memories and quantum simulations.

The use of metamaterials formed from lumped-element inductors and capacitors allows for the implementation of transmission lines with unconventional wave dispersion. In the case of left-handed dispersion, the wave frequency is a falling function of the wavenumber above an infrared cutoff frequency (fIR), below which waves are unable to propagate. In the context of cQED, left-handed metamaterials produce a dense spectrum of orthogonal microwave modes above fIR, which can be engineered to fall in the frequency range of conventional superconducting qubits.

Ring resonators have been used in integrated photonics systems to form compact optical resonances or whispering-gallery modes for a broad range of applications including microwave-optical transducers, microwave frequency combs, and multimode nonlinear optics. Superconducting ring resonators with right-handed dispersion have been used in cQED applications, resulting in novel properties, but require a large footprint to ensure that a minimum of one wavelength matches the circumference.

How Does the Interaction Between Artificial Atoms Work?

The interaction between artificial atoms is mediated by a multimode left-handed superconducting ring resonator. Forming such a metamaterial transmission line into a ring and coupling it to qubits at different points around the ring results in a multimode bus resonator with a compact footprint. Using flux-tunable qubits, the variation in the coupling strength between the two qubits and each of the ring-resonator modes is characterized and theoretically modeled.

Although the qubits have negligible direct coupling between them, their interactions with the multimode ring resonator result in both a transverse exchange coupling and a higher-order ZZ-interaction between the qubits. As the detuning between the qubits and their frequency relative to the ring-resonator modes is varied, significant variations in both of these inter-qubit interactions are observed, including zero crossings and changes of sign. The ability to modulate interaction terms such as the ZZ-scale between zero and large values for small changes in qubit frequency provides a promising pathway for implementing entangling gates in a system capable of hosting many qubits.

What is the Role of Theoretical Modeling in Understanding These Interactions?

Theoretical modeling plays a crucial role in understanding the interactions between artificial atoms. In the case of a superconducting ring resonator formed from a left-handed metamaterial transmission line with two transmon qubits coupled at different points around the ring, a detailed modeling of the standing-wave structure and degeneracy breaking in the ring resonator is performed. This allows for the prediction of the coupling energy scales between the qubits and each ring-resonator mode.

The multimode coupling between the qubits, with the ring resonator serving as a bus, results in significant variations in both the transverse exchange coupling between the qubits as well as higher-order ZZ-interactions as the qubits are tuned between different frequency regimes. The theoretical modeling of these interactions is in close agreement with experimental measurements.

How Can These Findings Be Applied in Quantum Computing?

The findings from this study have significant implications for the field of quantum computing. The ability to modulate the ZZ-interaction strength between zero and a large value for a small change in qubit frequency allows for the possibility of implementing fast, high-fidelity entangling gates between pairs of qubits located around the ring resonator.

This could potentially lead to more efficient quantum computing systems, as the ability to control the interaction between qubits is a key requirement for quantum computation. Furthermore, the use of a multimode bus resonator with a compact footprint could allow for the development of quantum processors with a higher density of qubits, thereby increasing their computational power.

What are the Future Directions for This Research?

The research conducted by the team from the Department of Physics at Syracuse University, the Peter Grünberg Institute, the Institute for Quantum Information at RWTH Aachen University, the Jülich-Aachen Research Alliance, and the Air Force Research Laboratory provides a promising pathway for future developments in quantum computing.

Further research is needed to explore the potential applications of these findings in the design and implementation of quantum processors. In particular, the ability to modulate the ZZ-interaction strength between qubits could be exploited to develop more efficient entangling gates, which are a crucial component of quantum computation.

Moreover, the use of left-handed metamaterials to produce a dense spectrum of orthogonal microwave modes could be further explored to develop more compact and efficient quantum computing systems. The findings from this study provide a solid foundation for future research in this exciting and rapidly evolving field.