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arXiv:2307.15695 · PRX Quantum

Entangling Interactions Between Artificial Atoms Mediated by a Multimode Left-Handed Superconducting Ring Resonator

Tianna McBroom, A. Schlabes, X. Xu, Jaseung Ku, B. Cole, Sagar Indrajeet, Matthew LaHaye, Mohammad H. Ansari, B. L. T. Plourde

Published May 1, 2024• 8 citations
arXivHTMLPDF

Abstract

Superconducting metamaterial transmission lines implemented with lumped circuit elements can exhibit left-handed dispersion, where the group and phase velocity have opposite sign, in a frequency range relevant for superconducting artificial atoms. 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, we characterize and theoretically model the variation in the coupling strength between the two qubits and each of the ring-resonator modes. 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 we vary the detuning between the qubits and their frequency relative to the ring-resonator modes, we observe significant variations in both of these interqubit interactions, 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. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.020325

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Superconducting metamaterial transmission lines implemented with lumped circuit elements can exhibit left-handed dispersion, where the group and phase velocity have opposite sign, in a frequency range relevant for superconducting artificial atoms. 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, we characterize and theoretically model the variation in the coupling strength between the two qubits and each of the ring-resonator modes. 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 we vary the detuning between the qubits and their frequency relative to the ring-resonator modes, we observe significant variations in both of these interqubit interactions, 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. Published by the American Physical Society 2024
Metamaterial resonant structures made from arrays of superconducting lumped-circuit elements can exhibit microwave-mode spectra with left-handed dispersion for the standing-wave resonances, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this regime for multimode circuit quantum electrodynamics, we perform a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we observe the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we probe the qubit dispersively and characterize the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we investigate the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. Through numerical simulations, we explore designs based on this scheme with enhanced coupling so that the coupling energy between the qubit and the metamaterial modes can exceed the intermode spacing in future devices with achievable circuit parameters. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation with microwave photons and quantum memories.
Superconducting circuits operated at low temperatures have led to rapid advances in quantum information processing as well as quantum optics in the microwave regime. Engineered quantum systems with a dense spectrum of modes coupled to artificial atoms, or qubits, formed from superconducting circuits offer an opportunity to explore large-scale entanglement or perform quantum simulations of many-body phenomena. Recent research efforts into artificial metamaterials have yielded microwave and optical systems with numerous counterintuitive properties, including left-handed transmission, where the group velocity and phase velocity for a wave point in opposite directions. Metamaterial resonators implemented with superconducting thin-film circuits provide a route to generating dense mode spectra in the microwave regime for coupling to qubits. In this thesis, we discuss the implementation of such superconducting metamaterial resonators. First, we derive the dispersion relation for one-dimensional metamaterial transmission lines and we describe the formation of resonators from such lines and their quality factors. Next, we describe the design and fabrication of transmission-line metamaterial resonators using superconducting thin films. We characterize the metamaterials through low-temperature microwave measurements as well as Laser Scanning Microscope (LSM) images of the microwave field distributions in the circuit. We compare these various measurements with numerical simulations of the microwave properties of the circuits, including simulated current density and charge density distributions for the excitation of different resonance modes. Following the successful realization of dense mode spectra in these circuits, we have initiated the first experiments with a superconducting transmon qubit coupled to a metamaterial resonator and we describe our progress in this direction.
Multimode microwave resonators that can be strongly coupled to superconducting qubits allow exploration of large-scale entanglement, or quantum simulations of many-body phenomena. Typically, long superconducting transmission lines or large arrays of transmission-line resonators are required. This work demonstrates superconducting metamaterial resonators with a dense mode spectrum above a low-frequency band gap. Imaging of the microwave fields shows that these devices exhibit a left-handed dispersion relation, consistent with modeling and simulations. This compact design is compatible with superconducting-qubit integration for applications in quantum information and communication.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Superconducting transmission line resonators (TLRs) have been widely applied to circuit quantum electrodynamical systems for superconducting quantum computation and single-photon detections. Recently, such a right-handed TLR has been generalized to electromagnetic metamaterials (MTMs), and its unconventional mode structure has been experimentally characterized (Wang et al. in Phys Rev Appl 11:054062, 2019). Here, we demonstrate another kind of MTM TLR, i.e., the superconducting quarter-wavelength composite right/left-handed (CRLH) TLRs composed of lumped elements. We design the devices and analyze their transport properties by developing a real-space approach, wherein the physical parameters at the device boundaries are utilized conveniently. Superconducting MTM TLRs with typical three unit cells were experimentally prepared by etching a superconducting aluminum film on a SiO[Formula: see text] substrate, and their microwave transport properties were measured at low temperatures of 50 mK. The results show that the modes spacing in such a quarter-wavelength CRLH-TLR is non-uniform, due to the nonlinear dispersion relation. This implies that it could be utilized to encode the superconducting qubits, analogously to the usual ones encoded by using the Josephson devices.
Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse interaction between qubits when they are nonresonant with the cavity but resonant with each other. We experimentally investigate the inverse scaling of the interqubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, we observe dark states of the coupled qubit-qubit system and analyze their relation to the symmetry of the applied driving field at different frequencies.