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Tailoring Tunable Interactions in Superconducting Circuits Using Many to No Modes

Gihwan Kim

Published May 1, 2026• 0 citations
Publisher

Abstract

Tunable couplings are a central requirement for scalable quantum processing with superconducting quantum circuits. Practical quantum processors must dynamically reconfigure their interaction landscape to accommodate different quantum operations, including idle, single-qubit gates, two-qubit gates, readout, and reset, while maintaining high coherence and suppressing spurious couplings. While widely used tunable interaction approaches rely on single-mode mediation, they are often constrained by nearest-neighbor connectivity, limited on-off ratios, and stringent requirements on qubit frequency allocation. This thesis develops and studies novel strategies for tailoring tunable interactions by moving beyond single-mode mediation, spanning multimode engineered interactions and modeless interaction schemes ("many to no modes"), while accounting for realistic constraints in superconducting hardware. Using a microwave metamaterial waveguide realized by coupled resonator arrays, I demonstrate tunable dissipative interactions that allow on-demand, fast, and high switching-ratio photon emission from a transmon used as a multi-level quantum emitter. This capability is leveraged to achieve deterministic generation of multidimensional photonic cluster states, as well as unconditional reset and leakage reduction of frequency-tunable superconducting qubits. Complementary to these multimode dissipative tunable interactions, this thesis also introduces architectures that realize tunable interactions mediated by many coherent modes or by no mediating modes. I discuss a long-range interaction scheme between superconducting dual-rail qubits mediated by spatially extended eigenmodes of a coupled-resonator array bus. Finally, I propose and analyze a novel modeless coupling architecture based on a SQUID coupler which provides intrinsic cross-Kerr interactions, enabling fast, hybridization-free CZ gates for far-detuned pairs, and discuss its implications for miniaturization of superconducting quantum processors.

DOI
10.7907/2td2-4z28

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Superconducting circuits are a leading platform for quantum computation and quantum simulation. Interactions are typically mediated by pairwise coupling elements between nearest neighbor qubits. The development of tunable couplers has been essential to achieving high fidelity entangling gates alongside high fidelity single qubit gates in quantum processors. In quantum simulators, tunable coupling allows flexibility in emulating different systems and the exploration of different parameter regimes of those models in a single physical device. Distributed element circuitry has enabled long range coupling and leveraging of interference effects and spatial mode variations to enhance device performance. In this thesis I will discuss work towards developing a distributed element tunable coupling circuit: a transmission line cavity terminated by SQUIDs, which serve as flux tunable impedances, at either boundary. With this device we hope to integrate the dynamic programmability of interactions mediated by a tunable coupler with the long-range, multi-qubit coupling enabled by distributed transmission lines in a single system. We experimentally demonstrate the core functionality, including tunability of the coupling rates, programmability of the connectivity graph, and parallel operation via multiplexing. Additionally, we utilize this device to explore photon blockade effects in the Tavis-Cummings Model, highlighting the value of tunability and controllability when simulating novel light-matter interactions in highly connected systems. These results contribute to ongoing research towards designing, calibrating, and operating highly connected superconducting circuit systems. Devices with high connectivity enable more efficient circuit compilation and are useful as quantum routers in quantum networks. In recent years, understanding the role of connectivity in quantum error correction has emerged as an important research focus. There is ongoing work evaluating the tradeoff between performance and connectivity in real devices. The development of coupling architectures that enable denser and/or longer range connectivity will play a critical role in optimizing this tradeoff.

•May 1, 2026•0 citations
Tunable couplings are a central requirement for scalable quantum processing with superconducting quantum circuits. Practical quantum processors must dynamically reconfigure their interaction landscape to accommodate different quantum operations, including idle, single-qubit gates, two-qubit gates, readout, and reset, while maintaining high coherence and suppressing spurious couplings. While widely used tunable interaction approaches rely on single-mode mediation, they are often constrained by nearest-neighbor connectivity, limited on-off ratios, and stringent requirements on qubit frequency allocation. This thesis develops and studies novel strategies for tailoring tunable interactions by moving beyond single-mode mediation, spanning multimode engineered interactions and modeless interaction schemes ("many to no modes"), while accounting for realistic constraints in superconducting hardware. Using a microwave metamaterial waveguide realized by coupled resonator arrays, I demonstrate tunable dissipative interactions that allow on-demand, fast, and high switching-ratio photon emission from a transmon used as a multi-level quantum emitter. This capability is leveraged to achieve deterministic generation of multidimensional photonic cluster states, as well as unconditional reset and leakage reduction of frequency-tunable superconducting qubits. Complementary to these multimode dissipative tunable interactions, this thesis also introduces architectures that realize tunable interactions mediated by many coherent modes or by no mediating modes. I discuss a long-range interaction scheme between superconducting dual-rail qubits mediated by spatially extended eigenmodes of a coupled-resonator array bus. Finally, I propose and analyze a novel modeless coupling architecture based on a SQUID coupler which provides intrinsic cross-Kerr interactions, enabling fast, hybridization-free CZ gates for far-detuned pairs, and discuss its implications for miniaturization of superconducting quantum processors.
Superconducting quantum circuits typically use capacitive charge-based linear coupling schemes to control interactions between elements such as qubits. While simple and effective, this coupling scheme makes it difficult to satisfy competing circuit design requirements such as maintaining large qubit anharmonicity and coherence along with a high degree of qubit connectivity and packing density. Moreover, tunable interactions using linear coupling elements produce dynamical variations in mode hybridization, which can induce non-adiabatic transitions, resulting in leakage errors and limiting gate speeds. In this work we attempt to address these challenges by proposing a junction-based coupling architecture based on SQUID (superconducting quantum interference device) couplers with relatively small Josephson energies. SQUID couplers provide intrinsic cross-Kerr interactions that can be controlled by external fluxes and that do not rely on mode hybridization. The small Josephson energies of the coupler maintain the interaction at a perturbative scale, which limits undesired higher-order mixing between coupled elements while achieving a sufficiently strong cross-Kerr interaction originating from diagonal coupling elements. Based on these properties, we show that a SQUID coupler can be used to implement a fast, adiabatic, and high-fidelity controlled-Z gate without introducing extra modes, and the operation is robust against junction asymmetry for high-frequency qubits. Although unconventional crosstalk may arise due to junction asymmetries and parasitic hybridization with spectator qubits, we show that these effects are sufficiently small for realistic circuit parameters. As an example of the utility of such junction-based coupling schemes, we present a scalable tiling strategy for a miniaturized superconducting quantum processor based on merged-element transmon qubits.
Superconducting qubits have achieved remarkable progress in gate fidelity and coherence, yet their typical nearest-neighbor connectivity presents constraints for implementing complex quantum circuits. Here, we introduce a cavity-mediated coupling architecture in which a shared cavity mode, accessed through tunable qubit-cavity couplers, enables dynamically reconfigurable interactions between non-adjacent qubits. By selectively activating the couplers, we demonstrate that high-fidelity iSWAP and CZ gates can be performed within 50 ns with simulated coherent error below 10−410^{-4}10−4, while residual ZZZZZZ interaction during idling remains below a few kilohertz. Extending to a four-qubit system, we also simulate gates between every qubit pair by selectively enabling the couplers with low qubit crosstalk. This approach provides a practical route toward enhanced interaction flexibility in superconducting quantum processors and may serve as a useful building block for devices that benefit from selective non-local coupling.
To scale superconducting quantum processors, it is essential to achieve long coherence times while engineering interactions that do not introduce additional decoherence channels. In superconducting qubit systems, this can be realized using multimode circuits that feature a protected qubit mode alongside a distinct mediator mode. Building on this concept, our recently developed P-mon qubit provides intrinsic protection against decoherence from the readout environment. We extend this approach to controlled two-qubit interactions, by exploiting the mediator modes of P-mons for on-demand coupling. Because direct interactions between the qubit modes are strongly suppressed, unwanted ZZZZZZ-type interactions are significantly reduced to below 3.6(5) kHz3.6(5)~\text{kHz}3.6(5) kHz in the idle state. When tuning the coupled mediator modes on resonance, the cross-Kerr interaction between the qubit and the hybridized mediator modes leads to a qubit-state dependent frequency shift. By selectively addressing these transitions, we implement a 180 ns180~\text{ns}180 ns long CZ gate and determine a fidelity of $99.62(4)~\text{%}$. These results represent a significant step toward a scalable superconducting architecture that maintains high performance at scale.
Superconducting qubits have achieved remarkable progress in gate fidelity and coherence, yet their typical nearest-neighbor connectivity presents constraints for implementing complex quantum circuits. Here, we introduce a cavity-mediated coupling architecture in which a shared cavity mode, accessed through tunable qubit–cavity couplers, enables dynamically reconfigurable interactions between non-adjacent qubits. By selectively activating the couplers, we demonstrate that high-fidelity iSWAP and CZ gates can be performed within 50 ns with simulated coherent error below 10−4, while residual ZZ interaction during idling remains below a few kilohertz. Extending to a four-qubit system, we also simulate gates between every qubit pair by selectively enabling the couplers with low qubit crosstalk. This approach provides a practical route toward enhanced interaction flexibility in superconducting quantum processors and may serve as a useful building block for devices that benefit from selective non-local coupling.
As systems for quantum computing keep growing in size and number of qubits, challenges in scaling the control capabilities are becoming increasingly relevant. Efficient schemes to simultaneously mediate coherent interactions between multiple quantum systems and to reduce decoherence errors can minimize the control overhead in next-generation quantum processors. Here, we present a superconducting qubit architecture based on tunable parametric interactions to perform two-qubit gates, reset, leakage recovery, and to read out the qubits. In this architecture, parametrically driven multielement couplers selectively couple qubits to resonators and neighboring qubits, according to the frequency of the drive. We consider a system with two qubits and one readout resonator interacting via a single coupling circuit and experimentally demonstrate a controlled- Z gate with a fidelity of 98.30 ± 0.23 % , a reset operation that unconditionally prepares the qubit ground state with a fidelity of 99.80 ± 0.02 % and a leakage recovery operation with a 98.5 ± 0.3 % success probability. Furthermore, we implement a parametric readout with a single-shot assignment fidelity of 88.0 ± 0.4 % . These operations are all realized using a single tunable coupler and a statically decoupled resonator, demonstrating the experimental feasibility of the proposed architecture and its potential for reducing the system complexity in scalable quantum processors.
Superconducting circuits are a leading platform for quantum computation and quantum simulation. Interactions are typically mediated by pairwise coupling elements between nearest neighbor qubits. The development of tunable couplers has been essential to achieving high fidelity entangling gates alongside high fidelity single qubit gates in quantum processors. In quantum simulators, tunable coupling allows flexibility in emulating different systems and the exploration of different parameter regimes of those models in a single physical device. Distributed element circuitry has enabled long range coupling and leveraging of interference effects and spatial mode variations to enhance device performance. In this thesis I will discuss work towards developing a distributed element tunable coupling circuit: a transmission line cavity terminated by SQUIDs, which serve as flux tunable impedances, at either boundary. With this device we hope to integrate the dynamic programmability of interactions mediated by a tunable coupler with the long-range, multi-qubit coupling enabled by distributed transmission lines in a single system. We experimentally demonstrate the core functionality, including tunability of the coupling rates, programmability of the connectivity graph, and parallel operation via multiplexing. Additionally, we utilize this device to explore photon blockade effects in the Tavis-Cummings Model, highlighting the value of tunability and controllability when simulating novel light-matter interactions in highly connected systems. These results contribute to ongoing research towards designing, calibrating, and operating highly connected superconducting circuit systems. Devices with high connectivity enable more efficient circuit compilation and are useful as quantum routers in quantum networks. In recent years, understanding the role of connectivity in quantum error correction has emerged as an important research focus. There is ongoing work evaluating the tradeoff between performance and connectivity in real devices. The development of coupling architectures that enable denser and/or longer range connectivity will play a critical role in optimizing this tradeoff.