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Designing and modeling of flexible and high-fidelity two-qubit gate and coupler for superconducting qubits

Zhongyi Jiang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum computing holds great promise for both scientific discovery and commercial applications. Superconducting quantum systems have become one of the leading architectures for large-scale quantum computing. Towards realizing practical quantum computing, improving two-qubit gate fidelity is a crucial task. It is relevant for both near-term pre-fault-tolerant quantum computers and future fault-tolerant quantum computers. This dissertation aims to provide a comprehensive study of two-qubit gates in superconducting systems. The major focus is on improving gate fidelity via using different drive schemes and coupler designs. The dissertation contains two primary original contributions. First, a novel method for implementing continuous fSim gates is proposed and analyzed in detail. The fSim gate set is a family of gates that combines $i$SWAP gate and CPHASE gate into one gate with variable rotation angles and conditional phase. This gate set is particularly interesting for quantum simulation of fermionic systems. Second, a theoretical framework for multi-mode couplers is developed. A multi-mode coupler design is proposed to enable fully localized decoupling among qubits and independent control of qubit-qubit interactions in different excitation subspaces. An example of two qubits coupled by a two-mode coupler is studied in detail. Building on the fSim gate theory and multi-mode coupler design, several future research directions are outlined. Pulse-level algorithms for simulating electronic systems are discussed as a key application of fSim gates. A three-mode coupler architecture is further introduced. In addition, the importance of incorporating open-system dynamics for accurate modeling of coupler behavior and gate performance is emphasized. Finally, a unified framework for modeling superconducting quantum processors is proposed, providing a systematic way to compare gate fidelities across theoretical approaches and ultimately guide improvements in quantum hardware performance.

DOI
10.18154/rwth-2026-06036

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Quantum computing holds great promise for both scientific discovery and commercial applications. Superconducting quantum systems have become one of the leading architectures for large-scale quantum computing. Towards realizing practical quantum computing, improving two-qubit gate fidelity is a crucial task. It is relevant for both near-term pre-fault-tolerant quantum computers and future fault-tolerant quantum computers. This dissertation aims to provide a comprehensive study of two-qubit gates in superconducting systems. The major focus is on improving gate fidelity via using different drive schemes and coupler designs. The dissertation contains two primary original contributions. First, a novel method for implementing continuous fSim gates is proposed and analyzed in detail. The fSim gate set is a family of gates that combines iiiSWAP gate and CPHASE gate into one gate with variable rotation angles and conditional phase. This gate set is particularly interesting for quantum simulation of fermionic systems. Second, a theoretical framework for multi-mode couplers is developed. A multi-mode coupler design is proposed to enable fully localized decoupling among qubits and independent control of qubit-qubit interactions in different excitation subspaces. An example of two qubits coupled by a two-mode coupler is studied in detail. Building on the fSim gate theory and multi-mode coupler design, several future research directions are outlined. Pulse-level algorithms for simulating electronic systems are discussed as a key application of fSim gates. A three-mode coupler architecture is further introduced. In addition, the importance of incorporating open-system dynamics for accurate modeling of coupler behavior and gate performance is emphasized. Finally, a unified framework for modeling superconducting quantum processors is proposed, providing a systematic way to compare gate fidelities across theoretical approaches and ultimately guide improvements in quantum hardware performance.
Quantum interactions are strikingly different from their classical counterparts, and they lead to counter-intuitive effects such as quantum entanglement. The advances in quantum science and technology over the past two decades have shown that such interactions can be harnessed in quantum devices to address hard computational problems. The field of quantum computation has emerged, and superconducting circuits have become a leading platform for quantum processors. Because of the large design space and the difficulty to simulate design prototypes on a classical computer, a key challenge in quantum processor engineering is to translate desired quantum characteristics into a circuit design. A particular obstacle has been the implementation of interactions between multiple quantum bits (qubits) in one coupling mechanism. Multi-qubit interactions are necessary for a number of applications in quantum annealing, analog quantum simulation, and digital quantum computation. In this work, we develop classical and quantum computational methods to address the challenge of implementing such interactions. We present a computational method for automated design of superconducting circuits. Our method performs a parallelized, closed-loop optimization to design superconducting circuit diagrams that match predefined properties, such as dispersion features and noise sensitivities. We employ it to design a coupler for superconducting flux qubits that mediates 4-qubit interactions. The coupler circuit is then realized experimentally. We find that it has the desired ground state dispersion properties versus flux and that it does not adversely affect the lifetime of a connected flux qubit. Moreover, the coupling concept can be extended by systematically adding loops to the coupler. In a second iteration, we implement a circuit architecture in which the coupler mediates interactions between three flux qubits. The system Hamiltonian is estimated via multi-qubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds. We verify that the multi-qubit system exhibits a 3-qubit coupling that is coherently tunable, which is important for practical applications. Finally, we address the challenge that complex multi-qubit circuits are difficult to simulate accurately on a classical computer as they become larger. As a solution, we propose quantum algorithms to design and test the performance of next-generation quantum hardware on a quantum computer. We have therefore addressed the challenge of quantum device design both from a classical optimization and from a quantum computational angle.
Future quantum information processors require tunable coupling architectures that can produce high-fidelity logical gates between two or more qubits. Parametric coupling is a powerful technique for generating tunable interactions between many qubits. Here, we present a highly flexible parametric coupling scheme with superconducting qubits that provides complete removal of residual Z Z coupling and the implementation of driven SWAP or SWAP-free controlled- Z ( C Z ) gates. Our fully integrated two-dimensional on-chip coupler design is only weakly flux tunable, cancels static linear coupling between the qubits, avoids internal coupler dynamics or excitations, and is extensible to multiqubit circuit-QED systems. Exploring gate fidelity versus gate duration allows us to maximize two-qubit gate fidelity, while providing insights into possible error sources for these gates. Randomized benchmarking over several hours reveals that the parametric SWAP C Z gate achieves an average fidelity of 99.44 ± 0.09 % in a gate duration of 70 ns and that a dispersively driven parametric SWAP-free C Z gate attains an average fidelity of 99.47 ± 0.07 % in only 30 ns. The fidelity remained above this value for over 8 h and peaked twice with a maximum of 99.67 ± 0.14 % . Overall, our parametric approach combines versatility, precision, speed, and high performance in one compact coupler design.
High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is essential for addressing coherent leakage to the coupler and parasitic longitudinal (ZZZZZZ) interactions during two-qubit gates. Here, we present a systematic approach that goes beyond the dispersive approximation to exploit the engineered level structure of the coupler and optimize its control. Using this approach, we experimentally demonstrate CZ and ZZZZZZ-free iSWAP gates with two-qubit interaction fidelities of 99.76±0.0799.76 \pm 0.0799.76±0.07% and 99.87±0.2399.87 \pm 0.2399.87±0.23%, respectively, which are close to their T1T_1T1​ limits.
Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.
High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502 (2020); Phys. Rev. Lett. 125, 240503 (2020)] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast ZZZZZZ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near ${10}^{\ensuremath{-}5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.
Three-qubit gates can be constructed using combinations of single-qubit and two-qubit gates, making their independent realization unnecessary. However, direct implementation of three-qubit gates reduces the depth of quantum circuits, streamlines quantum programming, and facilitates efficient circuit optimization, thereby enhancing overall performance in quantum computation. In this work, we propose and experimentally demonstrate a high-fidelity scheme for implementing a three-qubit controlled-controlled-z (ccz) gate in a flip-chip superconducting quantum processor with tunable couplers. This direct ccz gate is implemented by simultaneously leveraging two tunable couplers interspersed between three qubits to enable three-qubit interactions, achieving an average final state fidelity of 97.94% and a process fidelity of 93.54%. This high fidelity cannot be achieved through a simple combination of single- and two-qubit gate sequences from processors with similar performance levels. Our experiments also verify that multilayer direct implementation of the ccz gate exhibits lower leakage compared to decomposed gate approaches. As a showcase, we utilize the ccz gate as an oracle to implement the Grover search algorithm on three qubits, demonstrating high performance with the target probability amplitude significantly enhanced after two iterations. These results highlight the advantage of our approach, and facilitate the implementation of complex quantum circuits.