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arXiv:2606.14522

Quantum gates with parametrically driven multi-qubit couplers

Verena Feulner, Marjan Fani, Lukas Heunisch, Stephan Tasler, Michael J. Hartmann

quant-phSubmitted Jun 12, 2026• Announced Jun 15, 2026• 0 citations
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Abstract

Superconducting quantum processors could significantly profit from enhanced connectivity together with precise control of interactions and gates between qubits. Here we investigate plaquettes of four qubits that are coupled via a central tunable coupling circuit, so that not only gates between qubits connected by an edge of the plaquette can be executed but also between qubits across the diagonal. By numerically and analytically analyzing parametrically driven processes, we explore $\sqrt{\text{iSWAP}}$-gates between any pair of qubits, also across the diagonal, as well as three-qubit interactions and gates. For experimentally available circuit parameters, we for example find $\sqrt{\text{iSWAP}}$-gates with a gate time of 50 ns and 99.9\% fidelity, which is decreased to 99.4\% if two such gates are executed in parallel on disjoint qubit pairs in the plaquette. For three-qubit gates we find fidelities of 95\% fidelity at a gate time of 200 ns.

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Superconducting quantum processors could significantly profit from enhanced connectivity together with precise control of interactions and gates between qubits. Here we investigate plaquettes of four qubits that are coupled via a central tunable coupling circuit, so that not only gates between qubits connected by an edge of the plaquette can be executed but also between qubits across the diagonal. By numerically and analytically analyzing parametrically driven processes, we explore iSWAP\sqrt{\text{iSWAP}}iSWAP​-gates between any pair of qubits, also across the diagonal, as well as three-qubit interactions and gates. For experimentally available circuit parameters, we for example find iSWAP\sqrt{\text{iSWAP}}iSWAP​-gates with a gate time of 50 ns and 99.9% fidelity, which is decreased to 99.4% if two such gates are executed in parallel on disjoint qubit pairs in the plaquette. For three-qubit gates we find fidelities of 95% fidelity at a gate time of 200 ns.
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two or more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we theoretically and experimentally study a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iswap) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bswap). We find that the bswap gate is generally slower than the more commonly used iswap gate, but features favorable scalability properties with less severe frequency-crowding effects, which typically degrade the fidelity in multiqubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.
The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms.A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity.Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits.Using randomized benchmarking protocols we estimate an error per gate of 0.9 ± 0.03 and 1.3 ± 0.4% for the CZ and the iSWAP gate, respectively.We argue that spurious ZZ-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance.Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.
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.
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.
Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date, such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms. Here, we propose a single shot method for executing an i-Toffoli gate, a three-qubit gate with two control and one target qubit, using currently existing superconducting hardware. We show numerical evidence for a process fidelity over 99.5% and a gate time of 450 ns for superconducting qubits interacting via tunable couplers. Our method can straight forwardly be extended to implement gates with more than two control qubits at similar fidelities.
We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static ZZZZZZ coupling strength. We quantitatively calculate the dynamic ZZZZZZ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic ZZZZZZ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic ZZZZZZ coupling and high-order oscillation error degrades the parametric gate performance. This approach, which has not yet been previously explored, provides a guiding principle to improve gate fidelity of a parametric iswap gate by suppression of the unwanted qubit interactions. This controllable interaction, together with the parametric modulation technique, is desirable for crosstalk-free multiqubit quantum circuits and quantum simulation applications.