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
ZZ coupling strength. We quantitatively calculate the dynamic
ZZ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic
ZZ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic
ZZ 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.
Superconducting circuits are a leading platform for scalable quantum computing, where parametric modulation is a widely used technique for implementing high-fidelity multi-qubit operations. A critical challenge, however, is that this modulation can induce a dense landscape of parasitic couplings, leading to detrimental frequency collisions that constrain processor performance. In this work, we develop a comprehensive numerical framework, grounded in Floquet theory, to systematically analyze and mitigate these collisions. Our approach integrates this numerical analysis with newly derived analytical models for both qubit-modulated and coupler-modulated schemes, allowing us to characterize the complete map of parasitic sideband interactions and their distinct error budgets. This analysis forms the basis of a constraint-based optimization methodology designed to identify parameter configurations that satisfy the derived physical constraints, thereby avoiding detrimental parasitic interactions. We illustrate the utility of this framework with applications to analog quantum simulation and gate design. Our work provides a predictive tool for co-engineering device parameters and control protocols, enabling the systematic suppression of crosstalk and paving the way for large-scale, high-performance quantum processors.
A parametric oscillator is an oscillating system in which one of the parameters, typically either the resonance frequency or damping, can be modulated by an external pump. Parametric oscillations can be found in a wide variety of systems including radiofrequency circuits, optical and mechanical systems, and even single electrons in a Penning trap. In recent years, interest in parametric oscillators has revived in many areas of physics, ranging from basic physics to applications. For instance, they are being used as quantum-limited amplifiers in an increasingly large number of experiments in quantum information and computing. At the same time, interest in their basic physics in the quantum regime, in which they are a model system for driven, nonlinear systems, has grown commensurately. This chapter gives a largely self-contained introduction to the theoretical description of the dynamics of parametric oscillators, both classical and quantum, and reviews some of the recent experimental work in superconducting circuits.