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arXiv:cond-mat/0509799 · Physical Review B

Parametric coupling for superconducting qubits

Patrice Bertet, C. J. P. M. Harmans, Johan E. Mooij

Published Feb 14, 2006• 137 citations
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Abstract

We propose a scheme to couple two superconducting charge or flux qubits biased at their symmetry points with unequal energy splittings. Modulating the coupling constant between two qubits at the sum or difference of their two frequencies allows to bring them into resonance in the rotating frame. Switching on and off the modulation amounts to switching on and off the coupling which can be realized at a nanosecond speed. We discuss various physical implementations of this idea, and find that our scheme can lead to rapid operation of a two-qubit gate.

DOI
10.1103/physrevb.73.064512

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We propose a scheme to couple two superconducting charge or flux qubits biased at their symmetry points with unequal energy splittings. Modulating the coupling constant between two qubits at the sum or difference of their two frequencies allows to bring them into resonance in the rotating frame. Switching on and off the modulation amounts to switching on and off the coupling which can be realized at a nanosecond speed. We discuss various physical implementations of this idea, and find that our scheme can lead to rapid operation of a two-qubit gate.
Parametric modulation, valued for its versatility, is widely employed in superconducting circuits for quantum simulations and high-fidelity two-qubit gates. Conventionally, the qubit coupling strength is determined by the amplitude of the parametric flux pulse, which affects the qubit parameters dramatically. In this paper, we propose and implement a phase-modulation scheme to tune the interaction strength via adjustment of the relative phase between the parametric flux pulses applied to two coupled qubits. We characterize this modulation for sideband couplings, at both sweet and off-sweet spots, achieving a broad range of coupling strengths, as confirmed by both population dynamics and spectroscopy methods. This approach enables phase-controlled modulation of coupling strength, providing a promising candidate for parametrically driven quantum simulations and gate operations.
We discuss a practical design for tunably coupling a pair of flux qubits via the quantum inductance of a third high-frequency qubit. The design is particularly well suited for realizing a recently proposed microwave-induced parametric coupling scheme. This is attractive because the qubits can always remain at their optimal points. Furthermore, we will show that the resulting coupling also has an optimal point where it is insensitive to low-frequency flux noise. This is an important feature for the coherence of coupled qubits. The presented scheme is an experimentally realistic way of carrying out two-qubit gates and should be easily extended to multiqubit systems.
We propose a scheme with dc control of finite bandwidth to implement a two-qubit gate for superconducting flux qubits at the optimal point. We provide a detailed nonperturbative analysis on the dynamic evolution of the qubits interacting with a common quantum bus. An effective qubit-qubit coupling is induced while decoupling the quantum bus with proposed pulse sequences. The two-qubit gate is insensitive to the initial state of the quantum bus and applicable to nonperturbative coupling regime which enables rapid two-qubit operation. This scheme can be scaled up to multiqubit coupling.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.
High-fidelity parametric gates have been demonstrated with superconducting qubits via rf flux modulation of the qubit frequency. The modulation however leads to renormalization of the bare qubit-qubit coupling, thereby reducing the gate speed. Here, we realize a parametric-resonance gate, which is activated by bringing the average frequency of the modulated qubit in resonance with a static-frequency qubit while approximately retaining the bare qubit-qubit coupling. The activation of parametric-resonance gates does not depend on the frequency of modulation, allowing us to choose the modulation frequencies and avoid frequency collisions. Moreover, we show that this approach is compatible with tunable coupler architectures, which reduce always-on residual couplings. Using these techniques, we demonstrate iswap and controlled-ZZZ gates between two qubits coupled via a tunable coupler with average process fidelities as high as $99.3\mathrm{%}$ and $97.9\mathrm{%}$, respectively. The flexibility in activating parametric-resonance gates combined with a tunable coupler architecture provides a pathway for building large-scale quantum computers.
Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large Kerr nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal quantum computation, and studies of quantum many-body systems. It is of practical importance for these studies to realize fast and accurate tunable coupling between KPOs in a simple manner. We develop a simple scheme of fast tunable coupling of KPOs with high tunability in speed and amplitude using the fast transitionless rotation of a KPO in the phase space based on the shortcuts to adiabaticity. Our scheme enables rapid switching of the effective coupling between KPOs, and can be implemented with always-on linear coupling between KPOs, by controlling the phase of the pump field and the resonance frequency of the KPO without controlling the amplitude of the pump field nor using additional drive fields and couplers. We apply the coupling scheme to a two-qubit gate, and show that our scheme realizes high gate fidelity compared with a purely adiabatic one, by mitigating undesired nonadiabatic transitions.