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arXiv:2501.03578 · Physical Review A

Four-body coupler for superconducting qubits based on Josephson parametric oscillators

Ryoji Miyazaki, Tsuyoshi Yamamoto

Published Jun 10, 2025• 1 citation
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Abstract

We theoretically propose a circuit of the four-body coupler for superconducting qubits based on Josephson parametric oscillators (JPOs). Our coupler for the four-body interaction has a superconducting loop, similar to a capacitively shunted flux qubit, where an external magnetic flux set to half a flux quantum is threaded. This coupler circuit is a specific setup of the circuit called superconducting nonlinear asymmetric inductive elements (SNAIL) and also is a generalization of the previously proposed one for the four-body interaction of JPOs. We clarify roles of circuit parameters in the four-body interaction and, in particular, show that the four-body coupling constant in our circuit can be significantly increased by tuning capacitance of the coupler or the area ratio of the Josephson junctions of the coupler.

DOI
10.1103/physreva.111.062612

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We theoretically propose a circuit of the four-body coupler for superconducting qubits based on Josephson parametric oscillators (JPOs). Our coupler for the four-body interaction has a superconducting loop, similar to a capacitively shunted flux qubit, where an external magnetic flux set to half a flux quantum is threaded. This coupler circuit is a specific setup of the circuit called superconducting nonlinear asymmetric inductive elements (SNAIL) and also is a generalization of the previously proposed one for the four-body interaction of JPOs. We clarify roles of circuit parameters in the four-body interaction and, in particular, show that the four-body coupling constant in our circuit can be significantly increased by tuning capacitance of the coupler or the area ratio of the Josephson junctions of the coupler.
For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper, we derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is nonperturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the interqubit coupling, including nonstoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer approximation.
An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device (rf-SQUID) flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.
Superconducting quantum circuits are a leading platform for building a large-scale quantum processor [1]. A crucial component necessary for the high-fidelity readout of qubits in this framework, is an ultra-low-noise microwave amplifier. Thus, over the past two decades, superconducting Josephson parametric amplifiers (JPAs) have been developed that achieve near quantum-limited noise performance, an order of magnitude lower than competing microwave amplifiers based on semiconductor transistors [2]. Nevertheless, JPAs suffer from drawbacks such as limited bandwidth and compression power that makes them difficult to use in an eventual large-scale quantum processor. Thus, an ongoing theme in JPA development is to optimize the circuit to improve these specifications without sacrificing other desirable properties such as the noise performance, ease of construction and operation, etc. Here, we review some results of optimizing a specific JPA circuit called the SNAIL parametric amplifier [3]–[5], shown in Fig. 1, where the acronym SNAIL refers to the Superconducting Nonlinear Asymmetric Inductive eLement. The SNAIL is a composite element made from conventional Al/AlOx/Al Josephson junctions, which has a nonlinear current-phase relation that can be approximated as a nonlinear inductance. By applying a strong microwave frequency pump to modulate the nonlinear inductance, parametric amplification can be realized. By device and circuit engineering we have demonstrated two orders of magnitude improvement in compression power (Fig. 2) in such devices without sacrificing other desirable characteristics.
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 circuits and trapped ions are promising architectures for quantum information processing. However, the natural frequencies for controlling these systems---radio-frequency ion control and microwave domain superconducting qubit control---make direct Hamiltonian interactions between them weak. In this paper we describe a technique for coupling a trapped ion's motion to the fundamental mode of a superconducting circuit, by applying to the circuit a carefully modulated external magnetic flux. In conjunction with a nonlinear element (Josephson junction), this gives the circuit an effective time-dependent inductance. We then show how to tune the external flux to generate a resonant coupling between the circuit and ion's motional mode and discuss the limitations of this approach compared to using a time-dependent capacitance.
The authors propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables them to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator can be as large as submillimeters and qubits interact with it via mutual inductance, their scheme makes it possible to construct a quantum gate involving remote qubits.