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arXiv:2202.11594 · Journal of the Physical Society of Japan

Frequency Adjustable Resonator as a Tunable Coupler for Xmon Qubits

Hui Wang, Yan-Jun Zhao, Rui Wang, Xun‐Wei Xu, Qiang Liu, Jianhua Wang, Changxin Jin

Published Sep 16, 2022• 9 citations
arXivHTMLPDF

Abstract

We propose a scheme of tunable coupler based on quarter-wave resonator for scalable quantum integrated circuits. The open end of the T-type resonator is capacitively coupled to two Xmon qubits, while another end is an asymmetric dc-SQUID which dominates the inductive energy of coupler resonator. The dc-Current applied through the flux bias line could change the magnetic flux inside the dc-SQUID, so the frequency of coupler resonator can be effectively tuned and the qubit-qubit coupling can be totally switched off. As the increase of junction asymmetry for the dc-SQUID, the coupling of SQUID's effective phase difference and cavity modes become smaller at required working frequency regime of coupler resonator, and this could reduce the descent of the resonator's quality factor. The separation between two cross-capacitor can be larger with help of transverses width of the T-shape resonator, and then the ZZ crosstalk coupling can be effectively suppressed. The asymmetric dc-SQUID is about 5 millimeters away from the Xmon qubits and only needs a small current on the flux bias line, which in principle creates less flux noises to superconducting Xmon qubits.

DOI
10.7566/jpsj.91.104005

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•Jan 1, 2008•0 citations
We propose a scheme of tunable coupler based on quarter-wave resonator for scalable quantum integrated circuits. The open end of the T-type resonator is capacitively coupled to two Xmon qubits, while another end is an asymmetric dc-SQUID which dominates the inductive energy of coupler resonator. The dc-Current applied through the flux bias line could change the magnetic flux inside the dc-SQUID, so the frequency of coupler resonator can be effectively tuned and the qubit-qubit coupling can be totally switched off. As the increase of junction asymmetry for the dc-SQUID, the coupling of SQUID's effective phase difference and cavity modes become smaller at required working frequency regime of coupler resonator, and this could reduce the descent of the resonator's quality factor. The separation between two cross-capacitor can be larger with help of transverses width of the T-shape resonator, and then the ZZ crosstalk coupling can be effectively suppressed. The asymmetric dc-SQUID is about 5 millimeters away from the Xmon qubits and only needs a small current on the flux bias line, which in principle creates less flux noises to superconducting Xmon qubits.
We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., Phys. Rev. Lett. 113, 220502 (2014)]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse ${\ensuremath{\sigma}}^{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}^{x}$ coupling from that obtained in the harmonic approximation by about 15%, assuming typical qubit parameters. The second is to induce a small diagonal ${\ensuremath{\sigma}}^{z}\ensuremath{\bigotimes}{\ensuremath{\sigma}}^{z}$ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered. The approach used here can be applied to other complex nonlinear circuits arising in the design of superconducting hardware for quantum information processing.
We control the transition frequency of a superconducting flux qubit coupled to a frequency-tunable resonator comprising a direct current superconducting quantum interference device (dc SQUID) by microwave driving. The dc SQUID mediates the coupling between microwave photons in the resonator and a flux qubit. The polarity of the frequency shift depends on the sign of the flux bias for the qubit and can be both positive and negative. The absolute value of the frequency shift becomes larger by increasing the photon number in the resonator. These behaviors are reproduced by a model considering the magnetic interaction between the flux qubit and dc SQUID. The tuning range of the transition frequency of the flux qubit reaches $\ensuremath{\approx}1.9\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$. The effect of photon number fluctuation in the resonator to the dephasing rate of the flux qubit is also discussed.
We propose a theoretical scheme of using two fixed-frequency resonator couplers to tune the interaction between two Xmon qubits. The indirect interaction between two qubits induced by two resonators can cancel each other, so direct qubit-qubit coupling is not essential for the switching off. So, we can suppress the static ZZ coupling with the weak direct qubit-qubit coupling and even eliminate the static ZZ coupling through the destructive interferences of the double-path couplers. The cross-Kerr resonance can induce additional poles for the static ZZ coupling which should be kept away during the two-qubit gates. The double-resonator couplers scheme could unfreeze some restrictions during the design of superconducting quantum chips and mitigate the static ZZ coupling, which might supply a promising platform for future superconducting quantum chips.
Abstract Here we consider a tunable superconducting cavity that can be used either as a tunable coupler to a qubit inside the cavity or as a tunable low noise, low temperature, RF filter. Our design consists of an array of radio-frequency superconducting quantum interference devices (rf SQUIDs) inside a superconducting cavity. This forms a tunable metamaterial structure which couples to the cavity through its magnetic plasma frequency. By tuning the resonant frequency of the metamaterial through an applied magnetic flux, one can tune the cavity mode profile. This allows us to detune the cavity initially centered at 5.593 GHz by over 200 MHz. The maximum quality factor approaches that of the empty cavity, which is 4.5 × 106. The metamaterial electromagnetic response is controlled via a low-frequency or dc magnetic flux bias, and we present a control line architecture that is capable of applying sufficient magnetic flux bias with minimal parasitic coupling. Together this design allows for an in-situ tunable cavity which enables low-temperature quantum control applications.
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.
In this licentiate thesis design, fabrication, and measurements of tunable superconducting microwave transmission line resonators are described. The resonators are of quarter wavelength type were the tuning is achieved by changing one of the boundary conditions of the resonator through a tunable impedance. As tunable impedance the Josephson inductance in form of SQUIDs is used. The Josephson inductance can then be tuned by applying a magnetic field to the SQUID loop. A tuning range of 750 MHz for a 5 GHz resonator is achieved, and as a figure of merit it can be tuned over 200 line widths. The purpose of the tunable resonators is to use them for dynamic coupling of superconducting quantum bits, this requires that the resonators can be tuned fast on the timescale of the resonator-qubit coupling. To measure tuning speeds faster then the ring up time of the resonators a method that measures the leakage of energy out of a detuned resonator was developed. With this method a frequency shift of the energy stored in the resonator can be measured. A detuning of 330 MHz in less than 10 ns is demonstrated for a 4.5 GHz resonator with a quality factor of 104^44. Working in the few photon limit indicates that the devices can be used to change the frequency of individual photons, this is however still to be demonstrated. As a part of this work the dressed states of a superconducting charge qubit was also studied.