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Chinese Physics B

Tunable coupling between Xmon qubit and coplanar waveguide resonator*

Hekang Li, Ke-Min Li, Hang Dong, Qiujiang Guo, Wuxin Liu, Zhan Wang, Haohua Wang, Dongning Zheng

Published Aug 1, 2019• 7 citations
Publisher

Abstract

Realization of a flexible and tunable coupling scheme among qubits is critical for scalable quantum information processing. Here, we design and characterize a tunable coupling element based on Josephson junction, which can be adapted to an all-to-all connected circuit architecture where multiple Xmon qubits couple to a common coplanar waveguide resonator. The coupling strength is experimentally verified to be adjustable from 0 MHz to about 40 MHz, and the qubit lifetime can still be up to 12 μ s in the presence of the coupling element.

DOI
10.1088/1674-1056/28/8/080305

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Realization of a flexible and tunable coupling scheme among qubits is critical for scalable quantum information processing. Here, we design and characterize a tunable coupling element based on Josephson junction, which can be adapted to an all-to-all connected circuit architecture where multiple Xmon qubits couple to a common coplanar waveguide resonator. The coupling strength is experimentally verified to be adjustable from 0 MHz to about 40 MHz, and the qubit lifetime can still be up to 12 μ s in the presence of the coupling element.
We introduce a superconducting coplanar waveguide, in the form of a ring resonator, as a quantum bus for circuit quantum electrodynamics (circuit QED). Due to its unique symmetry, the amplitude of the electromagnetic field inside is uniform along the resonator, which in principle leads to a location independent coupling between qubits and the resonator. For an experimental demonstration, we designed and fabricated a ring resonator capacitively coupled to two tunable Xmon superconducting qubits. We showed that nearly identical coupling was achieved between individual qubits and the resonator. In addition, the resonator was also used as a high quality quantum bus for generating Bell states between the qubits with a fidelity of F=98.6%, although an interference effect must be included for understanding the effective coupling between the two qubits. Our results suggest that ring resonators can be a useful addition to the toolbox of circuit QED.
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.
A major challenge in the field of quantum computing is the construction of scalable qubit coupling architectures. Here, we demonstrate a novel tunable coupling circuit that allows superconducting qubits to be coupled over long distances. We show that the interqubit coupling strength can be arbitrarily tuned over nanosecond time scales within a sequence that mimics actual use in an algorithm. The coupler has a measured on/off ratio of 1000. The design is self-contained and physically separate from the qubits, allowing the coupler to be used as a module to connect a variety of elements such as qubits, resonators, amplifiers, and readout circuitry over distances much larger than nearest-neighbor. Such design flexibility is likely to be useful for a scalable quantum computer.
Voltage-tunable superconductor-semiconductor devices offer a unique platform to realize dynamic tunability in superconducting quantum circuits. By galvanically connecting a gated InAs\mathrm{In}\mathrm{As}InAs-Al\mathrm{Al}Al Josephson junction to a coplanar waveguide resonator, we demonstrate the use of a superconducting element with wideband gate tunability. We show that the resonant frequency is controlled via a gate-tunable Josephson inductance and that the nonlinearity of the InAs\mathrm{In}\mathrm{As}InAs-Al\mathrm{Al}Al junction is nondissipative as is the case with conventional AlOx-Al{\mathrm{Al}\mathrm{O}}_{\mathrm{x}}\text{-Al}AlOx​-Al junctions. As the gate voltage is decreased, the inductive participation of the junction increases up to $44\mathrm{%}$, resulting in the resonant frequency being tuned by over 2GHz2\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}2GHz. Utilizing the wide tunability of the device, we demonstrate that two resonant modes can be adjusted such that they strongly hybridize, exhibiting an avoided-level crossing with a coupling strength of 51MHz51\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}51MHz. Implementing such voltage-tunable resonators is the first step toward realizing wafer-scale continuous voltage control in superconducting circuits for qubit-qubit coupling, quantum limited amplifiers, and quantum memory platforms.
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.
Tunable coupling of superconducting qubits has been widely studied due to its importance for isolated gate operations in scalable quantum processor architectures.Here, we demonstrate a tunable qubit-qubit coupler based on a floating transmon device, which allows us to place qubits at least 2 mm apart from each other while maintaining over 50-MHz coupling between the coupler and the qubits.In the introduced tunable-coupler design, both the qubit-qubit and the qubit-coupler couplings are mediated by two waveguides instead of relying on direct capacitive couplings between the components, reducing the impact of the qubit-qubit distance on the couplings.This leaves space for each qubit to have an individual readout resonator and a Purcell filter, which is needed for fast high-fidelity readout.In addition, simulations show that the large qubit-qubit distance significantly lowers unwanted non-nearest-neighbor coupling and allows multiple control lines to cross over the structure with minimal crosstalk.Using the proposed flexible and scalable architecture, we demonstrate a controlled-Z gate with (99.81 ± 0.02)% fidelity.