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arXiv:1703.04501 · Applied Physics Letters

Characterization of hidden modes in networks of superconducting qubits

Sarah Sheldon, Martin Sandberg, Hanhee Paik, Baleegh Abdo, Jerry M. Chow, Matthias Steffen, Jay M. Gambetta

Published Nov 27, 2017• 18 citations
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Abstract

We present a method for detecting electromagnetic (EM) modes that couple to a superconducting qubit in a circuit quantum electrodynamics architecture. Based on measurement-induced dephasing, this technique allows the measurement of modes that have a high quality factor (Q) and may be difficult to detect through standard transmission and reflection measurements at the device ports. In this scheme, the qubit itself acts as a sensitive phase meter, revealing modes that couple to it through measurements of its coherence time. Such modes are indistinguishable from EM modes that do not couple to the qubit using a vector network analyzer. Moreover, this technique provides useful characterization parameters including the quality factor and the coupling strength of the unwanted resonances. We demonstrate the method for detecting both high-Q coupling resonators in planar devices as well as spurious modes produced by a 3D cavity.

DOI
10.1063/1.4990033

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We present a method for detecting electromagnetic (EM) modes that couple to a superconducting qubit in a circuit quantum electrodynamics architecture. Based on measurement-induced dephasing, this technique allows the measurement of modes that have a high quality factor (Q) and may be difficult to detect through standard transmission and reflection measurements at the device ports. In this scheme, the qubit itself acts as a sensitive phase meter, revealing modes that couple to it through measurements of its coherence time. Such modes are indistinguishable from EM modes that do not couple to the qubit using a vector network analyzer. Moreover, this technique provides useful characterization parameters including the quality factor and the coupling strength of the unwanted resonances. We demonstrate the method for detecting both high-Q coupling resonators in planar devices as well as spurious modes produced by a 3D cavity.
We present fabrication and characterization procedures of devices for circuit quantum electrodynamics (cQED). We have made 3-GHz cavities with quality factors in the range 10/sup 4/-10/sup 6/, which allow access to the strong coupling regime of cQED. The cavities are transmission line resonators made by photolithography. They are coupled to the input and output ports via gap capacitors. An Al-based Cooper pair box is made by e-beam lithography and Dolan bridge double-angle evaporation in superconducting resonators with high quality factor. An important issue is to characterize the quality factor of the resonators. We present an RF-characterization of superconducting resonators as a function of temperature and magnetic field. We have realized different versions of the system with different box-cavity couplings by using different dielectrics and by changing the box geometry. Moreover, the cQED approach can be used as a diagnostic tool of qubit internal losses.
Superconducting resonators with high quality factors are extremely sensitive detectors of the complex impedance of materials and devices coupled to them. This capability has been used to measure losses in multiple different materials and, in the case of circuit quantum electrodynamics (circuit QED), has been used to measure the coherent evolution of multiple different types of qubits. Here, we report on the implementation of a scanning resonator for probing quantum coherent devices. Our scanning setup enables tunable coherent coupling to systems of interest without the need for fabricating on-chip superconducting resonators. We measure the internal quality factor of our resonator sensor in the single-photon regime to be >104 and demonstrate capacitive imaging using our sensor with zeptoFarad sensitivity and micron spatial resolution at milliKelvin temperatures. We then use our setup to characterize the energy spectrum and coherence times of multiple transmon qubits with no on-chip readout circuitry. Our experiments introduce a new tool for using circuit QED to measure existing and proposed qubit platforms.
Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to an unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically induced transparency (EIT) between the resonator and qubit in the weak dispersive coupling regime. Applying a sideband drive signal to the qubit, we observe an interference dip originated from EIT in the qubit spectroscopy, originating from the quantum interference between the qubit probe signal and sideband transition. From the width and the depth of the dip, we are able to extract the single-photon linewidth of the resonator from an analytical model. Working in a previously unexplored regime in which the qubit has a larger linewidth than the resonator reduces the technical challenge of making a high-coherence qubit and is advantageous for remaining in the weakly invasive limit of coupling to the resonator. Furthermore, the sideband and the dispersive coupling between the resonator and the qubit can be tuned insituin\phantom{\rule{3.33333pt}{0ex}}situinsitu controlling the strength of the sideband drive power. This in situ tuneability allows the technique to be applied for efficient measurement of the resonator loss rate for any quality factor below a fixed upper bound, on the order of 108{10}^{8}108 for our device, allowing a wide range of quality factors to be probed using a single design.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.
High-fidelity control of superconducting quantum processors requires accurate characterization of electromagnetic coupling strengths among the device's constituent elements. Accurately extracting these couplings across large-scale architectures, presently featuring hundreds of qubits, poses a challenging multi-scale modeling problem. This requires resolving scales from the nanometer-scale geometry of Josephson junctions and their leads to the centimeter-scale size of the enclosing metallic packages. We present four numerical coupling extraction methods based on the avoided level crossing, the energy participation ratio, the induced electromotive force, and the impedance matrix. These methods are tailored to work with commercially available 3D electromagnetic solvers. We benchmark these techniques on a 10×1010\times1010×10 array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.
This thesis presents circuit quantum electrodynamic (cQED) experiments done with artificial atoms coupled to a high quality factor superconducting microwave resonator. This work discusses the theoretical framework, design, fabrication, implementation and characterization of a multi-qubit system using superconducting persistent current qubits, often referred as flux qubits. \n \nWe developed a new type of cryogenic aid for fast turnaround microwave experiments. The minimum turnaround time to perform microwave experiments in dilution refrigerators is typically a few days, as required by cooling down and warming up the entire refrigerator. The cryogenic microwave payload and wiring needed for each qubit and resonator add a significant heat load to \nthe system which typically only has a few µW s of cooling power at millikelvin temperatures. We present a new experimental approach we developed in which a suitable sample holder is attached to a cold-insertable probe and brought in contact with transmission lines permanently mounted inside the cryostat. The total turnaround time is reduced to 8 hours if the target temperature is 80 mK. This new measurement method increased our ability to successfully identify good devices with fast design-characterization iterations, while allowing months-long measurements at 30 mK. \n \nOur device architecture uses several qubits, each of which is controlled via on-chip fast flux bias lines. Readout of the qubit’s quantum state is performed by homodyne detection of the resonator field at large driving power. We observe long coherence times at the optimal bias point of the flux qubits and present decoherence measurements around this optimal point, where the \nflux qubits couple mostly to magnetic flux noise. Dynamical decoupling techniques employing fast microwave pulses are used to protect the qubit’s coherence and allow calculating the magnetic flux noise power spectral density of the qubit’s environment. Photon-mediated interaction between distant qubits in the resonator allows the implementation of a two-qubit controlled-NOT gate \nusing the selective darkening technique. \n \nThis multi-qubit superconducting design is an interesting platform to study the decoherence properties of flux qubits, the properties of strong interaction of electromagnetic radiation with macroscopic quantum systems. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.