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arXiv:1002.0624 · Physical Review B

Measurement crosstalk between two phase qubits coupled by a coplanar waveguide

Fabio Altomare, Katarina Cicak, Mika A. Sillanpää, Michael S. Allman, Adam J. Sirois, Dale Li, Jae I. Park, Joshua Strong, John D. Teufel, Jed D. Whittaker, Raymond W. Simmonds

Published Sep 14, 2010• 41 citations
arXivHTMLPDF

Abstract

We investigate measurement crosstalk in a system with two flux-biased phase qubits coupled by a resonant coplanar waveguide cavity. After qubit measurement, the superconducting phase undergoes damped oscillations in a deep anharmonic potential producing a frequency chirped voltage or crosstalk signal. We show experimentally that a coplanar waveguide cavity acts as a bandpass filter that can significantly reduce the propagation of this crosstalk signal when the qubits are far off resonance from the cavity. The transmission of the crosstalk signal $\ensuremath{\propto}{({\ensuremath{\omega}}_{q}{C}_{x})}^{2}$ can be further minimized by reducing the qubit frequencies and the coupling capacitance to the cavity. We model the large amplitude crosstalk signal and qubit response classically with results that agree well with the experimental data. We find that the maximum energy transferred by the crosstalk generating qubit roughly saturates for long energy relaxation times $({T}_{1}>100\text{ }\text{ns})$ while the delay time necessary for the crosstalk signal to propagate to the cavity scales linearly with ${T}_{1}$. Ultimately, the use of resonant cavities as coupling elements and crosstalk filters is extremely beneficial for future architectures incorporating many coupled qubits.

DOI
10.1103/physrevb.82.094510

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We investigate measurement crosstalk in a system with two flux-biased phase qubits coupled by a resonant coplanar waveguide cavity. After qubit measurement, the superconducting phase undergoes damped oscillations in a deep anharmonic potential producing a frequency chirped voltage or crosstalk signal. We show experimentally that a coplanar waveguide cavity acts as a bandpass filter that can significantly reduce the propagation of this crosstalk signal when the qubits are far off resonance from the cavity. The transmission of the crosstalk signal \ensuremath∝(\ensuremathωqCx)2\ensuremath{\propto}{({\ensuremath{\omega}}_{q}{C}_{x})}^{2}\ensuremath∝(\ensuremathωq​Cx​)2 can be further minimized by reducing the qubit frequencies and the coupling capacitance to the cavity. We model the large amplitude crosstalk signal and qubit response classically with results that agree well with the experimental data. We find that the maximum energy transferred by the crosstalk generating qubit roughly saturates for long energy relaxation times (T1>100 ns)({T}_{1}>100\text{ }\text{ns})(T1​>100 ns) while the delay time necessary for the crosstalk signal to propagate to the cavity scales linearly with T1{T}_{1}T1​. Ultimately, the use of resonant cavities as coupling elements and crosstalk filters is extremely beneficial for future architectures incorporating many coupled qubits.
We report experiments on superconducting flux qubits in a circuit quantum electrodynamics (cQED) setup. Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum contrast of 72%. We measure energy relaxation times at the symmetry point of 5 and $10\ensuremath{\mu}\mathrm{s}$, corresponding to 7 and $20\ensuremath{\mu}\mathrm{s}$ when relaxation through the resonator due to Purcell effect is subtracted out, and levels of flux noise of 2.6 and $2.7\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}/\sqrt{\text{Hz}}$ at 1 Hz for the two qubits. We discuss the origin of decoherence in the measured devices. The strong coupling between the qubits and the cavity leads to a large, cavity-mediated, qubit-qubit coupling. This coupling, which is characterized spectroscopically, reaches 38 MHz. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe T1{T}_{1}T1​ and T2{T}_{2}T2​ times of 1.6 and 1.9 $\ensuremath{\mu}$s, respectively. This work demonstrates how this qubit can be incorporated into quantum architectures.
We analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase qubits. The damped oscillations of the superconducting phase after the measurement of the first qubit may significantly excite the second qubit, leading to its measurement error. The first qubit, which is highly excited after the measurement, is described classically. The second qubit is treated both classically and quantum mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the frequency of two-qubit operations) for a given tolerable value of the measurement error probability.
We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [A. A. Abdumalikov, Jr. et al., Phys. Rev. B 78, 180502(R) (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinity of the qubit. In addition to yielding stronger coupling with respect to other proposals for flux qubit based circuit QED, this approach leads to a qubit-resonator coupling strength ggg which does not scale as the area of the qubit but is proportional to the total inductance shared between the resonator and the qubit. Strong coupling can thus be attained while still minimizing sensitivity to flux noise. Finally, we show that by taking advantage of the large kinetic inductance of a Josephson junction in the center conductor of the resonator can lead to coupling energies of several tens of percent of the resonator frequency, reaching the ultrastrong coupling regime of cavity QED where the rotating-wave approximation breaks down. This should allow an on-chip implementation of the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ Jahn-Teller model.
Hardware-efficient methods for high-fidelity quantum state measurements are crucial for superconducting qubit experiments, as qubit numbers grow and feedback and state reset begin to be employed for quantum error correction. We present a three-dimensional reentrant-cavity filter designed for frequency-multiplexed readout of superconducting qubits. The cavity filter is situated out of the plane of the qubit circuit and capacitively couples to an array of on-chip readout resonators in a manner that can scale to large qubit arrays. The reentrant cavity functions as a large-linewidth bandpass filter with intrinsic Purcell filtering. We demonstrate the concept with a four-qubit multiplexed device in which we achieve an average readout fidelity of 98.6% and measurement-induced crosstalk dephasing rates below 0.15 kHz.
We analyze the performance of a microwave chip mount that uses wirebonds to connect the chip and mount grounds. A simple impedance ladder model predicts that transmission crosstalk between two feedlines falls off exponentially with distance at low frequencies, but rises to near unity above a resonance frequency set by the chip to ground capacitance. Using SPICE simulations and experimental measurements of a scale model, the basic predictions of the ladder model were verified. In particular, by decreasing the capacitance between the chip and box grounds, the resonance frequency increased and transmission decreased. This model then influenced the design of a new mount that improved the isolation to − 65 dB at 6 GHz, even though the chip dimensions were increased to 1 cm × 1 cm, three times as large as our previous devices. We measured a coplanar resonator in this mount as preparation for larger qubit chips, and were able to identify cavity, slotline, and resonator modes.