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IEEE Transactions on Applied Superconductivity

Crosstalk Suppression and High-Fidelity Measurement in 2-D Tunneling of Coupled Josephson Junctions

A. Sadeghi, Hesam Zandi, Sina Ataollah Khorasani

Published Jul 28, 2012• 1 citation
Publisher

Abstract

We present a new configuration concept in which two similar Josephson junctions are coupled through a capacitor placed in parallel to a dc-superconducting quantum interference device (SQUID) to improve the characteristics of phase qubits. In real coupled quantum systems, because of mutual effects such as crosstalk, entangled quantum states cannot be independently measured. The proposed two-qubit system is demonstrated to have a negligible crosstalk, obtained from the application of a single measurement pulse and an appropriate external flux to one of the junctions and the dc-SQUID, respectively. Surprisingly, the theoretically predicted fidelity for a single-qubit design increases to 99.99% for typical Josephson junction parameters. The high-fidelity measurement is reached even with pulse times less than 1 ns, while the highest fidelities reported so far are obtained by wide temporal pulses through single-shot current pulse measurements. This is accomplished by proper coupling capacitance, which determines the coupling time, the measurement time, and their proportion. Furthermore, the ratio of decoherence time for this structure with respect to the one belonging to a typical qubit is found to be more than 1.42.

DOI
10.1109/tasc.2012.2193616

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IEEE Transactions on Applied Superconductivity•Jan 13, 2011•2 citations
We present a new configuration concept in which two similar Josephson junctions are coupled through a capacitor placed in parallel to a dc-superconducting quantum interference device (SQUID) to improve the characteristics of phase qubits. In real coupled quantum systems, because of mutual effects such as crosstalk, entangled quantum states cannot be independently measured. The proposed two-qubit system is demonstrated to have a negligible crosstalk, obtained from the application of a single measurement pulse and an appropriate external flux to one of the junctions and the dc-SQUID, respectively. Surprisingly, the theoretically predicted fidelity for a single-qubit design increases to 99.99% for typical Josephson junction parameters. The high-fidelity measurement is reached even with pulse times less than 1 ns, while the highest fidelities reported so far are obtained by wide temporal pulses through single-shot current pulse measurements. This is accomplished by proper coupling capacitance, which determines the coupling time, the measurement time, and their proportion. Furthermore, the ratio of decoherence time for this structure with respect to the one belonging to a typical qubit is found to be more than 1.42.
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We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.
We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. 1∕f1∕f1∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of 1∕f1∕f1∕f noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.
This thesis examines sources of dissipation and dephasing in a dc SQUID phase qubit. Coupling of the qubit to the bias lines and lossy dielectrics causes the qubit to lose quantum information through a process known generally as decoherence. Using knowledge of the possible sources of decoherence, a dc SQUID phase qubit is designed with parameters that should have made it resistant to dissipation and dephasing from those sources. Device PB9 was a dc SQUID with one small area 0.23 (μm)2 Josephson junction with a critical current of 130 nA, which was meant to be the qubit junction, and a larger area 5 (μm)2 junction with a critical current of 8.6 μA, which acted as part of an inductive isolation network. The qubit junction was shunted by a 1.5 pF low-loss interdigitated capacitor. The dc current bias line had an on-chip LC filter with a cutoff frequency of 180 MHz. The other control lines were also designed to minimize coupling of dissipative elements to the qubit. According to a theoretical model of the dissipation and dephasing, the qubit was expected to have an energy relaxation T1 ≤ 8.4 μs and dephasing time Tø ∼ 1 μs. Because of the relatively high Josephson inductance of the qubit junction, the device did not act perform like a conventional isolated single-junction phase qubit. Instead, the resonant modes that I observed were the normal modes of the entire SQUID. At 20 mK and a frequency of 4.047 GHz, the maximum energy relaxation time of the device was found to be 350 ± 70 ns, despite the optimized design. Through a study of T1 versus applied flux, T1 was found to depend on the strength of the coupling of the microwave drive line to the qubit. When the line was more coupled, T1 was shorter. This was evidence that the microwave line was overcoupled to the qubit, and was limiting the lifetime of the excited state T1. Through a study of the spectroscopic coherence time T2* , which measured the effects of low-frequency inhomogeneous broadening and higher frequency dephasing from noise, I discovered that device PB9 has several sweet spots. In particular, the presence of a sweet spot with respect to critical current fluctuations allowed me to identify critical current noise as a major source of broadening and dephasing in the qubit. From the spectroscopy I estimated the 1/f critical current noise power density at 1 Hz was SI01 (1Hz) ≈ 10 (nA) 2/Hz and the 1/f flux noise power spectral density at 1 Hz was SΦ (1Hz) ≈ (110 μΦ 0)2/Hz. Both of these values were quite high, possibly due to switching of the device between measurements.
Identifying Sources of Decoherence in a dc SQUID Phase Qubit With a Sub-μm\mu{\rm m}μm Junction and Interdigitated Capacitor
We fabricated a dc SQUID phase qubit with a sub- μm Al/AlOx/Al qubit junction and an interdigitated shunting capacitor on a sapphire substrate. The qubit junction had a critical current of 135 nA, and the isolation junction had a critical current of 8.3 μA. The shunting capacitance was about 1.5 pF. To reduce the unwanted effects of two-level systems and increase the relaxation timeT1, we have removed unnecessary dielectrics, used a small qubit junction area (450 nm × 500 nm), isolated the qubit from the leads with an on-chip LC filter, and fabricated the device on a bare sapphire substrate. However, at a temperature of 20 mK, we foundT1≈ 300 ns and the coherence timeT2≈ 110 ns, which was much lower than one would expect from loss attributed to the leads and to dielectrics in the tunnel junction and substrate. Measurements ofT1versus applied flux (which tuned the qubit frequency) revealed a correlation between the strength of the coupling of the microwave excitation line to the qubit and the rate of energy dissipation in the qubit. This result suggests that the relaxation time was being limited by coupling to the microwave line.