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New Journal of Physics

Experimental analysis of the measurement strength dependence of superconducting qubit readout using a Josephson bifurcation readout method

Kosuke Kakuyanagi, S Kagei, R. Koibuchi, Shiro Saito, Adrian Lupaşcu, Kouichi Semba, H Nakano

Published Apr 17, 2013• 9 citations
Publisher

Abstract

We succeeded in controlling the measurement strength of a macroscopic quantum system, namely a persistent current quantum bit (qubit), by using a transmission line type Josephson bifurcation amplifier (JBA: an ac-driven superconducting quantum interferometer device) as a probe. By employing a special pulse sequence, we found that the weighted average of the Ramsey fringe visibility ( α -value) can be used as an indicator of quantum state projection. The sudden change in the α -value magnitude at around the threshold suggests that an entangled state of the qubit–JBA composite system settles in one of the two possible classically correlated qubit–JBA states caused by strong decoherence. This is an important result in terms of understanding the mechanisms of quantum state measurement.

DOI
10.1088/1367-2630/15/4/043028

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•Aug 31, 2005•0 citations
We succeeded in controlling the measurement strength of a macroscopic quantum system, namely a persistent current quantum bit (qubit), by using a transmission line type Josephson bifurcation amplifier (JBA: an ac-driven superconducting quantum interferometer device) as a probe. By employing a special pulse sequence, we found that the weighted average of the Ramsey fringe visibility ( α -value) can be used as an indicator of quantum state projection. The sudden change in the α -value magnitude at around the threshold suggests that an entangled state of the qubit–JBA composite system settles in one of the two possible classically correlated qubit–JBA states caused by strong decoherence. This is an important result in terms of understanding the mechanisms of quantum state measurement.
We have controlled the measurement strength of the qubit readout process by using a Josephson bifurcation amplifier (JBA : an AC-driven SQUID). The optimum readout pulse changes the superposition state into an eigenstate. To clarify how a sufficiently strong measurement causes a projection phenomenon, we have studied the projection conditions in the JBA readout. We found that the projection occurs above the pulse height at which visibility starts to appear. Furthermore, the projection continues to occur as readout strength increases, even though the visibility vanishes. This result helps us understanding the JBA readout process.
We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically by calculating the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. When a qubit is initially in a superposition state, we have observed the qubit-probe (JBA) entangled state, and it is divided into two separable states at the moment the JBA transition begins. This corresponds to "projection." To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated. The waiting time is determined by the strength of the decoherence in the JBA.
Quantum measurements play a central role in quantum information processing. Understanding the mechanism of the quantum measurements is essential to both improve the visibility of the readout and decrease the projection error during measurement. Here, we describe and demonstrate an experimental protocol for quantifying a measurement backaction when we readout a superconducting flux qubit using a Josephson bifurcation amplifier. The coupling with the Josephson bifurcation amplifier induces a dephasing on the flux qubit during the readout. We have succeeded in estimating and controlling the strength of such a measurement-induced dephasing by changing the pulse height of the microwave driving. Our results are crucial for designing a suitable quantum readout technique for the realization of practical quantum devices.
The Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit is analyzed quantum mechanically. We examined the dynamics of the density operator of a detector (a driven nonlinear oscillator) and a qubit coupled system during the measurement process. We have observed the qubit-detector (JBA) entangled state and it is divided into two separable states at the moment the JBA transition begins. Moreover, we discuss the process from the viewpoint of time variations in information quantities, such as mutual information between the qubit and detector. We show that the measurement process corresponds to an information conversion from quantum to classical one.
We report on measurements of macroscopic quantum states in superconducting Josephson circuits using a highly sensitive hybrid quantum interferometer as the readout probe. The investigated Josephson circuit is one of the leading candidates as solid-state qubits (persistent current qubit), which are known to exhibit macroscopic quantum states with atomic-like properties. The readout device is a modified Andreev interferometer with semi-metallic normal segment in a “folded" geometry, and is designed to reduce the back action during measurement, as well as minimising the electromagnetic coupling between the circuit and the environment.\n A pulsed lock-in technique has been developed to perform continuous readout of the superconductor phase difference using pulse lengths down to 10 ns. The technique enables to control the energy of the probing quasiparticles in the normal segment of the interferometer, which in turn allows to control of the supercurrent owing in the SNS junction and prevents electron heating of the normal segment.\n An experimental set-up was designed and installed in a dilution fridge consisting of shielded wiring, magnetic screens, RF tight sample holder and printed circuit board to allow the injection of high frequency excitation signals, while minimising the environment effect on the qubit through careful electrical filtering. The effect of strong RF irradiation on Andreev interferometers allowed us to estimate the response time of the readout device to be less than 40 ps.\n The measurements show that two macroscopically distinct metastable states exist when the device is biased at the qubit degeneracy point, between which the system makes transitions that can be continuously monitored. Real time kinetics of the system has been investigated at different magnetic fluxes, pulse parameters, temperature and RF radiation. Based on statistical analysis of the transitions, we argue that the metastability is connected with macroscopic quantum tunnelling effects rather than thermal excitation. The experimental data support the hypothesis of a large low frequency noise causing low transition rates.
During this grant, we have invented, designed and successfully operated a new type of readout for charge-phase superconducting qubits. This new readout is based on the bifurcation of an RF-driven Josephson junction inserted in the loop of a split Cooper pair box. When the amplitude of the RF drive is in the vicinity of the bifurcation points a small change in the effective critical current of the junction is amplified into a large phase change in the reflected signal. The performance reached by the device is in agreement with theoretical predictions. The speed of this readout is unprecedented: we measure in 20ns the critical current increment corresponding to the transition between the 2 states of the qubit. The repetition rate is 10Mz. We have performed a series of experiments showing that the amplification mechanism behaves as expected. No quasiparticles are produced during the readout and the back-action on the qubit when the readout is OFF is minimal. We have performed decoherence measurements at dilution refrigerator temperatures on the quantronium qubit integrated with RF readout. These measurements involve all possible 1-qubit gate operations. Compared with the DC readout method we have gained in repetition rate (factor of 100), signal-to-noise ration on all coherence signals (factor of 10) but most importantly, on readout fidelity which now attains more than 60% (compared to 15%). This last improvement is very important for showing the entanglement produced by two-bit gate operations. The T1 has also been improved by 250%. We still have comparable T2 as before but we suspect this is due to insufficient filtering on the listening lines of our measurement apparatus and this problem is technically solvable. In parallel with this work on readout and decoherence of the quantronium qubit, we have designed a new 2-bit gate based on capacitive coupling between qubits and worked out the complete protocol of pulses.