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Sensors

Bifurcation Oscillator as an Advanced Sensor for Quantum State Control

D. S. Pashin, M. V. Bastrakova, Сатанин Аркадий Михайлович, N. V. Klenov

Published Aug 31, 2022• 3 citations
Publisher

Abstract

We study bifurcation behavior of a high-quality (high-Q) Josephson oscillator coupled to a superconducting qubit. It is shown that the probability of capture into the state of dynamic equilibrium is sensitive to qubit states. On this basis we present a new measurement method for the superposition state of a qubit due to its influence on transition probabilities between oscillator levels located in the energy region near the classical separatrix. The quantum-mechanical behavior of a bifurcation oscillator is also studied, which makes it possible to understand the mechanism of "entanglement" of oscillator and qubit states during the measurement process. The optimal parameters of the driving current and the state of the oscillator are found for performing one-qubit gates with the required precision, when the influence on the qubit from measurement back-action is minimal. A measurement protocol for state populations of the qubit entangled with the oscillator is presented.

DOI
10.3390/s22176580

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We study bifurcation behavior of a high-quality (high-Q) Josephson oscillator coupled to a superconducting qubit. It is shown that the probability of capture into the state of dynamic equilibrium is sensitive to qubit states. On this basis we present a new measurement method for the superposition state of a qubit due to its influence on transition probabilities between oscillator levels located in the energy region near the classical separatrix. The quantum-mechanical behavior of a bifurcation oscillator is also studied, which makes it possible to understand the mechanism of "entanglement" of oscillator and qubit states during the measurement process. The optimal parameters of the driving current and the state of the oscillator are found for performing one-qubit gates with the required precision, when the influence on the qubit from measurement back-action is minimal. A measurement protocol for state populations of the qubit entangled with the oscillator is presented.
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.
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.
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.
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 theoretically study a nonlinear Josephson oscillator (Josephson junction) in the effective potential, which form is a result of a driving current. We first consider the phase dynamics in the classical regime and then explore the problem in the quantum regime by solving the energy eigenvalue problem. Here we are going to pay special attention to the study of the effects of switching between the states of a nonlinear oscillator separated by a separatrix. For this purpose, we consider controlling the oscillator with a "two-color" current. In the classical view, the first high-frequency current component brings the oscillator to the bifurcation point. A second modulated high-frequency component produces a programmed system switching. A similar scenario is considered in the quantum regime.
We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of a rf-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high sensitivity, low backaction, and the absence of on-chip dissipation. Pulsed microwave reflection measurements on nanofabricated Al junctions show that actual devices attain the performance predicted by theory.