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arXiv:1909.12822 · Physical Review Applied

Quantum Functionalities Via Feedback Amplification

Rion Shimazu, Naoki Yamamoto

Published Apr 2, 2021• 10 citations
arXivHTMLPDF

Abstract

Feedback amplification is a key technique for synthesizing various functionalities, especially in electronic circuits involving op amps. This paper presents a quantum version of this methodology, where the general phase-preserving quantum amplifier and coherent (i.e., measurement-free) feedback are employed to construct various types of systems having useful functionalities: quantum versions of differentiator, integrator, self-oscillator, and active filters. The class of active filters includes the Butterworth filter, which can be used to enhance the capacity of an optical quantum communication channel, and the nonreciprocal amplifier, which enables measurement of a superconducting qubits system as well as protection of it by separating input from output fields. A particularly detailed investigation is performed on the active phase-canceling filter for realizing a broadband gravitational-wave detector; that is, the feedback-amplification method is used to construct an active filter that compensates the phase delay of the signal and eventually recovers the sensitivity in the high-frequency regime.

DOI
10.1103/physrevapplied.15.044006

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Feedback amplification is a key technique for synthesizing various functionalities, especially in electronic circuits involving op amps. This paper presents a quantum version of this methodology, where the general phase-preserving quantum amplifier and coherent (i.e., measurement-free) feedback are employed to construct various types of systems having useful functionalities: quantum versions of differentiator, integrator, self-oscillator, and active filters. The class of active filters includes the Butterworth filter, which can be used to enhance the capacity of an optical quantum communication channel, and the nonreciprocal amplifier, which enables measurement of a superconducting qubits system as well as protection of it by separating input from output fields. A particularly detailed investigation is performed on the active phase-canceling filter for realizing a broadband gravitational-wave detector; that is, the feedback-amplification method is used to construct an active filter that compensates the phase delay of the signal and eventually recovers the sensitivity in the high-frequency regime.
Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using nonclassical states and quantum filters, which modify both the noise and signal response. We find an approach to realizing quantum filters directly from their frequency-domain transfer functions, utilizing techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show an optical realization of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity. Anomalous dispersion has been shown to improve the bandwidth-sensitivity limit by signal amplification, but its unstable issue in operation needs additional feedback control. Here we propose a stable quantum amplifier enabled by two-mode non-degenerate parametric amplification. As the amplifier operates at threshold, one mode of the amplifier forms a parity-time(PT)-symmetric system with the mode of the original detector, while the other mode of the amplifier collects signal and gets extracted by a readout. Viewed more broadly in the context of coherent quantum control theory, we are attaching a controller that consists of a time reversal of the plant, which, by canceling the inertia of the plant, helps drive up the closed-loop signal gain. Examples of microwave cavity axion detectors and laser-interferometric gravitational-wave detectors will be discussed for this technique.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
Nowadays, it is possible to control and measure the quantum state of systems with a few degrees of freedom, whether they are microscopic objects like cold atoms and single photons, or macroscopic objects like superconducting circuits. Such delicate experiments require an interface which bridges the gap of orders of magnitudes in energy between the quantum object and the data acquisition system. This problem is solved by an active device: the amplifier. Although the amplifier is necessary to overcome the noise at the stage of data acquisition, it eventually alters the signal. We have developed an amplifier for microwave signals which adds only the minimum of noise allowed by quantum laws: the equivalent of half a photon of noise referred to the input. Our amplifier is based on a superconducting circuit of Josephson junctions in superconducting resonators. We found a way to make it practical to use by tuning its center frequency over 500 MHz. We are now trying to increase its bandwidth for a given gain using more compact resonators. In this talk, I will show how the amplifier works and also its applications to quantum information processing. This circuit can be used to generate and combine twin microwave photons within an integrated circuit. Finally, I will show that such an amplifier allows real time measurement of the state of a qubit and quantum feedback protocols.