We study a new quantum heat engine (QHE), which is assisted by a Maxwell's demon. The QHE requires three steps: thermalization, quantum measurement, and quantum feedback controlled by the Maxwell demon. We derive the positive-work condition and operation efficiency of this composite QHE. Using controllable superconducting quantum circuits as an example, we show how to construct our QHE. The essential role of the demon is explicitly demonstrated in this macroscopic QHE. Introduction.-A Maxwell demon is a construct that can distinguish the velocities of individual gas molecules and then separate hot and cold molecules into two domains of a container, so that the two domains will have different temperatures [1]. This result seems to contradict the second law of thermodynamics, because one can put a heat engine between them to extract work. The solution of this puzzle [1] refers to the so-called Landauer's principle [2,3] that essentially links information theory with fundamental physics [4]. Several quantum heat engines (QHEs) assisted by Maxwell's demons have been proposed in Refs. [5,6,7].Here, we propose a new QHE model integrated with a built-in quantum Maxwell's demon performing both: the quantum measurement on the working substance, and the feedback control for the system according to the measurement. We demonstrate the role of Maxwell's demon in a fully quantum manner. The thermodynamic cycle in our setup contains three fundamental stages: (i) a CNOT operation, making a pre-measurement to extract information from the working substance; (ii) the feedbackaction of the demon controlling the working substance to extract work; and (iii) the disentanglement process that thermalizes the working substance and the demon by two separate thermal baths. The demon plays a role in the first two steps.We further illustrate how to implement our QHE using superconducting qubit circuits [8,9]. In our setup, the demon-assisted working substance does work via two CNOT operations, which can be realized by single-qubit operations and an easily realized i-SWAP operation. The CNOT operation performs the basic functions of the quantum demon.Maxwell's demon-assisted thermodynamic cycle in twoqubit system.-Our QHE cycle is similar to a quantum Otto cycle [10] described in Ref. [11] and generalized in Ref. [12]. Here, the QHE, shown in Fig. 1, is a composite system consisting of two qubits: the "working substance" S and the quantum Maxwell's demon D. They

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We propose and study an active cooling mechanism for the nanomechanical resonator (NAMR) based on periodical coupling to a Cooper pair box (CPB), which is implemented by a designed series of magnetic flux pluses threading through the CPB. When the initial phonon number of the NAMR is not too large, this cooling protocol is efficient in decreasing the phonon number by 2 to 3 orders of magnitude. Our proposal is theoretically universal in cooling various boson systems of a single mode. It can be specifically generalized to prepare the nonclassical state of the NAMR.