Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection. It can be implemented to realize quantum state transfer between microwave and optical modes.Quantum transducers (QT) can convert quantum signals from one bosonic mode to another, which may have different frequencies, polarizations, or even mode carriers. QT enables quantum information transfer between different physical platforms, which is crucial for hybrid quantum networks [1,2]. There have been significant advances toward quantum state transfer between different bosonic systems, such as conversion between microwave and mechanical/spin-wave modes [3][4][5], between optical and mechanical/spin-wave modes [6][7][8][9], and etc. Motivated by the hybrid quantum networks with optical quantum communication and microwave quantum information processing, recently there are experimental demonstrations of coherent conversion between microwave and optical signals with decent conversion efficiencies [10][11][12], but the signal attenuation and added noise still prevent us from achieving quantum transduction between microwave and optical modes.Most investigations of quantum transduction are based on the direct quantum transduction (DQT) protocol. As illustrated in Fig. 1(a), QDT protocol has a simple structure that injects quantum signals to the input port and retrieves them from the output port of the mode converter, which can hybridize different modes with enhanced bilinear couplings betweeen localized modes ( Fig. 1(b)). The energy mismatch between the input and output states can be compensated by parametric processes and stiff pumps [10,11,[13][14][15]. Unlike classical signals, quantum signals are vulnerable to both attenuation and amplification, which irreversibly add noise and induce decoherence. Hence, DQT protocol requires the matching condition (MC) -the subblock of the scattering matrix associated with the input and output ports should be equivalent to the identity matrix -so that every excitation entering the input port can be faithfully converted into an excitation exiting the output port, without affecting other ports [8,16,17]. In practice, however, MC is not always feasible, due to limited tunability of device parameters [18] and undesired parametric con- c between two internal modes a1 and a2 with coupling strengths g and g , and external coupli...