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Nonlinear transformations are important in quantum machine learning and other quantum numerical applications, which can be reduced to the implementation of element-wise polynomials through polynomial approximation. Existing works establish the feasibility of transformations and improve query or auxiliary-space efficiency, but circuit depth remains linear in scale with degree.
Abstract Quantum teleportation is the process of transferring quantum information using classical communication and pre-shared entanglement. This process can benefit from the use of catalysts, which are ancillary entangled states that can enhance teleportation without being consumed.
1. Introduction Quantum resource theory originally comes from the resource theory of quantum entanglement [1,2,3,4,5,6]. With the further evolution of quantum information, it has been gradually extended to other quantum resource theories such as coherence [7,8,9,10,11], asymmetry [12,13], reference frames [14,15], thermodynamics [16,17] and so on. In this paper, we focus on the resource theory of quantum coherence.
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