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Quantum technologies are being fervidly developed to outperform classical devices for sensing, communications, and computation. The latter application relates to the fundamental question: can any physical model of computation be efficiently simulated by a Turing machine? Quantum mechanics predicts that no, and that instead some problems, intractable for classical computers, can be solved efficiently on a quantum computer, with important applications. However, quantum advantage has not yet been convincingly demonstrated, as only small quantum processors are implemented so far. New information encodings and hardware, based on the use of Continuous-Variable (CV) systems, could improve scalability.Not all CV quantum computers yield quantum advantage. In this project, I will pinpoint the origin of quantum advantage in CV. So far, only necessary conditions were given, based on the negativity of the Wigner function. As an original methodology, I will merge this approach with time-complexity scaling arguments. This will allow me to derive sufficient conditions in terms of the scaling of the Wigner function negativity with the circuit size. First, I will consider simple architectures, and assess whether a reference scaling exists, such that if the input state negativity surpasses it, quantum advantage is displayed. Then I will generalize to arbitrary CV quantum circuits. This study is essential in order to design computationally useful quantum architectures in CV.
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- Vetenskapsrådet (VR) (Offentlig, Sweden)