A general statistical approach to quantum algorithms in a circuit model based on the expectation and standard deviation of each gate separately

• URL: http://arxiv.org/abs/2410.11918v1
• Date: Tue, 15 Oct 2024 11:48:44 GMT
• Title: A general statistical approach to quantum algorithms in a circuit model based on the expectation and standard deviation of each gate separately
• Abstract summary: We describe quantum algorithms as a quantum state with amplitudes constructed from the expected value and standard deviation of each quantum gate or a sub-sequence of gates in the algorithm. We present a more fundamental identity that, unlike the previous one, allows us to switch the basis of the states into a desired form.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, there has been a growing literature exploring the generalization of quantum algorithms, such that different quantum algorithms are special examples of a more fundamental structure. In this short paper, we provide a general approach to describe quantum algorithms as a quantum state with amplitudes that are constructed from the expected value and standard deviation of each quantum gate or a sub-sequence of gates in the algorithm. The proposed statistical-based description relies on the celebrated Aharonov-Vaidman identity. We present a more fundamental identity that, unlike the previous one, allows us to switch the basis of the states into a desired form.

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