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The Majorization Principle is a fundamental statement governing the dynamicsof information processing in optimal and efficient quantum algorithms. Whilequantum computation can be modeled to be reversible, due to the unitaryevolution undergone by the system, these quantum algorithms are conjectured toobey a quantum arrow of time dictated by the Majorization Principle: theprobability distribution associated to the outcomes gets ordered step-by-stepuntil achieving the result of the computation. Here we report on theexperimental observation of the effects of the Majorization Principle for twoquantum algorithms, namely the quantum fast Fourier transform and a recentlyintroduced validation protocol for the certification of genuine many-bosoninterference. The demonstration has been performed by employing integrated 3-Dphotonic circuits fabricated via femtosecond laser writing technique, whichallows to monitor unambiguously the effects of majorization along the executionof the algorithms. The measured observables provide a strong indication thatthe Majorization Principle holds true for this wide class of quantumalgorithms, thus paving the way for a general tool to design new optimalalgorithms with a quantum speedup.

Observation of Majorization Principle for quantum algorithms via 3-D integrated photonic circuits