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

TL;DR

This paper experimentally demonstrates that the Majorization Principle governs the probability dynamics of quantum algorithms, using 3-D integrated photonic circuits to observe its effects in quantum Fourier transform and boson interference validation.

Contribution

It provides the first experimental evidence that the Majorization Principle applies to quantum algorithms, supporting its role in designing optimal quantum computations.

Findings

Majorization observed in quantum Fourier transform

Majorization confirmed in boson interference validation

Supports the principle as a tool for quantum algorithm design

Abstract

The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution undergone by the system, these quantum algorithms are conjectured to obey a quantum arrow of time dictated by the Majorization Principle: the probability distribution associated to the outcomes gets ordered step-by-step until achieving the result of the computation. Here we report on the experimental observation of the effects of the Majorization Principle for two quantum algorithms, namely the quantum fast Fourier transform and a recently introduced validation protocol for the certification of genuine many-boson interference. The demonstration has been performed by employing integrated 3-D photonic circuits fabricated via femtosecond laser writing technique, which allows to monitor unambiguously the effects of majorization along the execution of the algorithms. The measured observables provide a strong indication that the Majorization Principle holds true for this wide class of quantum algorithms, thus paving the way for a general tool to design new optimal algorithms with a quantum speedup.