A duality between bosons and fermions and the Boson-Sampling computer.

Subir Sachdev A

V. S. Shchesnovich

We explore the conditions under which identical particles in unitary linear networks behave as the other species, i.e. bosons as fermions and fermions as bosons. It is found that the Boson-Sampling computer of Aaronson & Arkhipov can be implemented in an interference experiment with non-interacting fermions in an appropriately entangled state. Moreover, a scheme is proposed which simulates the scattershot version of the Boson-Sampling computer by preparing, on the fly, the required entangled state of fermions from an unentangled one.

Won Sang Chung, Abdullah Algin

Franziska Barkhausen, Laura Ares, Stefan Schumacher +1 more

Boson sampling is one of the most prominent methods to verify quantum advantage, harnessing the computational complexity of the permanent of a network matrix. Similar quantum sampling problems utilize other expressions for the output probabilities, such as the fermion-based analog applying determinants. In this work, we study sampling setups of interacting light-matter systems, combining fermion and boson sampling. The mixed network input consists of fermionic and bosonic excitations. Sampling the output probability of the modes then yields contributions that are neither purely determinant nor permanent but general immanants. Specifically, we prove that these immanant contributions are linearly independent from determinants and permanents, rendering our mixed sampling network an ideal candidate for light-matter quantum application beyond pure fermion and boson sampling. Furthermore, quantum sampling with statistics that are neither bosonic nor fermionic results in expressions which even exceed immanants, further extending the functionality of quantum samplers.

V. S. Shchesnovich

We explore the conditions under which identical particles in unitary linear networks behave as the other species, i.e. bosons as fermions and fermions as bosons. It is found that the Boson-sampling (BS) computer of Aaronson and Arkhipov can be implemented in an interference experiment with non-interacting fermions in an appropriately entangled state. Moreover, a scheme is proposed which simulates the scattershot version of the BS computer by preparing, on the fly, the required entangled state of fermions from an unentangled one.

Morikazu TODA