Boson sampling of multiple quantum random walkers on a lattice

Presenting Author: Gopikrishnan Muraleedharan, University of New Mexico CQuIC
Contributing Author(s): Ivan H. Deutsch, Akimasa Miyake

A quantum device capable of performing an information-processing task more efficiently than current state of the art classical computers is said to demonstrate “quantum supremacy”. One path to achieving this is via “sampling complexity”; random samples are drawn from a probability distribution by measuring a complex quantum state in a defined basis. Surprisingly, a gas of identical noninteracting bosons can yield sampling complexity due solely to quantum statistics, dubbed “boson sampling,” in the context of identical photons scattering from a linear optical network. We study here an analogous problem in case of multiple boson continuous-time quantum random walkers on a lattice, e.g., bosonic atoms in an optical lattice.Results are presented for the special case of a 1D lattice with nearest neighbor and uniform hopping amplitude.We demonstrate that the sampling problem is classically tractable until the time of evolution passes the logarithmic scale in the number of particles.We also conjecture that this problem is classically hard beyond the logarithmic scale. We present a protocol for generating any arbitrary unitary transformation using microwave induced transport in a spinor lattice.By using this protocol we try to approximate a Haar-random unitary map on a single boson, and quantum statistics yields the many-body complexity. We quantify the degree of randomness of the unitarity map using different techniques from random matrix theory, unitary t-designs and Renyi entropy.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


SQuInT Chief Organizer
Akimasa Miyake, Assistant Professor

SQuInT Co-Organizer
Mark M. Wilde, Assistant Professor LSU

SQuInT Administrator
Gloria Cordova
505 277-1850

SQuInT Founder
Ivan Deutsch, Regents' Professor

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