# Exact Boson Sampling using Gaussian continuous variable measurements

## TL;DR

This paper introduces a method for exact Boson Sampling using Gaussian continuous-variable measurements, demonstrating classical hardness for exact sampling, but not for approximate sampling, thus advancing quantum computational complexity understanding.

## Contribution

It presents a novel device setup combining Fock states, linear interactions, and Gaussian measurements that achieves classically hard exact sampling, extending Boson Sampling concepts.

## Key findings

- Exact sampling is classically hard for the proposed device.
- Gaussian measurements do not imply hardness for approximate sampling.
- The paper discusses conditions needed for approximate sampling hardness.

## Abstract

BosonSampling is a quantum mechanical task involving Fock basis state preparation and detection and evolution using only linear interactions. A classical algorithm for producing samples from this quantum task cannot be efficient unless the polynomial hierarchy of complexity classes collapses, a situation believe to be highly implausible. We present method for constructing a device which uses Fock state preparations, linear interactions and Gaussian continuous-variable measurements for which one can show exact sampling would be hard for a classical algorithm in the same way as Boson Sampling. The detection events used from this arrangement does not allow a similar conclusion for the classical hardness of approximate sampling to be drawn. We discuss the details of this result outlining some specific properties that approximate sampling hardness requires.