Continuous-Variable Sampling from Photon-Added or Photon-Subtracted Squeezed States

TL;DR

This paper introduces a new class of continuous-variable quantum circuits using photon-added or photon-subtracted squeezed states, demonstrating their computational hardness and potential for experimental realization.

Contribution

It presents a novel quantum circuit model with proven classical hardness based on complexity theory, extending boson sampling concepts to continuous variables.

Findings

The output distribution cannot be efficiently simulated classically.

Hardness results hold for both worst-case and average-case scenarios.

The model generalizes boson sampling with eight-port homodyne detection.

Abstract

We introduce a new family of quantum circuits in Continuous Variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution cannot be efficiently simulated by a classical computer. These circuits are composed of input photon-subtracted (or photon-added) squeezed states, passive linear optics evolution, and eight-port homodyne detection. We address the proof of hardness for the exact probability distribution of these quantum circuits by exploiting mappings onto different architectures of sub-universal quantum computers. We obtain both a worst-case and an average-case hardness result. Hardness of Boson Sampling with eight-port homodyne detection is obtained as the zero squeezing limit of our model. We conclude with a discussion on the relevance and interest of the present model in connection to experimental applications and classical simulations.