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Non-Gaussian state teleportation with a nonlinear feedforward

Vojtěch Kala, Mattia Walschaers, Radim Filip, Petr Marek

TL;DR

The paper analyzes teleportation of non-Gaussian states through small Gaussian CV cluster states, showing that nonlinear feedforward can transfer higher nonlinear squeezing than standard linear teleportation. By modeling deterministic and probabilistic regimes and employing finite-energy non-Gaussian ancilla, it demonstrates that nonlinear feedforward can improve the preservation of non-Gaussian resources, even with current experimental resources and modest losses. The work formulates a Heisenberg-picture model, parameterizes two-mode Gaussian clusters, and uses numerical optimization to maximize nonlinear squeezing at the output, providing a practical route toward incorporating non-Gaussian elements into CV cluster-state quantum computing. The findings suggest that a careful combination of non-Gaussian ancilla, nonlinear processing, and postselection can extend the capabilities of measurement-based quantum computation with continuous variables.

Abstract

Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation propagating the states through the cluster accompanied by non-Gaussian measurements and feedforward control. We analyze such propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state and show that when a nonlinear feedforward is involved in the teleportation protocol, higher nonlinear squeezing can be transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing.

Non-Gaussian state teleportation with a nonlinear feedforward

TL;DR

The paper analyzes teleportation of non-Gaussian states through small Gaussian CV cluster states, showing that nonlinear feedforward can transfer higher nonlinear squeezing than standard linear teleportation. By modeling deterministic and probabilistic regimes and employing finite-energy non-Gaussian ancilla, it demonstrates that nonlinear feedforward can improve the preservation of non-Gaussian resources, even with current experimental resources and modest losses. The work formulates a Heisenberg-picture model, parameterizes two-mode Gaussian clusters, and uses numerical optimization to maximize nonlinear squeezing at the output, providing a practical route toward incorporating non-Gaussian elements into CV cluster-state quantum computing. The findings suggest that a careful combination of non-Gaussian ancilla, nonlinear processing, and postselection can extend the capabilities of measurement-based quantum computation with continuous variables.

Abstract

Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation propagating the states through the cluster accompanied by non-Gaussian measurements and feedforward control. We analyze such propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state and show that when a nonlinear feedforward is involved in the teleportation protocol, higher nonlinear squeezing can be transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing.
Paper Structure (12 sections, 47 equations, 6 figures)

This paper contains 12 sections, 47 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Teleportation, linear and nonlinear
  3. Deterministic regime
  4. Probabilistic regime
  5. Nonlinear squeezing
  6. Results
  7. Deterministic scheme
  8. Probabilistic regime
  9. Conclusion
  10. Model in Heisenberg picture
  11. Parametrization of the general two-mode cluster state and its optimization
  12. Optimization of the cluster state

Figures (6)

  • Figure 1: a) Regular teleportation scheme transferring the quantum state through the cluster state. b) Optical scheme equivalent to parameterization of the cluster state considered for the analyzed schemes. c) Optical scheme showing the nonlinear cubic phase measurement applied to one part of the cluster state. The measurement is decomposed into an ideal cubic nonlinearity followed by homodyne measurement. The measurement result is used in a feedforwarded displacement on the second mode. d) Nonlinear teleportation with nonlinear feedforward and ancillary state in the mode Q.
  • Figure 2: Nonlinear squeezing at the output mode, when the available Gaussian squeezing is limited to certain value [dB] during optimization. The two-mode cluster state is pure and optimized for each scheme. Output nonlinear squeezing is shown for regular and nonlinear teleportation of the superposition of vacuum state and single photon \ref{['approx2']} and the state with 2-photon non-Gaussianity \ref{['approx3']}, both with optimized coefficients. Finally the results obtained with the finitely squeezed cubic state \ref{['idf']} and nonlinear cubic phase measurement.
  • Figure 3: Nonlinear squeezing at the output mode, when the available Gaussian squeezing is limited to certain value $[dB]$ during optimization. The two-mode cluster state carries $n=0.1$ additional thermal noise.
  • Figure 4: Nonlinear squeezing teleported by linear (dotted line) and nonlinear (solid line) teleportation. The input state and parameters of the optical scheme are optimized for the deterministic scenario. Quantum states depending on the measurement results with best nonlinear squeezing are aggregated up to a given probability.
  • Figure 5: Scheme for conditioned regular/nonlinear teleportation including the preparation of the ancillary state.
  • ...and 1 more figures