Continuous-variable gate teleportation and bosonic-code error correction

TL;DR

This paper demonstrates how continuous-variable gate teleportation using specific entangled states can implement non-Gaussian operations and enable error correction for bosonic qubits, all without active squeezing, simplifying optical quantum computing.

Contribution

It introduces a method to realize non-unitary, non-Gaussian quantum operations via gate teleportation with product states and derives the associated Kraus operators, advancing bosonic-code error correction techniques.

Findings

Gate teleportation can realize non-Gaussian, non-unitary operations.

Error correction for GKP-encoded bosonic qubits is achievable via this method.

Active squeezing is unnecessary, easing experimental implementation.

Abstract

We examine continuous-variable gate teleportation using entangled states made from pure product states sent through a beamsplitter. We show that such states are Choi states for a (typically) non-unitary gate, and we derive the associated Kraus operator for teleportation, which can be used to realize non-Gaussian, non-unitary quantum operations on an input state. With this result, we show how gate teleportation is used to perform error correction on bosonic qubits encoded using the Gottesman-Kitaev-Preskill code. This result is presented in the context of deterministically produced macronode cluster states, generated by constant-depth linear optical networks, supplemented with a probabilistic supply of GKP states. The upshot of our technique is that state injection for both gate teleportation and error correction can be achieved without active squeezing operations -- an experimental bottleneck for quantum optical implementations.