All-optical generation of states for "Encoding a qubit in an oscillator"

TL;DR

This paper proposes a practical method to generate approximate GKP states for quantum computing by combining superpositions of optical coherent states, squeezing, and linear optical techniques, enabling fault-tolerant quantum information encoding.

Contribution

It introduces a novel approach to prepare GKP states using optical superpositions, advancing the feasibility of continuous-variable quantum computing.

Findings

Proposes a method to generate approximate GKP states with optical techniques.

Utilizes superpositions of coherent states, squeezing, and homodyne detection.

Facilitates fault-tolerant quantum computation in oscillator systems.

Abstract

Both discrete and continuous systems can be used to encode quantum information. Most quantum computation schemes propose encoding qubits in two-level systems, such as a two-level atom or an electron spin. Others exploit the use of an infinite-dimensional system, such as a harmonic oscillator. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schr\"odinger cat states"), squeezing, linear optical devices, and homodyne detection.