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Quantum 2.0 Conference and Exhibition

Free-Electron Radiation in the Form of Optical Cat and GKP States

Gefen Baranes, Raphael Dahan, Alexey A. Gorlach, Ron Ruimy, Nicholas Rivera, Ido E. Kaminer

Published Jan 1, 2022• 1 citation
Publisher

Abstract

We show how coherent modulation of free-electron wavefunctions can alter the quantum nature of the light they emit. We utilize this concept to create Schrödinger-cat and GKP states, which are sought-after for fault-tolerant quantum computation.
DOI
10.1364/quantum.2022.qth3c.5

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A theoretical framework is developed to analyze the generation of the optical GKP state using a single-photon-added squeezed vacuum. This state, defined by the squeezing parameter rrr, is injected into a 50:50 beam splitter, and the optical GKP state is obtained through conditional measurement at one output port. The single-photon-added squeezed vacuum is especially prominent in this context because it provides a simpler and more experimentally accessible ingredient than Schrodinger cat states, while conditional measurement ensures projection onto a state that closely approximates the finite-energy GKP form. Fidelity is employed to quantify this closeness, and the analysis demonstrates that the scheme achieves a maximum fidelity of 85% at a squeezing level of 3.76 dB3.76 \ \text{dB}3.76 dB. This performance surpasses approaches based on squeezed optical odd Schrodinger cat states, underscoring the single-photon-added squeezed vacuum as a practical and effective pathway toward fault-tolerant photonic quantum computing.
Most quantum computation schemes propose encoding qubits in two-level systems. Others exploit the use of an infinite-dimensional system. 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 "Schrödinger cat states"), squeezing, linear optical devices, and homodyne detection.