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Conference on Lasers and Electro-Optics

Generating Gottesman-Kitaev-Preskill Qubits Over Continuous-Variable Cluster States with Photon-Number-Resolving Measurements

Miller Eaton, Carlos González-Arciniegas, Rafael N. Alexander, Nicolas C. Menicucci, Olivier Pfister

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We develop a method to embed Schrödinger Cat states in continuous-variable cluster states with high probability using photon-number-resolving detection. Embedded cat states can then be bred into Gottesman-Kitaev-Preskill qubits with Gaussian measurements on the cluster.
DOI
10.1364/cleo_qels.2022.ff2i.7

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We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. This method stabilizes cat states against Gaussian noise and perpetuates non-Gaussianity within the cluster. We show that existing protocols for breeding cat states can be embedded into cluster state processing using PhANTM.
Continuous-variable quantum-computing (CVQC) is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and MMM-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M=2M=2M=2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.
Abstract Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman–Kitaev–Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and M -symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states ( M = 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.