[Paper Review] Gottesman-Kitaev-Preskill state preparation by photon catalysis

Miller Eaton, Rajveer Nehra+1 more|arXiv (Cornell University)|Mar 5, 2019

Quantum Information and Cryptography42 references4 citations

TL;DR

This paper proposes a theoretical framework for generating Gottesman-Kitaev-Preskill (GKP) states in continuous-variable quantum computing using photon catalysis—interfering coherent states with single photons followed by photon-number-resolved detection. By combining this with photon-counting-based state breeding, the method enables the creation of non-Gaussian states like squeezed Schrödinger cat states and ultimately paves the way for scalable, fault-tolerant GKP state preparation.

ABSTRACT

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 $M$-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.

Motivation & Objective

• To address the experimental challenge of generating non-Gaussian resources essential for universal continuous-variable quantum computing.
• To explore photon catalysis as a mechanism for engineering exact displaced single-photon states and M-symmetric superpositions of squeezed vacuum (SSV) states.
• To demonstrate the feasibility of scaling SSV states toward GKP states using photon-counting-based state breeding.
• To establish a theoretical pathway for fault-tolerant quantum computation in CVQC via deterministic, non-Gaussian state preparation.

Proposed method

• Photon catalysis is employed by interfering a coherent state with a single-photon Fock state on a beam splitter, followed by photon-number-resolved detection.
• The measurement outcome projects the system into a non-Gaussian superposition state, including displaced single-photon states and M-symmetric SSV states.
• The method leverages the conditional nature of photon counting to conditionally prepare entangled non-Gaussian states from Gaussian inputs.
• State breeding is applied iteratively to enlarge the SSV states, increasing their non-classicality and enabling the construction of GKP-like superpositions.
• Theoretical analysis shows that repeated applications of photon catalysis and state breeding can generate states approaching the GKP encoding.
• The approach relies on linear optics, photon-number-resolving detectors, and coherent state inputs, making it compatible with current photonic hardware.

Experimental results

Research questions

• RQ1 Can photon catalysis be used to generate exactly displaced single-photon states from Gaussian inputs?
• RQ2 Can M-symmetric superpositions of squeezed vacuum states (including squeezed cat states for M=2) be prepared deterministically via photon catalysis?
• RQ3 How can photon-counting-based state breeding be combined with photon catalysis to scale non-Gaussian states toward GKP states?
• RQ4 What is the theoretical feasibility of generating GKP states using only linear optics and photon-number-resolved detection?
• RQ5 Can this framework enable fault-tolerant quantum computation in continuous-variable quantum computing?

Key findings

• Photon catalysis enables the deterministic preparation of exactly displaced single-photon states through interference of coherent and single-photon states followed by photon-number-resolved detection.
• The method generates M-symmetric superpositions of squeezed vacuum states, including squeezed cat states for M=2, with high fidelity to the target non-Gaussian superpositions.
• Iterative state breeding based on photon counting allows the enlargement of SSV states, increasing their non-classical character and enabling progression toward GKP state preparation.
• Theoretical analysis confirms that the combination of photon catalysis and state breeding can generate states approaching the GKP encoding, a critical requirement for fault-tolerant quantum computation.
• The proposed framework operates within the constraints of linear optics and current photonic detection technologies, offering a scalable path to non-Gaussian resource states.