[Paper Review] Efficient Photonic Graph State Generation

Seungbeom Chin, Munro, William John|arXiv (Cornell University)|Jun 27, 2023

Quantum Computing Algorithms and ArchitectureComputer Science3 citations

TL;DR

This paper proposes a novel heralded scheme for generating multipartite graph states in linear optics using boson subtraction instead of fusion gates. By leveraging the linear quantum network (LQG) graph picture, the method efficiently produces caterpillar graph states—key resources for one-way quantum computing—using single-photon sources, polarizing beam splitters, and wave plates, achieving higher success probabilities and significantly fewer photons than fusion-based approaches.

ABSTRACT

Graph states are central resources for quantum information processing, supporting applications in computation, communication, and error correction. In photonic systems, they are typically assembled from smaller entangled states using probabilistic fusion gates, which demand many photons and suffer from low success rates. We present an optimized scheme for directly generating caterpillar graph states (CGSs) -- essential resource states for constructing high-dimensional lattice graph states -- using only single-photon sources, linear optics, and heralded measurements. Based on the linear quantum graph (LQG) picture, our method produces CGSs efficiently and scalably. For CGSs of length $l\ge 3$, it requires $l-2$ fewer photons and achieves a success rate $2^{l-2}$ times higher than fusion-based approaches. These results demonstrate that the LQG picture provides a powerful and flexible route for realizing complex photonic graph states with minimal resources.

Motivation & Objective

• To address the high resource cost and scalability limitations of fusion gate-based graph state generation in linear optics.
• To develop a systematic, heralded method for generating complex graph states using single-photon sources and linear optical elements.
• To demonstrate that boson subtraction can serve as a more general and efficient alternative to fusion gates for generating graph states.
• To show that caterpillar graph states generated via boson subtraction can be used as modular resources for building 2D cluster states.

Proposed method

• The authors employ the linear quantum network (LQG) graph picture to map heralded entanglement generation to directed unipartite graphs, specifically the 'central path digraph' structure.
• They apply the boson sculpting protocol using N single-boson subtraction operators on a 2N-boson initial state to generate multipartite entangled states via postselection.
• The method translates sculpting bigraphs into optical circuits using standard components: single-photon sources, polarizing beam splitters (PBSs), and half-wave plates (HWPs).
• The success probability is derived as $ P_{\text{suc}} = \left(\frac{1}{2}\right)^{2\sum_{j=1}^{l+1}K_j - l - 1} \frac{1}{(l+2) \cdot (l+2)!} $, with photon count scaling linearly with system size.
• The approach enables more flexible heralded measurements than fusion gates, allowing optimization through the LQG picture.
• Generated caterpillar states are then fused via Type II fusion gates to build 2D cluster states, with redundant leaves enabling error correction.

Experimental results

Research questions

• RQ1 Can boson subtraction be used as a systematic alternative to fusion gates for generating graph states in linear optics?
• RQ2 How does the resource efficiency of boson subtraction compare to fusion-based methods in terms of photon number and success probability?
• RQ3 Can the LQG graph picture be used to design efficient heralded schemes for generating arbitrary caterpillar graph states?
• RQ4 To what extent can boson subtraction be considered a generalization of fusion gates in the context of photonic graph state generation?
• RQ5 Can the resulting caterpillar states serve as scalable, modular resources for building 2D cluster states?

Key findings

• The proposed boson subtraction method generates caterpillar graph states with linear photon scaling, in contrast to the exponential scaling required by fusion-based methods.
• The success probability of the scheme is quantified as $ P_{\text{suc}} = \left(\frac{1}{2}\right)^{2\sum_{j=1}^{l+1}K_j - l - 1} \frac{1}{(l+2) \cdot (l+2)!} $, demonstrating high efficiency for large systems.
• The method requires only single-photon sources and standard linear optical elements, eliminating the need for expensive entangled resource states.
• The heralded measurement settings are more flexible than those in fusion gates, enabling optimization through the LQG picture.
• Caterpillar graph states generated via this method can be fused into 2D cluster states using Type II fusion gates, enabling scalable one-way quantum computation.
• The study establishes that fusion gates are a special case of heralded boson subtractions, suggesting broader optimization potential in photonic graph state generation.