Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics

Paul Hilaire1,2, Leonid Vidro3, Hagai S. Eisenberg3, and Sophia E. Economou1

1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
2Huygens-Kamerlingh Onnes Laboratory, Leiden University
3Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

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Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.

Creating large entangled states of photonic qubits is critical for quantum communications and for building a large photonic quantum computer.
Unfortunately, we cannot easily create entanglement between photonic qubits. Using linear-optical processing, the "easy way" to manipulate photons, entanglement can only be created probabilistically using, for example, the so-called "fusion gates". Yet, the success rate of building larger photonic states leads to either vanishingly small success probability or daunting resource overhead.

An alternative to creating photonic entanglement is to build it "at creation" from quantum emitters, i.e., by using atoms with the correct level structure that can sequentially emit photons entangled with the atomic qubit. Recent works have experimentally demonstrated such sources of entangled photons using natural atoms or quantum dots.

Yet, the entanglement structure of the photonic state that a single atom can produce is not universal for quantum computing and thus cannot create the types of photonic states that are useful for quantum technology applications. To circumvent this limitation, we propose a hybrid approach, combining these sources of photons and linear optics building a large class of photonic entangled states called graph states (including universal resource states for quantum computing). We show how we can create these graph states near-deterministically by proposing a variant of the initial fusion gates compatible with these sources of entangled photons.

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