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arXiv:1105.5211 · Optics Express

Experimental realization of a four-photon seven-qubit graph state for one-way quantum computation

Sang Min Lee, Hee Su Park, Jaeyoon Cho, Yoonshik Kang, Jae Yong Lee, Heonoh Kim, Dong-Hoon Lee, Sang-Kyung Choi

Published Mar 12, 2012• 17 citations
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Abstract

We propose and demonstrate the scaling up of photonic graph states through path qubit fusion. Two path qubits from separate two-photon four-qubit states are fused to generate a two-dimensional seven-qubit graph state composed of polarization and path qubits. Genuine seven-qubit entanglement is verified by evaluating the witness operator. Six qubits from the graph state are used to demonstrate the Deutsch-Jozsa algorithm for general two-bit functions with a success probability greater than 90%.

DOI
10.1364/oe.20.006915

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We propose and demonstrate the scaling up of photonic graph states through path qubit fusion. Two path qubits from separate two-photon four-qubit states are fused to generate a two-dimensional seven-qubit graph state composed of polarization and path qubits. Genuine seven-qubit entanglement is verified by evaluating the witness operator. Six qubits from the graph state are used to demonstrate the Deutsch-Jozsa algorithm for general two-bit functions with a success probability greater than 90%.
We describe an experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a two-bit Boolean function in the framework of one-way quantum computation. For this purpose, a two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at  1~1 1 kHz success rate, demonstrates the correct implementation of the algorithm.
Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states--originally generated on-demand from a quantum emitter--into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.
Integrated photonics provides a scalable platform for quantum information processing. In this context, measurement-based quantum computing (MBQC) offers an attractive approach in which quantum computation is realised by adaptive measurements on highly entangled graph states, circumventing the need for deterministic photon-photon interactions. Here, we demonstrate MBQC on an integrated silicon photonic chip capable of generating photonic graph states with up to four qubits. We achieve fidelities of FStar=(83.5±1.8) %F_{Star} = (83.5 \pm 1.8)\,\%FStar​=(83.5±1.8)% and FLin=(75.6±1.1) %F_{Lin} = (75.6 \pm 1.1)\,\%FLin​=(75.6±1.1)% for four-photon star and linear graph states, respectively. We use these resource states to implement MBQC-based single- and two-qubit gates and to demonstrate Grover's search algorithm and the Deutsch-Jozsa algorithm. These results establish the feasibility of reconfigurable four-photon MBQC on an integrated photonic platform and provide a foundation for future larger-scale implementations.
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and controlling operations between them is one of the promising ways to navigate the probabilistic behavior. Using single-photon discrete-time quantum walk in combination with polarization and path degrees-of-freedom, we experimentally demonstrate the realization of a universal set of quantum gates with high fidelity at room temperature. The deterministic realization of quantum gates through photonic quantum walk are characterized via quantum state tomography. For a three-qubit system using a single photon, the first qubit is encoded using polarization information, and the other two qubits are encoded using path information, closely resembling a Galton-board setup. To generate a six-qubit Greenberger-Horne-Zeilinger state, entangled photon pairs are used to entangle the two three-qubit modules on which gate operations are performed. We also provide insights into the mapping of photonic quantum walk operations to quantum circuits and propose methods to resourcefully scale. This demonstration marks a significant progress towards using quantum walks for quantum computing and provides a framework for using fewer photons in combination with different degrees-of-freedom of photon to scale the number of qubits.